Manual de Problemas Resueltos by Ayose Lomba Pérez

Uni ver s i daddeLasPal masdeGr anCanar i a Es cuel aTécni caSuper i ordeI ngeni er osI ndus t r i al es I ngeni er í aI ndus t r i al

Sof t war edeanál i s i sdeci r cui t osl i neal es medi ant emét odosavanzadosde r es ol uci ónpar aus odocent e.

ManualdePr obl emasRes uel t os

Aut or :

Tut or es : Fecha:

Ayos eLombaPér ez Jos eMi guelMonzónVer ona Ant oni oAndr ésOcónCar r er as Sept i embr e2009

Software de Análisis de Cir uitos Lineales mediante Métodos Avanzados de Resolu ión para Uso Do ente. Manual de Problemas Resueltos.

Ayose Lomba Pérez Septiembre 2009

ร ndi e general

Introdu iรณn

1. Cir uito RC on ex ita iรณn en ontinua. 1.1. Datos Generales. . . . . . . . . . . . . . 1.1.1. Datos generales del ir uito . . . 1.1.2. Los valores dados al ir uito son: 1.2. Matriz T. . . . . . . . . . . . . . . . . . 1.2.1. Valores de la Matriz T . . . . . . 1.2.2. Captura de la Matriz T . . . . . 1.3. Solu iones . . . . . . . . . . . . . . . . . 1.3.1. Primer anรกlisis. . . . . . . . . . . 1.4. Comproba iรณn de resultados. . . . . . .

2. Cir uito RC sin exita iรณn.

2.1. Datos Generales. . . . . . . . 2.2. Solu iones . . . . . . . . . . . 2.2.1. Primer anรกlisis . . . . 2.3. Comproba iรณn de resultados.

. . . .

3. Cir uito RL on exita iรณn ontรญnua. 3.1. Datos Generales. . . . . . . . 3.2. Solu iones . . . . . . . . . . . 3.2.1. Primer anรกlisis . . . . 3.3. Comproba iรณn de resultados.

. . . .

. . . . . . . . .

. . . .

12 12 12 12 12 13 13 13 16

19 20 20 23

27 28 28 31

4. Cir uito RC on exita iรณn senoidal.

5. Cir uito RL on exita iรณn senoidal.

4.1. Datos Generales. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2. Solu iones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.1. Primer anรกlisis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1. Datos Generales. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2. Solu iones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.1. Primer anรกlisis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6. Cir uito RL sin exita iรณn. 6.1. Datos Generales. . . . 6.2. Solu iones . . . . . . . 6.2.1. Primer anรกlisis 6.3. Compara iรณn. . . . . .

. . . .

. . . . 3

. . . .

35 36 36 41 42 42

47 48 48 51

ÍNDICE GENERAL

7. Cir uito RL on ex ita ión es alón.

8. Cir uito RLC serie.

9. Cir uito RLC sin ex ita ión.

10.Cir uito RLC paralelo.

11.Cir uito RLC paralelo sin ex ita ión.

12.Cir uito RLC paralelo sin ex ita ión on EA.

13.Cir uito on a oplamiento magnéti o simple.

105

14.Cir uito on a oplamiento magnéti o.

113

15.Cir uito on fuente de tensión dependiente de tensión.

127

16.Cir uito on fuente de intensidad dependiente de tensión.

139

17.Cir uito on transformador.

147

7.1. Datos Generales. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2. Solu iones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2.1. Primer análisis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.1. Datos Generales. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2. Solu iones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2.1. Primer análisis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.1. Datos Generales. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.2. Solu iones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.2.1. Primer análisis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.1. Datos Generales. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.2. Solu iones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.2.1. Primer análisis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1. Datos Generales. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2. Solu iones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2.1. Primer análisis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.1. Datos Generales. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.2. Solu iones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.2.1. Primer análisis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

53 54 54 59 60 60 65 66 66 79 80 80 89 90 90 97 98 98

13.1. Datos Generales. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 13.2. Solu iones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 13.2.1. Primer análisis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 14.1. Datos Generales. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 14.2. Solu iones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 14.2.1. Primer análisis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 15.1. Datos Generales. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 15.2. Solu iones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128 15.2.1. Primer análisis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128 16.1. Datos Generales. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 16.2. Solu iones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 16.2.1. Primer análisis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 17.1. Datos Generales. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147 17.2. Solu iones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 17.2.1. Primer análisis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148

ÍNDICE GENERAL 18.Cir uito on bipuerto on parámetros híbridos.

153

18.1. Datos Generales. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154 18.2. Solu iones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155 18.2.1. Primer análisis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155

Introdu ión.

En el presente manual de ejer i ios resueltos se elaboran una ole ión de ejer i ios bási os en los que se utilizan las apa idades del proye to para el estudio de diferentes ir uitos en régimen transitorio y esta ionario. Para todos ellos se seguirá la misma estru tura de análisis y se presentarán los datos obtenidos de la misma forma, estru turada según: Esquema del ir uito Ar hivo *.sp generado por X ir uit Tipo de análisis realizado • Datos introdu idos • Condi iones Ini iales

Datos Generales. En este punto se detallan datos omo el número de nodos, elementos del grupo A2, et . Matriz T • Valores de la Matriz T ensamblada para la resolu ión. • Captura de la distribu ión de valores en la Matriz.

Solu iones • Esta ionario • Transitorio ◦ Fi hero on datos numéri os de solu ión por olumnas. ◦ Grá o de salida. ◦ S ript utilizado para el grá o.

En los primeros ejemplos además se realizará un estudio omparativo de los resultados del programa on las expresiones teóri as obtenidas por métodos tradi ionales de análisis, de esta forma se podrá demostrar el orre to fun ionamiento del software.

Problemas Resueltos on ﾃ」alon.

Capítulo 1 Cir uito RC on ex ita ión en ontinua.

Sabiendo que la onstante de tiempo de un ir uito de este tipo es τ = RC y que se llega al permanente pasados aproximadamente 5 ve es este valor (5τ ), pasemos a al ular el régimen transitorio de este simple ir uito suponiendo que el ondensador se en uentra ini ialmente des argado, por lo que no existirá diferen ia de poten ial entre sus pla as, he ho que ayuda a estable er las ondi iones ini iales onsistentes que nos soli itará el programa para el ál ulo del transitorio.

Figura 1.1: Cir uito RC on ex ita ión en ontinua Las expresiones teóri as de las variables del ir uito son: Tensión en resisten ia, que será la diferen ia entre tensión en nudo 1 y en nudo 2 en nuestro programa t

VR = V · e− RC

(1.1)

Tensión en Condensador es la tensión en el nudo 2 en Ávalon t Vc = V · 1 − e− RC

(1.2)

Intensidad de resisten ia que oin ide on la de la fuente y por tanto la de la úni a malla del ir uito it =

t V · e− RC R

(1.3)

Carga del ondensador. Dire tamente nuestro programa no nos fa ilita esta expresión así que si deseamos al ular la magnitud de arga del ondesador tendremos que tomar los valores de su tensión y multipli arlos por la apa idad tal y omo podemos dedu ir de su e ua ión fundamental q = V C analizada en el apítulo Teoría bási a previa, de la memoria de este proye to. t qt = V C · 1 − e− RC

(1.4)

En este ir uito RC se al ularán las tensiones en los nudos 1 y 2 además de las intensidad que pasa por la malla que forma el ir uito. Nótese que debido al fun ionamiento del programa y 11

1. Cir uito RC on ex ita ión en ontinua.

naturaleza del método, este nos fa ilita las tensiones de los nudos y aquellas intensidades de los elementos que pertene en al Grupo 2, es de ir aquellos que debido a su e ua ión de onstitu ión no es posible ensamblarlos en la matriz T en fun ión de su admitan ia, por lo que ontribuyen al sistema on una nueva e ua ión adi ional que nos propor iona su intensidad.

Ar hivo *.sp *SPICE ir uit <ejemplo/ej_01_01>from XCir uit v3.6 rev 135 21010201 1 1 0 2 2 1 0 10 4 1 0 2 1 0 0 1 rho f a b A B C D .end Tipo de análisis realizado Análisis esta ionario Análisis transitorio 1.1.

1.1.1.

⊠ ⊠

Datos Generales.

Datos generales del ir uito

Elementos del Cto: 3 EA: 0 Nodos: 2 A2: 2 No nulos: 8 Densidad: 0.5 Dispersion: 0.5

1.1.2.

Los valores dados al ir uito son: Elemento Fuente independiente de Tensión Resisten ia Condensador

Magnitud 1V 10 Ω 1F

Cuadro 1.1: Datos del Cir uito ej_01_01 Tiempo Ini ial Tiempo Final Paso de Tiempo Theta

0 50 0,5 1 (Euler)

Cuadro 1.2: Datos del Transitorio ej_01_01

1.2.

1.2.1.

Matriz T.

Valores de la Matriz T

row 0: (2, -1) (3, 1)

1.3. Solu iones

row 1: (1, 0 + 1 i) (2, 1) row 2: (0, -1) (1, 1) (2, -10) row 3: (0, 1)

1.2.2.

1.3.

1.3.1.

Captura de la Matriz T

Solu iones

Primer an谩lisis.

Esta ionario Tensi贸n en nodo 1: 1 + 3.25261e-19 i Tensi贸n en nodo 2: 0.00990099 - 0.0990099 i I Resisten ia entre nodos 2, 1: -0.0990099 - 0.00990099 i I de Fuente tension entre nodos 1, 0: -0.0990099 - 0.00990099 i

Transitorio 1 0.047619 -0.0952381 -0.0952381 0 1 0.0929705 -0.0907029 -0.0907029 0.5 1 0.136162 -0.0863838 -0.0863838 1 1 0.177298 -0.0822702 -0.0822702 1.5 1 0.216474 -0.0783526 -0.0783526 2 1 0.253785 -0.0746215 -0.0746215 2.5 1 0.289319 -0.0710681 -0.0710681 3 1 0.323161 -0.0676839 -0.0676839 3.5 1 0.355391 -0.0644609 -0.0644609 4 1 0.386087 -0.0613913 -0.0613913 4.5 1 0.415321 -0.0584679 -0.0584679 5 1 0.443163 -0.0556837 -0.0556837 5.5 1 0.469679 -0.0530321 -0.0530321 6 1 0.494932 -0.0505068 -0.0505068 6.5 1 0.518983 -0.0481017 -0.0481017 7 1 0.541888 -0.0458112 -0.0458112 7.5 1 0.563703 -0.0436297 -0.0436297 8 1 0.584479 -0.0415521 -0.0415521 8.5 1 0.604266 -0.0395734 -0.0395734 9 1 0.623111 -0.0376889 -0.0376889 9.5 1 0.641058 -0.0358942 -0.0358942 10 1 0.65815 -0.034185 -0.034185 10.5 1 0.674429 -0.0325571 -0.0325571 11 1 0.689932 -0.0310068 -0.0310068 11.5 1 0.704697 -0.0295303 -0.0295303 12 1 0.718759 -0.0281241 -0.0281241 12.5 1 0.732152 -0.0267848 -0.0267848 13

1. Cir uito RC on ex ita i贸n en ontinua.

1 0.744906 -0.0255094 -0.0255094 13.5 1 0.757054 -0.0242946 -0.0242946 14 1 0.768623 -0.0231377 -0.0231377 14.5 1 0.779641 -0.0220359 -0.0220359 15 1 0.790134 -0.0209866 -0.0209866 15.5 1 0.800127 -0.0199873 -0.0199873 16 1 0.809645 -0.0190355 -0.0190355 16.5 1 0.81871 -0.018129 -0.018129 17 1 0.827343 -0.0172657 -0.0172657 17.5 1 0.835564 -0.0164436 -0.0164436 18 1 0.843395 -0.0156605 -0.0156605 18.5 1 0.850852 -0.0149148 -0.0149148 19 1 0.857954 -0.0142046 -0.0142046 19.5 1 0.864718 -0.0135282 -0.0135282 20 1 0.87116 -0.012884 -0.012884 20.5 1 0.877296 -0.0122704 -0.0122704 21 1 0.883139 -0.0116861 -0.0116861 21.5 1 0.888703 -0.0111297 -0.0111297 22 1 0.894003 -0.0105997 -0.0105997 22.5 1 0.899051 -0.0100949 -0.0100949 23 1 0.903858 -0.00961421 -0.00961421 23.5 1 0.908436 -0.00915639 -0.00915639 24 1 0.912796 -0.00872037 -0.00872037 24.5 1 0.916949 -0.00830512 -0.00830512 25 1 0.920904 -0.00790964 -0.00790964 25.5 1 0.92467 -0.00753299 -0.00753299 26 1 0.928257 -0.00717427 -0.00717427 26.5 1 0.931674 -0.00683264 -0.00683264 27 1 0.934927 -0.00650728 -0.00650728 27.5 1 0.938026 -0.00619741 -0.00619741 28 1 0.940977 -0.00590229 -0.00590229 28.5 1 0.943788 -0.00562123 -0.00562123 29 1 0.946464 -0.00535355 -0.00535355 29.5 1 0.949014 -0.00509862 -0.00509862 30 1 0.951442 -0.00485583 -0.00485583 30.5 1 0.953754 -0.0046246 -0.0046246 31 1 0.955956 -0.00440438 -0.00440438 31.5 1 0.958054 -0.00419465 -0.00419465 32 1 0.960051 -0.0039949 -0.0039949 32.5 1 0.961953 -0.00380467 -0.00380467 33 1 0.963765 -0.00362349 -0.00362349 33.5 1 0.965491 -0.00345095 -0.00345095 34 1 0.967134 -0.00328662 -0.00328662 34.5 1 0.968699 -0.00313011 -0.00313011 35 1 0.970189 -0.00298106 -0.00298106 35.5 1 0.971609 -0.0028391 -0.0028391 36 1 0.972961 -0.00270391 -0.00270391 36.5 1 0.974248 -0.00257515 -0.00257515 37 1 0.975475 -0.00245252 -0.00245252 37.5 1 0.976643 -0.00233574 -0.00233574 38 1 0.977755 -0.00222451 -0.00222451 38.5 1 0.978814 -0.00211858 -0.00211858 39 1 0.979823 -0.0020177 -0.0020177 39.5 1 0.980784 -0.00192162 -0.00192162 40

1.3. Solu iones

1 0.981699 -0.00183011 -0.00183011 40.5 1 0.98257 -0.00174296 -0.00174296 41 1 0.9834 -0.00165996 -0.00165996 41.5 1 0.984191 -0.00158092 -0.00158092 42 1 0.984944 -0.00150564 -0.00150564 42.5 1 0.985661 -0.00143394 -0.00143394 43 1 0.986343 -0.00136566 -0.00136566 43.5 1 0.986994 -0.00130063 -0.00130063 44 1 0.987613 -0.00123869 -0.00123869 44.5 1 0.988203 -0.00117971 -0.00117971 45 1 0.988765 -0.00112353 -0.00112353 45.5 1 0.9893 -0.00107003 -0.00107003 46 1 0.989809 -0.00101907 -0.00101907 46.5 1 0.990295 -0.000970547 -0.000970547 47 1 0.990757 -0.000924331 -0.000924331 47.5 1 0.991197 -0.000880315 -0.000880315 48 1 0.991616 -0.000838395 -0.000838395 48.5 1 0.992015 -0.000798471 -0.000798471 49 1 0.992396 -0.000760449 -0.000760449 50

S ript. set grid set autos ale set t i t l e ' Grafi ado por d e f e t o de l a s s o l u i o n e s d e l i r u i t o ' plot ' s o l _ t r a n s . data ' using 5 : 1 t i t l e 'V en nodo 1 ' with l i n e s , ' s o l _ t r a n s . data ' using 5 : 2 t i t l e 'V en nodo 2 ' with l i n e s , ' s o l _ t r a n s . data ' using 5 : 3 t i t l e ' I R e s i s t e n i a e n t r e nodos 2 , 1 ' with l i n e s , ' s o l _ t r a n s . data ' using 5 : 4 t i t l e ' I de Fuente t e n s i o n e n t r e nodos 1 , 0 ' with l i n e s set terminal p o s t s r i p t o l o r s o l i d set output ' /home/ ayose / Programa ion /AVALON/debug / s r / ejemplo / ej_01_01_grafi a . ps '

replot

Grรก o de salida.

1.4.

1. Cir uito RC on ex ita ión en ontinua.

Comproba ión de resultados.

Ha llegado la hora de omprobar si los datos obtenidos on el programa son orre tos por lo que se pro ederá a superponer las grá as de las expresiones teóri as on la de la solu ión aportada por el software. Empezaremos on la superposi ión de la e ua ión 1.2 on los datos de tensión en nudo 2.

Corriente de la malla del ir uito. Superposi ión de la e ua ión 1.3 on la obtenida on Ávalon. Cabe desta ar que tal y omo se estable e el riterio de signos de los elementos del programa nos

1.4. Comproba ión de resultados.

sale la intensidad on signo negativo, esto quiere de ir que la misma es en sentido ontrario al que por defe to toma el programa para realizar los ál ulos. Pro edamos a superponer las grá as para ver los resultados obtenidos.

Tensión en la resisten ia del ir uito. Para su ompara ión se ha e uso de la e ua ión 1.1 y los datos propor ionados por el programa. Deberemos tener presente que en el Método Nodal modi ado lo que se obtienen son tensiones en nudos e intensidades en elementos, por lo que para poder omprobar si los datos que nos ha propor ionado el programa son orre tos, debemos restar los valores del nodo 1 on el del 2 para así obtener diferen ia de tensión existente en la resisten ia.

Por último nos queda analizar la arga del ondensador a lo largo del tiempo de estudio para eso nuevamente se solaparán la e ua ión 1.4 on los datos del programa.

1. Cir uito RC on ex ita i贸n en ontinua.

Capítulo 2 Cir uito RC sin exita ión.

En este ejemplo se analizará la des arga de un ondensador en un ir uito RC simple. Supondremos por tanto que el ondensador está ini ialmente argado. 1

Las expresiones teóri as de las variables del ir uito son: Tensión en resisten ia t

VR = −V · e− RC

(2.1)

Tensión en Condensador t

Vc = V · e− RC

(2.2)

Intensidad de resisten ia y por tanto la de la úni a malla del ir uito it = −

V t · e− RC R

(2.3)

Carga del ondensador. Dire tamente nuestro programa no nos fa ilita esta expresión así que si deseamos al ular la magnitud de arga del ondesador tendremos que tomar los valores de su tensión y multipli arlos por la apa idad tal y omo podemos dedu ir de su e ua ión fundamental q = V C analizada en el apítulo teoría bási a previa la memoria de este proye to. t

qt = V C · e− RC 2.1.

Datos Generales.

Ar hivo *.sp ∗ SPICE i r u i t <ejemplo02> from XCir uit v3 . 6 rev 135

1 1 0 2 0 1 0 5 2 1 0 1 1 0 0 2 . end 19

(2.4)

2. Cir uito RC sin exita ión.

Tipo de análisis realizado Análisis esta ionario Análisis transitorio

⊠ ⊠

Datos generales del ir uito Elementos del Cto: 2 EA: 0 Nodos: 1 A2: 1 No nulos: 4 Densidad: 1 Dispersion: 0

Los valores dados al ir uito son: Elemento Resisten ia Condensador

Magnitud 5Ω 2F

Cuadro 2.1: Datos del Cir uito ej_02

Matriz T. Valores de la Matriz T row 0: (0, 0 + 2 i) (1, -1) row 1: (0, -1) (1, -5)

2.2.

2.2.1.

Solu iones

Primer análisis

Nuevamente se realizará un análisis omprendido entre 0 segundos y 5 ve es su onstante de tiempo, es de ir 50 segundos. Tiempo Ini ial Tiempo Final Paso de Tiempo Theta

0 50 0,5 1 (Euler)

Cuadro 2.2: Datos del Transitorio ej_02

2.2. Solu iones

Esta ionario Resultados sistema esta ionario: Tensi贸n en nodo 1: 0 I Resisten ia entre nodos 0, 1: 0

Transitorio 1.90476 -0.380952 0 1.81406 -0.362812 0.5 1.72768 -0.345535 1 1.6454 -0.329081 1.5 1.56705 -0.31341 2 1.49243 -0.298486 2.5 1.42136 -0.284273 3 1.35368 -0.270736 3.5 1.28922 -0.257844 4 1.22783 -0.245565 4.5 1.16936 -0.233872 5 1.11367 -0.222735 5.5 1.06064 -0.212129 6 1.01014 -0.202027 6.5 0.962034 -0.192407 7 0.916223 -0.183245 7.5 0.872593 -0.174519 8 0.831041 -0.166208 8.5 0.791468 -0.158294 9 0.753779 -0.150756 9.5 0.717885 -0.143577 10 0.6837 -0.13674 10.5 0.651143 -0.130229 11 0.620136 -0.124027 11.5 0.590606 -0.118121 12 0.562481 -0.112496 12.5 0.535697 -0.107139 13 0.510187 -0.102037 13.5 0.485893 -0.0971785 14 0.462755 -0.092551 14.5 0.440719 -0.0881438 15 0.419732 -0.0839465 15.5 0.399745 -0.079949 16 0.38071 -0.0761419 16.5 0.362581 -0.0725161 17 0.345315 -0.069063 17.5 0.328871 -0.0657743 18 0.313211 -0.0626421 18.5 0.298296 -0.0596592 19 0.284091 -0.0568183 19.5 0.270563 -0.0541126 20 0.257679 -0.0515358 20.5 0.245409 -0.0490818 21 0.233723 -0.0467445 21.5 0.222593 -0.0445186 22 0.211993 -0.0423987 22.5

2. Cir uito RC sin exita i贸n.

0.201898 -0.0403797 23 0.192284 -0.0384568 23.5 0.183128 -0.0366256 24 0.174407 -0.0348815 24.5 0.166102 -0.0332205 25 0.158193 -0.0316385 25.5 0.15066 -0.0301319 26 0.143485 -0.0286971 26.5 0.136653 -0.0273306 27 0.130146 -0.0260291 27.5 0.123948 -0.0247896 28 0.118046 -0.0236092 28.5 0.112425 -0.0224849 29 0.107071 -0.0214142 29.5 0.101972 -0.0203945 30 0.0971166 -0.0194233 30.5 0.092492 -0.0184984 31 0.0880876 -0.0176175 31.5 0.083893 -0.0167786 32 0.0798981 -0.0159796 32.5 0.0760934 -0.0152187 33 0.0724699 -0.014494 33.5 0.069019 -0.0138038 34 0.0657323 -0.0131465 34.5 0.0626022 -0.0125204 35 0.0596212 -0.0119242 35.5 0.0567821 -0.0113564 36 0.0540782 -0.0108156 36.5 0.051503 -0.0103006 37 0.0490505 -0.0098101 37.5 0.0467147 -0.00934295 38 0.0444902 -0.00889805 38.5 0.0423716 -0.00847433 39 0.040354 -0.00807079 39.5 0.0384323 -0.00768647 40 0.0366022 -0.00732044 40.5 0.0348593 -0.00697185 41 0.0331993 -0.00663986 41.5 0.0316184 -0.00632368 42 0.0301127 -0.00602255 42.5 0.0286788 -0.00573576 43 0.0273131 -0.00546263 43.5 0.0260125 -0.0052025 44 0.0247738 -0.00495477 44.5 0.0235941 -0.00471882 45 0.0224706 -0.00449412 45.5 0.0214006 -0.00428011 46 0.0203815 -0.0040763 46.5 0.0194109 -0.00388219 47 0.0184866 -0.00369732 47.5 0.0176063 -0.00352126 48 0.0167679 -0.00335358 48.5 0.0159694 -0.00319389 49 0.015209 -0.0030418 49.5 50

2.3. Comproba ión de resultados.

Algorithm 1 S ript por defe to del ej_02 set terminal png set output ' /home/ ayose / Programa ion /AVALON/debug / s r / o l e i o n / G r a f i o s / o l e i o n p r o b l e m a s /2/ e j e m p l o 0 2 _ g r a f i a . png '

using 3 : 2 t i t l e ' I R e s i s t e n i a e n t r e nodos 0 , 1 ' with l i n e s Grá o de salida.

2.3.

Comproba ión de resultados.

2. Cir uito RC sin exita ión.

Corriente de la malla del ir uito superposi ión de la e ua ión 2.3 on la obtenida on Ávalon. Pro edamos a superponer las grá as para ver los resultados obtenidos.

Tensión en la resisten ia del ir uito se ha e uso de la e ua ión 2.1 y los datos propor ionados por el programa.

2.3. Comproba ión de resultados.

Por último nos queda analizar la arga del ondensador a lo largo del tiempo de estudio para eso nuevamente se solaparán la e ua ión 2.4 on los datos del programa.

Cal ularemos también en este ir uito la poten ia de la resisten ia basándonos en la expresión

p = RI 2

2. Cir uito RC sin exita i贸n.

Capítulo 3 Cir uito RL on exita ión ontínua.

Ahora analizaremos el omportamiento de un ir uito RL on ex ita ión ontínua en el que su L onstante de tiempo es τ = R por lo que el análisis lo realizaremos para in o ve es el mendionado valor.

Las expresiones teóri as de las variables del ir uito son: Tensión en Resisten ia R VR = V · 1 − e− L t

Tensión en la Bobina

(3.1)

(3.2)

VL = −V · e− L t

Intensidad de resisten ia y por tanto la de la úni a malla del ir uito it = 3.1.

R V · 1 − e− L t R

(3.3)

Datos Generales.

Ar hivo *.sp ∗ SPICE i r u i t <ejemplo03> from XCir uit v3 . 6 rev 135

3 1 0 2 0 2 0 10 1 1 0 2 2 1 0 2 4 1 0 2 1 0 0 2 rho f a b A B C D . end Tipo de análisis realizado Análisis esta ionario Análisis transitorio 27

⊠ ⊠

3. Cir uito RL on exita ión ontínua.

Datos generales del ir uito Elementos del Cto: 3 EA: 0 Nodos: 2 A2: 3 No nulos: 10 Densidad: 0.4 Dispersion: 0.6

Los valores dados al ir uito son: Elemento Resisten ia Bobina

Magnitud 2Ω 10 H

Matriz T. Valores de la Matriz T row 0: (2, -1) (3, 1) row 1: (2, 1) (4, -1) row 2: (0, -1) (1, 1) (2, -2) row 3: (0, 1) row 4: (1, -1) (4, -0 - 10 i)

3.2.

3.2.1.

Solu iones

Primer análisis

Nuevamente se realizará un análisis omprendido entre 0 segundos y 5 ve es su onstante de tiempo, es de ir 50 segundos. Tiempo Ini ial Tiempo Final Paso de Tiempo Theta

0 25 0,25 1 (Euler)

Esta ionario Resultados sistema esta ionario: Tensión en nodo 1: 2 - 2.1684e-19 i Tensión en nodo 2: 1.92308 + 0.384615 i I Resisten ia entre nodos 2, 1: -0.0384615 + 0.192308 i I de Fuente tension entre nodos 1, 0: -0.0384615 + 0.192308 i I de Bobina entre nodos 0, 2: -0.0384615 + 0.192308 i

3.2. Solu iones

Transitorio 2 1.90476 -0.047619 -0.047619 -0.047619 0 2 1.81406 -0.0929705 -0.0929705 -0.0929705 0.25 2 1.72768 -0.136162 -0.136162 -0.136162 0.5 2 1.6454 -0.177298 -0.177298 -0.177298 0.75 2 1.56705 -0.216474 -0.216474 -0.216474 1 2 1.49243 -0.253785 -0.253785 -0.253785 1.25 2 1.42136 -0.289319 -0.289319 -0.289319 1.5 2 1.35368 -0.323161 -0.323161 -0.323161 1.75 2 1.28922 -0.355391 -0.355391 -0.355391 2 2 1.22783 -0.386087 -0.386087 -0.386087 2.25 2 1.16936 -0.415321 -0.415321 -0.415321 2.5 2 1.11367 -0.443163 -0.443163 -0.443163 2.75 2 1.06064 -0.469679 -0.469679 -0.469679 3 2 1.01014 -0.494932 -0.494932 -0.494932 3.25 2 0.962034 -0.518983 -0.518983 -0.518983 3.5 2 0.916223 -0.541888 -0.541888 -0.541888 3.75 2 0.872593 -0.563703 -0.563703 -0.563703 4 2 0.831041 -0.584479 -0.584479 -0.584479 4.25 2 0.791468 -0.604266 -0.604266 -0.604266 4.5 2 0.753779 -0.623111 -0.623111 -0.623111 4.75 2 0.717885 -0.641058 -0.641058 -0.641058 5 2 0.6837 -0.65815 -0.65815 -0.65815 5.25 2 0.651143 -0.674429 -0.674429 -0.674429 5.5 2 0.620136 -0.689932 -0.689932 -0.689932 5.75 2 0.590606 -0.704697 -0.704697 -0.704697 6 2 0.562481 -0.718759 -0.718759 -0.718759 6.25 2 0.535697 -0.732152 -0.732152 -0.732152 6.5 2 0.510187 -0.744906 -0.744906 -0.744906 6.75 2 0.485893 -0.757054 -0.757054 -0.757054 7 2 0.462755 -0.768623 -0.768623 -0.768623 7.25 2 0.440719 -0.779641 -0.779641 -0.779641 7.5 2 0.419732 -0.790134 -0.790134 -0.790134 7.75 2 0.399745 -0.800127 -0.800127 -0.800127 8 2 0.38071 -0.809645 -0.809645 -0.809645 8.25 2 0.362581 -0.81871 -0.81871 -0.81871 8.5 2 0.345315 -0.827343 -0.827343 -0.827343 8.75 2 0.328871 -0.835564 -0.835564 -0.835564 9 2 0.313211 -0.843395 -0.843395 -0.843395 9.25 2 0.298296 -0.850852 -0.850852 -0.850852 9.5 2 0.284091 -0.857954 -0.857954 -0.857954 9.75 2 0.270563 -0.864718 -0.864718 -0.864718 10 2 0.257679 -0.87116 -0.87116 -0.87116 10.25 2 0.245409 -0.877296 -0.877296 -0.877296 10.5 2 0.233723 -0.883139 -0.883139 -0.883139 10.75 2 0.222593 -0.888703 -0.888703 -0.888703 11 2 0.211993 -0.894003 -0.894003 -0.894003 11.25 2 0.201898 -0.899051 -0.899051 -0.899051 11.5 2 0.192284 -0.903858 -0.903858 -0.903858 11.75 2 0.183128 -0.908436 -0.908436 -0.908436 12 2 0.174407 -0.912796 -0.912796 -0.912796 12.25 2 0.166102 -0.916949 -0.916949 -0.916949 12.5 2 0.158193 -0.920904 -0.920904 -0.920904 12.75

3. Cir uito RL on exita i贸n ont铆nua.

2 0.15066 -0.92467 -0.92467 -0.92467 13 2 0.143485 -0.928257 -0.928257 -0.928257 13.25 2 0.136653 -0.931674 -0.931674 -0.931674 13.5 2 0.130146 -0.934927 -0.934927 -0.934927 13.75 2 0.123948 -0.938026 -0.938026 -0.938026 14 2 0.118046 -0.940977 -0.940977 -0.940977 14.25 2 0.112425 -0.943788 -0.943788 -0.943788 14.5 2 0.107071 -0.946464 -0.946464 -0.946464 14.75 2 0.101972 -0.949014 -0.949014 -0.949014 15 2 0.0971166 -0.951442 -0.951442 -0.951442 15.25 2 0.092492 -0.953754 -0.953754 -0.953754 15.5 2 0.0880876 -0.955956 -0.955956 -0.955956 15.75 2 0.083893 -0.958054 -0.958054 -0.958054 16 2 0.0798981 -0.960051 -0.960051 -0.960051 16.25 2 0.0760934 -0.961953 -0.961953 -0.961953 16.5 2 0.0724699 -0.963765 -0.963765 -0.963765 16.75 2 0.069019 -0.965491 -0.965491 -0.965491 17 2 0.0657323 -0.967134 -0.967134 -0.967134 17.25 2 0.0626022 -0.968699 -0.968699 -0.968699 17.5 2 0.0596212 -0.970189 -0.970189 -0.970189 17.75 2 0.0567821 -0.971609 -0.971609 -0.971609 18 2 0.0540782 -0.972961 -0.972961 -0.972961 18.25 2 0.051503 -0.974248 -0.974248 -0.974248 18.5 2 0.0490505 -0.975475 -0.975475 -0.975475 18.75 2 0.0467147 -0.976643 -0.976643 -0.976643 19 2 0.0444902 -0.977755 -0.977755 -0.977755 19.25 2 0.0423716 -0.978814 -0.978814 -0.978814 19.5 2 0.040354 -0.979823 -0.979823 -0.979823 19.75 2 0.0384323 -0.980784 -0.980784 -0.980784 20 2 0.0366022 -0.981699 -0.981699 -0.981699 20.25 2 0.0348593 -0.98257 -0.98257 -0.98257 20.5 2 0.0331993 -0.9834 -0.9834 -0.9834 20.75 2 0.0316184 -0.984191 -0.984191 -0.984191 21 2 0.0301127 -0.984944 -0.984944 -0.984944 21.25 2 0.0286788 -0.985661 -0.985661 -0.985661 21.5 2 0.0273131 -0.986343 -0.986343 -0.986343 21.75 2 0.0260125 -0.986994 -0.986994 -0.986994 22 2 0.0247738 -0.987613 -0.987613 -0.987613 22.25 2 0.0235941 -0.988203 -0.988203 -0.988203 22.5 2 0.0224706 -0.988765 -0.988765 -0.988765 22.75 2 0.0214006 -0.9893 -0.9893 -0.9893 23 2 0.0203815 -0.989809 -0.989809 -0.989809 23.25 2 0.0194109 -0.990295 -0.990295 -0.990295 23.5 2 0.0184866 -0.990757 -0.990757 -0.990757 23.75 2 0.0176063 -0.991197 -0.991197 -0.991197 24 2 0.0167679 -0.991616 -0.991616 -0.991616 24.25 2 0.0159694 -0.992015 -0.992015 -0.992015 24.5 2 0.015209 -0.992396 -0.992396 -0.992396 25

set terminal png set output ' /home/ ayose / Programa ion /AVALON/debug / s r / o l e i o n / G r a f i o s / o l e i o n p r o b l e m a s /3/ e j e m p l o 0 3 _ g r a f i a . png '

set en oding iso_8859_1 set grid

3.3. Comproba ión de resultados.

set autos ale set key top r i g h t t i t l e ' V a r i a b l e s ' box set t i t l e ' Grafi ado por d e f e t o de l a s s o l u i o n e s d e l i r u i t o ' plot ' /home/ ayose / Programa ion /AVALON/debug / s r / o l e i o n / G r a f i o s / o l e i o n p r o b l e m a s /3/ ejemplo03_x_trans . data ' using 6 : 1 t i t l e 'V en nodo 1 ' with l i n e s , ' /home/ ayose / Programa ion /AVALON/debug / s r / o l e i o n / G r a f i o s / o l e i o n p r o b l e m a s /3/ ejemplo03_x_trans . data '

using 6 : 2 t i t l e 'V en nodo 2 ' with l i n e s , ' /home/ ayose / Programa ion

/AVALON/debug / s r / o l e i o n / G r a f i o s / o l e i o n p r o b l e m a s /3/ ejemplo03_x_trans . data ' using 6 : 3 t i t l e ' I R e s i s t e n i a e n t r e nodos 2 , 1 ' with l i n e s , ' /home/ ayose / Programa ion /AVALON/debug / s r / o l e i o n / G r a f i o s / o l e i o n p r o b l e m a s /3/ ejemplo03_x_trans . data ' using 6 : 4 t i t l e ' I de Fuente t e n s i o n e n t r e nodos 1 , 0 ' with l i n e s , ' /home/ ayose / Programa ion /AVALON/debug / s r / o l e i o n / G r a f i o s / o l e i o n p r o b l e m a s /3/ ejemplo03_x_trans . data ' using 6 : 5 t i t l e ' I de Bobina e n t r e nodos 0 , 2 ' with l i n e s

Grá o de salida.

3.3.

Comproba ión de resultados.

Ahora se omprobará si los datos obtenidos on el programa son orre tos, por lo que se pro ederá a superponer las grá as de las expresiones teóri as on la de la solu ión aportada por el software. Empezaremos on la superposi ión de la e ua ión 3.2 en la página~27 on los datos de tensión en nudo 2.

3. Cir uito RL on exita ión ontínua.

Corriente de la malla del ir uito superposi ión de la e ua ión 3.3 on la obtenida on Ávalon. Pro edamos a ver las grá as para analizar los resultados obtenidos.

Tensión en la resisten ia del ir uito se ha e uso de la e ua ión 3.1 y los datos propor ionados por el programa. Debemos tener presente que para la obten ión de esta grá a on el programa se deben restar las olumnas 1 y 2 que es la diferen ia de tensión a la que se en uentra la resisten ia, re ordemos que el programa sólo porpor iona tensiones e intensidades.

3.3. Comproba i贸n de resultados.

Capítulo 4 Cir uito RC on exita ión senoidal.

En este ejemplo se analizará un ir uito RL on ondi iones ini iales.

4.1.

Datos Generales.

Ar hivo *.sp ∗ SPICE i r u i t <CTOr > from XCir uit v3 . 6 rev 135

2 1 0 1 0 2 0 0 ,001 1 1 0 2 2 1 0 2 4 1 0 2 1 0 1 0 0 50 a b 1 B C D . end Tipo de análisis realizado Análisis esta ionario Análisis transitorio

Datos generales del ir uito Elementos del Cto: 3 EA: 0 Nodos: 2 A2: 2 No nulos: 8 Densidad: 0.5 Dispersion: 0.5

Los valores dados al ir uito son: Elemento Resisten ia Condensador 35

Magnitud 2Ω 0, 001 F

⊠ ⊠

4. Cir uito RC on exita ión senoidal.

Matriz T. Valores de la Matriz T row 0: (2, -1) (3, 1) row 1: (1, 0 + 0.001 i) (2, 1) row 2: (0, -1) (1, 1) (2, -2) row 3: (0, 1)

4.2.

4.2.1.

Solu iones

Primer análisis

Nuevamente se realizará un análisis omprendido entre 0 segundos y 5 ve es su onstante de tiempo, es de ir 50 segundos. Tiempo Ini ial Tiempo Final Paso de Tiempo Theta

0 0, 1 0, 001

1 (Euler)

Esta ionario Resultados sistema esta ionario: Tensión en nodo 1: 1 - 2.16841e-19 i Tensión en nodo 2: 0.999996 - 0.00199999 i I Resisten ia entre nodos 2, 1: -1.99999e-06 - 0.000999996 i I de Fuente tension entre nodos 1, 0: -1.99999e-06 - 0.000999996 i

Transitorio 0.309017 0.103006 -0.103006 -0.103006 0 0.587785 0.264599 -0.161593 -0.161593 0.001 0.809017 0.446072 -0.181473 -0.181473 0.002 0.951057 0.6144 -0.168328 -0.168328 0.003 1 0.742933 -0.128533 -0.128533 0.004 0.951056 0.812308 -0.0693744 -0.0693744 0.005 0.809017 0.811211 0.00109691 0.00109691 0.006 0.587785 0.736736 0.0744752 0.0744752 0.007 0.309017 0.594163 0.142573 0.142573 0.008 -1.49218e-07 0.396108 0.198054 0.198054 0.009 -0.309017 0.161067 0.235042 0.235042 0.01 -0.587785 -0.0885508 0.249617 0.249617 0.011 -0.809017 -0.328706 0.240155 0.240155 0.012 -0.951057 -0.536156 0.20745 0.20745 0.013 -1 -0.690771 0.154615 0.154615 0.014 -0.951056 -0.777533 0.0867618 0.0867618 0.015 -0.809017 -0.788027 0.0104947 0.0104947 0.016 -0.587785 -0.72128 -0.0667475 -0.0667475 0.017

4.2. Solu iones

-0.309017 -0.583859 -0.137421 -0.137421 0.018 2.98435e-07 -0.389239 -0.19462 -0.19462 0.019 0.309017 -0.156487 -0.232752 -0.232752 0.02 0.587786 0.0916039 -0.248091 -0.248091 0.021 0.809017 0.330742 -0.239138 -0.239138 0.022 0.951057 0.537513 -0.206772 -0.206772 0.023 1 0.691676 -0.154162 -0.154162 0.024 0.951056 0.778136 -0.0864603 -0.0864603 0.025 0.809017 0.788429 -0.0102936 -0.0102936 0.026 0.587785 0.721548 0.0668815 0.0668815 0.027 0.309017 0.584037 0.13751 0.13751 0.028 -4.47653e-07 0.389358 0.194679 0.194679 0.029 -0.309017 0.156566 0.232792 0.232792 0.03 -0.587786 -0.091551 0.248117 0.248117 0.031 -0.809017 -0.330706 0.239155 0.239155 0.032 -0.951057 -0.53749 0.206783 0.206783 0.033 -1 -0.69166 0.15417 0.15417 0.034 -0.951056 -0.778125 0.0864655 0.0864655 0.035 -0.809017 -0.788422 0.0102971 0.0102971 0.036 -0.587785 -0.721543 -0.0668792 -0.0668792 0.037 -0.309016 -0.584034 -0.137509 -0.137509 0.038 5.96871e-07 -0.389356 -0.194678 -0.194678 0.039 0.309018 -0.156565 -0.232791 -0.232791 0.04 0.587786 0.0915521 -0.248117 -0.248117 0.041 0.809017 0.330707 -0.239155 -0.239155 0.042 0.951057 0.53749 -0.206783 -0.206783 0.043 1 0.69166 -0.15417 -0.15417 0.044 0.951056 0.778126 -0.0864653 -0.0864653 0.045 0.809017 0.788423 -0.010297 -0.010297 0.046 0.587785 0.721543 0.0668793 0.0668793 0.047 0.309016 0.584034 0.137509 0.137509 0.048 -7.46088e-07 0.389356 0.194678 0.194678 0.049 -0.309018 0.156565 0.232791 0.232791 0.05 -0.587786 -0.0915522 0.248117 0.248117 0.051 -0.809017 -0.330707 0.239155 0.239155 0.052 -0.951057 -0.53749 0.206783 0.206783 0.053 -1 -0.69166 0.15417 0.15417 0.054 -0.951056 -0.778126 0.0864653 0.0864653 0.055 -0.809016 -0.788423 0.0102969 0.0102969 0.056 -0.587785 -0.721543 -0.0668793 -0.0668793 0.057 -0.309016 -0.584034 -0.137509 -0.137509 0.058 8.95306e-07 -0.389356 -0.194678 -0.194678 0.059 0.309018 -0.156565 -0.232791 -0.232791 0.06 0.587786 0.0915523 -0.248117 -0.248117 0.061 0.809018 0.330707 -0.239155 -0.239155 0.062 0.951057 0.537491 -0.206783 -0.206783 0.0629999 1 0.69166 -0.15417 -0.15417 0.064 0.951056 0.778126 -0.0864653 -0.0864653 0.065 0.809016 0.788423 -0.0102969 -0.0102969 0.066 0.587784 0.721543 0.0668794 0.0668794 0.067 0.309016 0.584034 0.137509 0.137509 0.068 -1.04452e-06 0.389356 0.194678 0.194678 0.069 -0.309018 0.156564 0.232791 0.232791 0.07 -0.587786 -0.0915524 0.248117 0.248117 0.071

4. Cir uito RC on exita i贸n senoidal.

-0.809018 -0.330708 0.239155 0.239155 0.072 -0.951057 -0.537491 0.206783 0.206783 0.073 -1 -0.69166 0.15417 0.15417 0.074 -0.951056 -0.778126 0.0864653 0.0864653 0.075 -0.809016 -0.788423 0.0102969 0.0102969 0.076 -0.587784 -0.721543 -0.0668794 -0.0668794 0.077 -0.309016 -0.584034 -0.137509 -0.137509 0.078 1.19374e-06 -0.389356 -0.194678 -0.194678 0.079 0.309018 -0.156564 -0.232791 -0.232791 0.08 0.587786 0.0915525 -0.248117 -0.248117 0.081 0.809018 0.330708 -0.239155 -0.239155 0.082 0.951057 0.537491 -0.206783 -0.206783 0.083 1 0.69166 -0.15417 -0.15417 0.084 0.951056 0.778126 -0.0864652 -0.0864652 0.085 0.809016 0.788423 -0.0102968 -0.0102968 0.086 0.587784 0.721543 0.0668795 0.0668795 0.087 0.309016 0.584034 0.137509 0.137509 0.088 -1.34296e-06 0.389356 0.194678 0.194678 0.089 -0.309018 0.156564 0.232791 0.232791 0.09 -0.587786 -0.0915526 0.248117 0.248117 0.091 -0.809018 -0.330708 0.239155 0.239155 0.092 -0.951057 -0.537491 0.206783 0.206783 0.093 -1 -0.691661 0.15417 0.15417 0.094 -0.951056 -0.778126 0.0864652 0.0864652 0.095 -0.809016 -0.788423 0.0102968 0.0102968 0.096 -0.587784 -0.721543 -0.0668795 -0.0668795 0.097 -0.309016 -0.584034 -0.137509 -0.137509 0.098 1.49218e-06 -0.389355 -0.194678 -0.194678 0.1

set terminal png set output ' /home/ ayose / Programa ion /AVALON/debug / s r / o l e i o n / G r a f i o s / o l e i o n p r o b l e m a s /4/ CTOr _grafi a . png '

set en oding iso_8859_1 set grid set autos ale set key bottom r i g h t t i t l e ' V a r i a b l e s ' box set t i t l e ' Grafi ado por d e f e t o de l a s s o l u i o n e s d e l i r u i t o ' plot ' /home/ ayose / Programa ion /AVALON/debug / s r / o l e i o n / G r a f i o s / o l e i o n p r o b l e m a s /4/CTOr _x_trans . data ' using 5 : 1 t i t l e 'V en nodo 1 ' with l i n e s , ' /home/ ayose / Programa ion /AVALON/debug / s r / o l e i o n / G r a f i o s / o l e i o n p r o b l e m a s /4/CTOr _x_trans . data ' using 5 : 2 t i t l e 'V en nodo 2 ' with l i n e s , ' /home/ ayose / Programa ion / AVALON/debug / s r / o l e i o n / G r a f i o s / o l e i o n p r o b l e m a s /4/ CTOr _x_trans . data ' using 5 : 3 t i t l e ' I R e s i s t e n i a e n t r e nodos 2 , 1 ' with l i n e s , ' /home/ ayose / Programa ion /AVALON/debug / s r / o l e i o n / G r a f i o s / o l e i o n p r o b l e m a s /4/CTOr _x_trans . data ' using 5 : 4 t i t l e ' I de Fuente t e n s i o n e n t r e nodos 1 , 0 ' with p o i n t s

Gr谩 o de salida. Como las variables de intensidad que al ula el ir uito para la fuente y la resisten ia oin iden se ha modi ado el s ript para que la orriente de la tensi贸n se represente on puntos.

4.2. Solu iones

Capítulo 5 Cir uito RL on exita ión senoidal.

En este ejemplo se analizará un ir uito RL on ondi iones ini iales.

5.1.

Datos Generales.

Ar hivo *.sp ∗ SPICE i r u i t <ejemplo03> from XCir uit v3 . 6 rev 135

3 1 0 2 0 2 0 0 ,001 1 1 0 2 2 1 0 2 4 1 0 2 1 0 1 0 0 50 a b 1 B C D . end Tipo de análisis realizado Análisis esta ionario Análisis transitorio

Datos generales del ir uito Elementos del Cto: 3 EA: 0 Nodos: 2 A2: 3 No nulos: 10 Densidad: 0.4 Dispersion: 0.6

Los valores dados al ir uito son: Elemento Resisten ia Bobina 41

Magnitud 2Ω 0, 001 H

⊠ ⊠

5. Cir uito RL on exita ión senoidal.

Matriz T. Valores de la Matriz T row 0: (2, -1) (3, 1) row 1: (2, 1) (4, -1) row 2: (0, -1) (1, 1) (2, -2) row 3: (0, 1) row 4: (1, -1) (4, -0 - 0.001 i)

5.2.

5.2.1.

Solu iones

Primer análisis

Nuevamente se realizará un análisis omprendido entre 0 segundos y 5 ve es su onstante de tiempo, es de ir 50 segundos. Tiempo Ini ial Tiempo Final Paso de Tiempo Theta

0 0, 1 0, 001

1 (Euler)

Esta ionario Resultados sistema esta ionario: Tensión en nodo 1: 1 - 5.46025e-14 i Tensión en nodo 2: 2.5e-07 + 0.0005 i I Resisten ia entre nodos 2, 1: -0.5 + 0.00025 i I de Fuente tension entre nodos 1, 0: -0.5 + 0.00025 i I de Bobina entre nodos 0, 2: -0.5 + 0.00025 i

Transitorio 0.618034 0.206011 -0.206011 -0.206011 -0.206011 0 0.587785 0.0585875 -0.264599 -0.264599 -0.264599 0.001 0.809017 0.0932731 -0.357872 -0.357872 -0.357872 0.002 0.951057 0.0784375 -0.43631 -0.43631 -0.43631 0.003 1 0.0424603 -0.47877 -0.47877 -0.47877 0.004 0.951056 -0.00216106 -0.476609 -0.476609 -0.476609 0.005 0.809017 -0.0480669 -0.428542 -0.428542 -0.428542 0.006 0.587785 -0.0897662 -0.338776 -0.338776 -0.338776 0.007 0.309017 -0.122845 -0.215931 -0.215931 -0.215931 0.008 -1.49218e-07 -0.143954 -0.0719769 -0.0719769 -0.0719769 0.009 -0.309017 -0.15099 0.0790134 0.0790134 0.0790134 0.01 -0.587785 -0.143253 0.222266 0.222266 0.222266 0.011 -0.809017 -0.121495 0.343761 0.343761 0.343761 0.012 -0.951057 -0.0878448 0.431606 0.431606 0.431606 0.013 -1 -0.0455961 0.477202 0.477202 0.477202 0.014 -0.951056 0.00111584 0.476086 0.476086 0.476086 0.015

5.2. Solu iones

-0.809017 0.0477185 0.428368 0.428368 0.428368 0.016 -0.587785 0.0896501 0.338718 0.338718 0.338718 0.017 -0.309017 0.122806 0.215911 0.215911 0.215911 0.018 2.98435e-07 0.143941 0.0719704 0.0719704 0.0719704 0.019 0.309017 0.150986 -0.0790156 -0.0790156 -0.0790156 0.02 0.587786 0.143251 -0.222267 -0.222267 -0.222267 0.021 0.809017 0.121494 -0.343761 -0.343761 -0.343761 0.022 0.951057 0.0878446 -0.431606 -0.431606 -0.431606 0.023 1 0.045596 -0.477202 -0.477202 -0.477202 0.024 0.951056 -0.00111586 -0.476086 -0.476086 -0.476086 0.025 0.809017 -0.0477185 -0.428368 -0.428368 -0.428368 0.026 0.587785 -0.0896501 -0.338718 -0.338718 -0.338718 0.027 0.309017 -0.122806 -0.215911 -0.215911 -0.215911 0.028 -4.47653e-07 -0.143941 -0.0719703 -0.0719703 -0.0719703 0.029 -0.309017 -0.150986 0.0790157 0.0790157 0.0790157 0.03 -0.587786 -0.143251 0.222267 0.222267 0.222267 0.031 -0.809017 -0.121494 0.343761 0.343761 0.343761 0.032 -0.951057 -0.0878446 0.431606 0.431606 0.431606 0.033 -1 -0.045596 0.477202 0.477202 0.477202 0.034 -0.951056 0.00111589 0.476086 0.476086 0.476086 0.035 -0.809017 0.0477185 0.428368 0.428368 0.428368 0.036 -0.587785 0.0896501 0.338717 0.338717 0.338717 0.037 -0.309016 0.122806 0.215911 0.215911 0.215911 0.038 5.96871e-07 0.143941 0.0719702 0.0719702 0.0719702 0.039 0.309018 0.150986 -0.0790158 -0.0790158 -0.0790158 0.04 0.587786 0.143251 -0.222267 -0.222267 -0.222267 0.041 0.809017 0.121494 -0.343762 -0.343762 -0.343762 0.042 0.951057 0.0878446 -0.431606 -0.431606 -0.431606 0.043 1 0.0455959 -0.477202 -0.477202 -0.477202 0.044 0.951056 -0.00111592 -0.476086 -0.476086 -0.476086 0.045 0.809017 -0.0477185 -0.428368 -0.428368 -0.428368 0.046 0.587785 -0.0896502 -0.338717 -0.338717 -0.338717 0.047 0.309016 -0.122806 -0.215911 -0.215911 -0.215911 0.048 -7.46088e-07 -0.143941 -0.0719702 -0.0719702 -0.0719702 0.049 -0.309018 -0.150986 0.0790159 0.0790159 0.0790159 0.05 -0.587786 -0.143251 0.222267 0.222267 0.222267 0.051 -0.809017 -0.121494 0.343762 0.343762 0.343762 0.052 -0.951057 -0.0878445 0.431606 0.431606 0.431606 0.053 -1 -0.0455959 0.477202 0.477202 0.477202 0.054 -0.951056 0.00111595 0.476086 0.476086 0.476086 0.055 -0.809016 0.0477186 0.428368 0.428368 0.428368 0.056 -0.587785 0.0896502 0.338717 0.338717 0.338717 0.057 -0.309016 0.122806 0.215911 0.215911 0.215911 0.058 8.95306e-07 0.143941 0.0719701 0.0719701 0.0719701 0.059 0.309018 0.150986 -0.0790159 -0.0790159 -0.0790159 0.06 0.587786 0.143251 -0.222267 -0.222267 -0.222267 0.061 0.809018 0.121494 -0.343762 -0.343762 -0.343762 0.062 0.951057 0.0878445 -0.431606 -0.431606 -0.431606 0.0629999 1 0.0455959 -0.477202 -0.477202 -0.477202 0.064 0.951056 -0.00111597 -0.476086 -0.476086 -0.476086 0.065 0.809016 -0.0477186 -0.428367 -0.428367 -0.428367 0.066 0.587784 -0.0896502 -0.338717 -0.338717 -0.338717 0.067 0.309016 -0.122806 -0.215911 -0.215911 -0.215911 0.068 -1.04452e-06 -0.143941 -0.07197 -0.07197 -0.07197 0.069

5. Cir uito RL on exita ión senoidal.

-0.309018 -0.150986 0.079016 0.079016 0.079016 0.07 -0.587786 -0.143251 0.222267 0.222267 0.222267 0.071 -0.809018 -0.121494 0.343762 0.343762 0.343762 0.072 -0.951057 -0.0878445 0.431606 0.431606 0.431606 0.073 -1 -0.0455959 0.477202 0.477202 0.477202 0.074 -0.951056 0.00111598 0.476086 0.476086 0.476086 0.075 -0.809016 0.0477186 0.428367 0.428367 0.428367 0.076 -0.587784 0.0896502 0.338717 0.338717 0.338717 0.077 -0.309016 0.122806 0.215911 0.215911 0.215911 0.078 1.19374e-06 0.143941 0.0719699 0.0719699 0.0719699 0.079 0.309018 0.150986 -0.0790161 -0.0790161 -0.0790161 0.08 0.587786 0.143251 -0.222267 -0.222267 -0.222267 0.081 0.809018 0.121494 -0.343762 -0.343762 -0.343762 0.082 0.951057 0.0878445 -0.431606 -0.431606 -0.431606 0.083 1 0.0455959 -0.477202 -0.477202 -0.477202 0.084 0.951056 -0.00111601 -0.476086 -0.476086 -0.476086 0.085 0.809016 -0.0477186 -0.428367 -0.428367 -0.428367 0.086 0.587784 -0.0896502 -0.338717 -0.338717 -0.338717 0.087 0.309016 -0.122806 -0.215911 -0.215911 -0.215911 0.088 -1.34296e-06 -0.143941 -0.0719699 -0.0719699 -0.0719699 0.089 -0.309018 -0.150986 0.0790161 0.0790161 0.0790161 0.09 -0.587786 -0.143251 0.222268 0.222268 0.222268 0.091 -0.809018 -0.121494 0.343762 0.343762 0.343762 0.092 -0.951057 -0.0878445 0.431606 0.431606 0.431606 0.093 -1 -0.0455958 0.477202 0.477202 0.477202 0.094 -0.951056 0.00111603 0.476086 0.476086 0.476086 0.095 -0.809016 0.0477186 0.428367 0.428367 0.428367 0.096 -0.587784 0.0896502 0.338717 0.338717 0.338717 0.097 -0.309016 0.122806 0.215911 0.215911 0.215911 0.098 1.49218e-06 0.143941 0.0719698 0.0719698 0.0719698 0.1

set terminal png set output ' /home/ ayose / Programa ion /AVALON/debug / s r / o l e i o n / G r a f i o s / o l e i o n p r o b l e m a s /5/ e j e m p l o 0 5 _ g r a f i a . png '

set en oding iso_8859_1 set grid set autos ale set yrange [ 1 . 8 : − 1 . 8 ℄ set key bottom r i g h t t i t l e ' V a r i a b l e s ' box set t i t l e ' Grafi ado por d e f e t o de l a s s o l u i o n e s d e l i r u i t o ' plot ' /home/ ayose / Programa ion /AVALON/debug / s r / o l e i o n / G r a f i o s / o l e i o n p r o b l e m a s /5/ ejemplo05_x_trans . data ' using 6 : 1 t i t l e 'V en nodo 1 ' with l i n e s , ' /home/ ayose / Programa ion /AVALON/debug / s r / o l e i o n / G r a f i o s / o l e i o n p r o b l e m a s /5/ ejemplo05_x_trans . data '

using 6 : 2 t i t l e 'V en nodo 2 ' with l i n e s , ' /home/ ayose / Programa ion

/AVALON/debug / s r / o l e i o n / G r a f i o s / o l e i o n p r o b l e m a s /5/ ejemplo05_x_trans . data ' using 6 : 3 t i t l e ' I R e s i s t e n i a e n t r e nodos 2 , 1 ' with p o i n t s , ' /home/ ayose / Programa ion /AVALON/debug / s r / o l e i o n / G r a f i o s / o l e i o n p r o b l e m a s /5/ ejemplo05_x_trans . data ' using 6 : 4 t i t l e ' I de Fuente t e n s i o n e n t r e nodos 1 , 0 ' with p o i n t s , ' /home/ ayose / Programa ion /AVALON/debug / s r / o l e i o n / G r a f i o s / o l e i o n p r o b l e m a s /5/ ejemplo05_x_trans . data ' using 6 : 5 t i t l e ' I de Bobina e n t r e nodos 0 , 2 ' with l i n e s

5.2. Solu iones

Gr谩 o de salida. Nuevamente se modi 贸 ligeramente el s ript de ploteo por defe to para que pudiesen apre iarse bien las variables de intensidad que da el programa que obviamente deben ser iguales.

Capítulo 6 Cir uito RL sin exita ión.

En este ejemplo se analizará un ir uito RL on ondi iones ini iales. 1

6.1.

Datos Generales.

Ar hivo *.sp ∗ SPICE i r u i t <ejemplo04> from XCir uit v3 . 6 rev 135

1 1 0 2 0 1 0 0 ,5 3 1 0 2 1 0 0 0 ,0001 . end Tipo de análisis realizado Análisis esta ionario Análisis transitorio

Datos generales del ir uito Elementos del Cto: 2 EA: 0 Nodos: 1 A2: 2 No nulos: 6 Densidad: 0.666667 Dispersion: 0.3333333333

Los valores dados al ir uito son: Elemento Resisten ia Bobina 47

Magnitud 0, 5 Ω 0, 0001 H

⊠ ⊠

6. Cir uito RL sin exita i贸n.

Matriz T. Valores de la Matriz T row 0: (1, -1) (2, 1) row 1: (0, -1) (1, -0.5) row 2: (0, 1) (2, -0 - 0.0001 i)

6.2.

6.2.1.

Solu iones

Primer an谩lisis Tiempo Ini ial Tiempo Final Paso de Tiempo Theta

0 0, 001 0, 00001

1 (Euler)

Esta ionario Resultados sistema esta ionario: Tensi贸n en nodo 1: 0 I Resisten ia entre nodos 0, 1: 0 I de Bobina entre nodos 1, 0: 0

Transitorio -1.90476 3.80952 3.80952 0 -1.81406 3.62812 3.62812 1e-05 -1.72768 3.45535 3.45535 2e-05 -1.6454 3.29081 3.29081 3e-05 -1.56705 3.1341 3.1341 4e-05 -1.49243 2.98486 2.98486 5e-05 -1.42136 2.84273 2.84273 6e-05 -1.35368 2.70736 2.70736 7e-05 -1.28922 2.57844 2.57844 8e-05 -1.22783 2.45565 2.45565 9e-05 -1.16936 2.33872 2.33872 0.0001 -1.11367 2.22735 2.22735 0.00011 -1.06064 2.12129 2.12129 0.00012 -1.01014 2.02027 2.02027 0.00013 -0.962034 1.92407 1.92407 0.00014 -0.916223 1.83245 1.83245 0.00015 -0.872593 1.74519 1.74519 0.00016 -0.831041 1.66208 1.66208 0.00017 -0.791468 1.58294 1.58294 0.00018 -0.753779 1.50756 1.50756 0.00019 -0.717885 1.43577 1.43577 0.0002 -0.6837 1.3674 1.3674 0.00021 -0.651143 1.30229 1.30229 0.00022

Condi iones Ini iales V nodo 1 I Resisten ia entre nodos 0, 1 I Bobina entre nodos 1, 0

Valor 0 4 4

6.2. Solu iones

-0.620136 1.24027 1.24027 0.00023 -0.590606 1.18121 1.18121 0.00024 -0.562481 1.12496 1.12496 0.00025 -0.535697 1.07139 1.07139 0.00026 -0.510187 1.02037 1.02037 0.00027 -0.485893 0.971785 0.971785 0.00028 -0.462755 0.92551 0.92551 0.00029 -0.440719 0.881438 0.881438 0.0003 -0.419732 0.839465 0.839465 0.00031 -0.399745 0.79949 0.79949 0.00032 -0.38071 0.761419 0.761419 0.00033 -0.362581 0.725161 0.725161 0.00034 -0.345315 0.69063 0.69063 0.00035 -0.328871 0.657743 0.657743 0.00036 -0.313211 0.626421 0.626421 0.00037 -0.298296 0.596592 0.596592 0.00038 -0.284091 0.568183 0.568183 0.00039 -0.270563 0.541126 0.541126 0.0004 -0.257679 0.515358 0.515358 0.00041 -0.245409 0.490818 0.490818 0.00042 -0.233723 0.467445 0.467445 0.00043 -0.222593 0.445186 0.445186 0.00044 -0.211993 0.423987 0.423987 0.00045 -0.201898 0.403797 0.403797 0.00046 -0.192284 0.384568 0.384568 0.00047 -0.183128 0.366256 0.366256 0.00048 -0.174407 0.348815 0.348815 0.00049 -0.166102 0.332205 0.332205 0.0005 -0.158193 0.316385 0.316385 0.00051 -0.15066 0.301319 0.301319 0.00052 -0.143485 0.286971 0.286971 0.00053 -0.136653 0.273306 0.273306 0.00054 -0.130146 0.260291 0.260291 0.00055 -0.123948 0.247896 0.247896 0.00056 -0.118046 0.236092 0.236092 0.00057 -0.112425 0.224849 0.224849 0.00058 -0.107071 0.214142 0.214142 0.00059 -0.101972 0.203945 0.203945 0.0006 -0.0971166 0.194233 0.194233 0.00061 -0.092492 0.184984 0.184984 0.00062 -0.0880876 0.176175 0.176175 0.00063 -0.083893 0.167786 0.167786 0.00064 -0.0798981 0.159796 0.159796 0.00065 -0.0760934 0.152187 0.152187 0.00066 -0.0724699 0.14494 0.14494 0.00067 -0.069019 0.138038 0.138038 0.00068 -0.0657323 0.131465 0.131465 0.00069 -0.0626022 0.125204 0.125204 0.0007 -0.0596212 0.119242 0.119242 0.00071 -0.0567821 0.113564 0.113564 0.00072 -0.0540782 0.108156 0.108156 0.00073 -0.051503 0.103006 0.103006 0.00074 -0.0490505 0.098101 0.098101 0.00075 -0.0467147 0.0934295 0.0934295 0.00076

6. Cir uito RL sin exita i贸n.

-0.0444902 0.0889805 0.0889805 0.00077 -0.0423716 0.0847433 0.0847433 0.00078 -0.040354 0.0807079 0.0807079 0.00079 -0.0384323 0.0768647 0.0768647 0.0008 -0.0366022 0.0732044 0.0732044 0.00081 -0.0348593 0.0697185 0.0697185 0.00082 -0.0331993 0.0663986 0.0663986 0.00083 -0.0316184 0.0632368 0.0632368 0.00084 -0.0301127 0.0602255 0.0602255 0.00085 -0.0286788 0.0573576 0.0573576 0.00086 -0.0273131 0.0546263 0.0546263 0.00087 -0.0260125 0.052025 0.052025 0.00088 -0.0247738 0.0495477 0.0495477 0.00089 -0.0235941 0.0471882 0.0471882 0.000900001 -0.0224706 0.0449412 0.0449412 0.000910001 -0.0214006 0.0428011 0.0428011 0.000920001 -0.0203815 0.040763 0.040763 0.000930001 -0.0194109 0.0388219 0.0388219 0.000940001 -0.0184866 0.0369732 0.0369732 0.000950001 -0.0176063 0.0352126 0.0352126 0.000960001 -0.0167679 0.0335358 0.0335358 0.000970001 -0.0159694 0.0319389 0.0319389 0.000980001 -0.015209 0.030418 0.030418 0.000990001

set terminal png set output ' /home/ ayose / Programa ion /AVALON/debug / s r / o l e i o n / G r a f i o s / o l e i o n p r o b l e m a s /6/ e j e m p l o 0 6 _ g r a f i a . png '

using 4 : 2 t i t l e ' I R e s i s t e n i a e n t r e nodos 0 , 1 ' with l i n e s , ' /home

/ ayose / Programa ion /AVALON/debug / s r / o l e i o n / G r a f i o s / o l e i o n p r o b l e m a s /6/ ejemplo06_x_trans . data ' using 4 : 3 t i t l e ' I de Bobina e n t r e nodos 1 , 0 ' with l i n e s

Gr谩 o de salida.

6.3. Compara ión.

6.3.

Compara ión.

Comparemos la intensidad obtenida on el programa on su expresión ideal it =

V −R Lt Re

Capítulo 7 Cir uito RL on ex ita ión es alón.

En este ejemplo se analizará un ir uito RL omo el visto anteriormente pero utilizando una fuente de ex ita ión es alón. Los datos obtenidos serán similares a los del ejemplo 3 en la página~27pero teniendo en uenta que la fuente no omenzará a alimentar el ir uito hasta llegado el valor de salto a los 5 segundos. 1

7.1.

Datos Generales.

Ar hivo *.sp ∗ SPICE i r u i t <ejemplo07> from XCir uit v3 . 6 rev 135

3 1 0 2 0 2 0 10 1 1 0 2 2 1 0 2 4 1 0 2 1 0 4 0 rho f 5 b 0 1 C D . end Como vemos se ha es ogido una ex ita ión tipo es alón ya que en la posi ión 7 del ve tor de de ni ión de la fuente hay un 4. A su vez en la posi ión 11 se en uentra un 5 que es el valor de tiempo en que salta el es alón. Falta por de nir los valores entre los que se mueve di ho es alón que para este ejemplo han sido desde 0 a 1. Tipo de análisis realizado Análisis esta ionario Análisis transitorio

Datos generales del ir uito Elementos del Cto: 3 EA: 0 Nodos: 2 A2: 3 53

⊠ ⊠

7. Cir uito RL on ex ita ión es alón.

No nulos: 10 Densidad: 0.4 Dispersion: 0.6

Los valores dados al ir uito son: Elemento Resisten ia Bobina

Magnitud 2Ω 10 H

Matriz T. Valores de la Matriz T row 0: (2, -1) (3, 1) row 1: (2, 1) (4, -1) row 2: (0, -1) (1, 1) (2, -2) row 3: (0, 1) row 4: (1, -1) (4, -0 - 10 i)

7.2.

7.2.1.

Solu iones

Primer análisis Tiempo Ini ial Tiempo Final Paso de Tiempo Theta

0 30 0, 3

1 (Euler)

Esta ionario Resultados sistema esta ionario: Tensión en nodo 1: 1.26117e-44 - 1.36736e-63 i Tensión en nodo 2: 1.21266e-44 + 2.42532e-45 i I Resisten ia entre nodos 2, 1: -2.42532e-46 + 1.21266e-45 i I de Fuente tension entre nodos 1, 0: -2.42532e-46 + 1.21266e-45 i I de Bobina entre nodos 0, 2: -2.42532e-46 + 1.21266e-45 i

Transitorio 000000 0 0 0 0 0 0.3 0 0 0 0 0 0.6 0 0 0 0 0 0.9 0 0 0 0 0 1.2 1 0.943396 -0.0283019 -0.0283019 -0.0283019 1.5 1 0.889996 -0.0550018 -0.0550018 -0.0550018 1.8 1 0.839619 -0.0801904 -0.0801904 -0.0801904 2.1 1 0.792094 -0.103953 -0.103953 -0.103953 2.4

7.2. Solu iones

1 0.747258 -0.126371 -0.126371 -0.126371 2.7 1 0.704961 -0.14752 -0.14752 -0.14752 3 1 0.665057 -0.167471 -0.167471 -0.167471 3.3 1 0.627412 -0.186294 -0.186294 -0.186294 3.6 1 0.591898 -0.204051 -0.204051 -0.204051 3.9 1 0.558395 -0.220803 -0.220803 -0.220803 4.2 1 0.526788 -0.236606 -0.236606 -0.236606 4.5 1 0.496969 -0.251515 -0.251515 -0.251515 4.8 1 0.468839 -0.26558 -0.26558 -0.26558 5.1 1 0.442301 -0.27885 -0.27885 -0.27885 5.4 1 0.417265 -0.291367 -0.291367 -0.291367 5.7 1 0.393646 -0.303177 -0.303177 -0.303177 6 1 0.371364 -0.314318 -0.314318 -0.314318 6.3 1 0.350344 -0.324828 -0.324828 -0.324828 6.6 1 0.330513 -0.334743 -0.334743 -0.334743 6.9 1 0.311805 -0.344098 -0.344098 -0.344098 7.2 1 0.294155 -0.352922 -0.352922 -0.352922 7.5 1 0.277505 -0.361247 -0.361247 -0.361247 7.8 1 0.261797 -0.369101 -0.369101 -0.369101 8.1 1 0.246979 -0.376511 -0.376511 -0.376511 8.4 1 0.232999 -0.383501 -0.383501 -0.383501 8.7 1 0.21981 -0.390095 -0.390095 -0.390095 9 1 0.207368 -0.396316 -0.396316 -0.396316 9.3 1 0.19563 -0.402185 -0.402185 -0.402185 9.6 1 0.184557 -0.407722 -0.407722 -0.407722 9.9 1 0.17411 -0.412945 -0.412945 -0.412945 10.2 1 0.164255 -0.417873 -0.417873 -0.417873 10.5 1 0.154957 -0.422521 -0.422521 -0.422521 10.8 1 0.146186 -0.426907 -0.426907 -0.426907 11.1 1 0.137912 -0.431044 -0.431044 -0.431044 11.4 1 0.130105 -0.434947 -0.434947 -0.434947 11.7 1 0.122741 -0.43863 -0.43863 -0.43863 12 1 0.115793 -0.442103 -0.442103 -0.442103 12.3 1 0.109239 -0.445381 -0.445381 -0.445381 12.6 1 0.103056 -0.448472 -0.448472 -0.448472 12.9 1 0.0972222 -0.451389 -0.451389 -0.451389 13.2 1 0.091719 -0.45414 -0.45414 -0.45414 13.5 1 0.0865274 -0.456736 -0.456736 -0.456736 13.8 1 0.0816296 -0.459185 -0.459185 -0.459185 14.1 1 0.0770091 -0.461495 -0.461495 -0.461495 14.4 1 0.0726501 -0.463675 -0.463675 -0.463675 14.7 1 0.0685378 -0.465731 -0.465731 -0.465731 15 1 0.0646583 -0.467671 -0.467671 -0.467671 15.3 1 0.0609984 -0.469501 -0.469501 -0.469501 15.6 1 0.0575457 -0.471227 -0.471227 -0.471227 15.9 1 0.0542884 -0.472856 -0.472856 -0.472856 16.2 1 0.0512154 -0.474392 -0.474392 -0.474392 16.5 1 0.0483164 -0.475842 -0.475842 -0.475842 16.8 1 0.0455816 -0.477209 -0.477209 -0.477209 17.1 1 0.0430015 -0.478499 -0.478499 -0.478499 17.4 1 0.0405674 -0.479716 -0.479716 -0.479716 17.7 1 0.0382711 -0.480864 -0.480864 -0.480864 18 1 0.0361049 -0.481948 -0.481948 -0.481948 18.3 1 0.0340612 -0.482969 -0.482969 -0.482969 18.6

7. Cir uito RL on ex ita i贸n es al贸n.

1 0.0321332 -0.483933 -0.483933 -0.483933 18.9 1 0.0303143 -0.484843 -0.484843 -0.484843 19.2 1 0.0285984 -0.485701 -0.485701 -0.485701 19.5 1 0.0269797 -0.48651 -0.48651 -0.48651 19.8 1 0.0254525 -0.487274 -0.487274 -0.487274 20.1 1 0.0240118 -0.487994 -0.487994 -0.487994 20.4 1 0.0226526 -0.488674 -0.488674 -0.488674 20.7 1 0.0213704 -0.489315 -0.489315 -0.489315 21 1 0.0201608 -0.48992 -0.48992 -0.48992 21.3 1 0.0190196 -0.49049 -0.49049 -0.49049 21.6 1 0.017943 -0.491028 -0.491028 -0.491028 21.9 1 0.0169274 -0.491536 -0.491536 -0.491536 22.2 1 0.0159692 -0.492015 -0.492015 -0.492015 22.5 1 0.0150653 -0.492467 -0.492467 -0.492467 22.8 1 0.0142125 -0.492894 -0.492894 -0.492894 23.1 1 0.0134081 -0.493296 -0.493296 -0.493296 23.4 1 0.0126491 -0.493675 -0.493675 -0.493675 23.7 1 0.0119331 -0.494033 -0.494033 -0.494033 24 1 0.0112577 -0.494371 -0.494371 -0.494371 24.3 1 0.0106204 -0.49469 -0.49469 -0.49469 24.6 1 0.0100193 -0.49499 -0.49499 -0.49499 24.9 1 0.00945215 -0.495274 -0.495274 -0.495274 25.2 1 0.00891713 -0.495541 -0.495541 -0.495541 25.5 1 0.00841238 -0.495794 -0.495794 -0.495794 25.8 1 0.00793621 -0.496032 -0.496032 -0.496032 26.1 1 0.00748699 -0.496257 -0.496257 -0.496257 26.4 1 0.0070632 -0.496468 -0.496468 -0.496468 26.7 1 0.00666339 -0.496668 -0.496668 -0.496668 27 1 0.00628622 -0.496857 -0.496857 -0.496857 27.3 1 0.0059304 -0.497035 -0.497035 -0.497035 27.6 1 0.00559471 -0.497203 -0.497203 -0.497203 27.9 1 0.00527803 -0.497361 -0.497361 -0.497361 28.2 1 0.00497928 -0.49751 -0.49751 -0.49751 28.5 1 0.00469743 -0.497651 -0.497651 -0.497651 28.8 1 0.00443154 -0.497784 -0.497784 -0.497784 29.1 1 0.0041807 -0.49791 -0.49791 -0.49791 29.4

set terminal png set output ' /home/ ayose / Programa ion /AVALON/debug / s r / o l e i o n / G r a f i o s / o l e i o n p r o b l e m a s /7/ e j e m p l o 0 7 _ g r a f i a . png '

set en oding iso_8859_1 set grid set autos ale set key top r i g h t t i t l e ' V a r i a b l e s ' box set t i t l e ' Grafi ado por d e f e t o de l a s s o l u i o n e s d e l i r u i t o ' plot ' /home/ ayose / Programa ion /AVALON/debug / s r / o l e i o n / G r a f i o s / o l e i o n p r o b l e m a s /7/ ejemplo07_x_trans . data ' using 6 : 1 t i t l e 'V en nodo 1 ' with l i n e s , ' /home/ ayose / Programa ion /AVALON/debug / s r / o l e i o n / G r a f i o s / o l e i o n p r o b l e m a s /7/ ejemplo07_x_trans . data '

using 6 : 2 t i t l e 'V en nodo 2 ' with l i n e s , ' /home/ ayose / Programa ion

/AVALON/debug / s r / o l e i o n / G r a f i o s / o l e i o n p r o b l e m a s /7/ ejemplo07_x_trans . data ' using 6 : 3 t i t l e ' I R e s i s t e n i a e n t r e nodos 2 , 1 ' with l i n e s , ' /home/ ayose / Programa ion /AVALON/debug / s r / o l e i o n / G r a f i o s / o l e i o n p r o b l e m a s /7/ ejemplo07_x_trans . data '

7.2. Solu iones

using 6 : 4 t i t l e ' I de Fuente t e n s i o n e n t r e nodos 1 , 0 ' with l i n e s ,

' /home/ ayose / Programa ion /AVALON/debug / s r / o l e i o n / G r a f i o s / o l e i o n p r o b l e m a s /7/ ejemplo07_x_trans . data ' using 6 : 5 t i t l e ' I de Bobina e n t r e nodos 0 , 2 ' with l i n e s

Grรก o de salida.

Hagamos una modi a iรณn en el s ript para ha er un zoom sobre los 5 primeros segundos, de esta forma apre iaremos mejor la parte de la grรก a que no se ve orre tamente, ademรกs pasaremos las representa iones de la intensidad a puntos para ver omo abe esperar que oin idan entre los elementos.

7. Cir uito RL on ex ita i贸n es al贸n.

Capítulo 8 Cir uito RLC serie.

Con este ejemplo se pro edera al analisis ir uitos de segundo orden. Este es un ir uito RLC serie on ex ita ión ontinua y analizaremos su respuesta transitoria y esta ionaria. 1

8.1.

Datos Generales.

Ar hivo *.sp ∗ SPICE i r u i t <ejemplo08> from XCir uit v3 . 6 rev 135

2 3 1 4

1 1 1 1

0 0 0 0

1 2 2 2

0 3 2 1

3 2 1 0

0 0 0 0

0 ,0000001 0 ,0001 3 1 rho f a b A B C D

. end Tipo de análisis realizado Análisis esta ionario Análisis transitorio

Datos generales del ir uito Elementos del Cto: 4 EA: 0 Nodos: 3 A2: 3 No nulos: 13 Densidad: 0.361111 Dispersion: 0.6388888889 59

⊠ ⊠

8. Cir uito RLC serie.

Los valores dados al ir uito son: Elemento Resisten ia Bobina Condensador Fuente de tensión

Magnitud 0, 2 Ω 0, 0001 H 10−6 F 1V

Matriz T. Valores de la Matriz T row 0: (3, -1) (4, 1) row 1: (3, 1) (5, -1) row 2: (2, 0 + 1e-07 i) (5, 1) row 3: (0, -1) (1, 1) (3, -0.2) row 4: (0, 1) row 5: (1, -1) (2, 1) (5, -0 - 0.0001 i)

8.2.

8.2.1.

Solu iones

Primer análisis Tiempo Ini ial Tiempo Final Paso de Tiempo Theta

0 0, 0001 0, 000001

1 (Euler)

Esta ionario Resultados sistema esta ionario: Tensión en nodo 1: 1 + 1.01526e-13 i Tensión en nodo 2: 1 - 2.00001e-08 i Tensión en nodo 3: 1 - 2.00001e-08 i I Resisten ia entre nodos 2, 1: -2.00002e-15 - 1.00001e-07 i I de Fuente tension entre nodos 1, 0: -2.00002e-15 - 1.00001e-07 i I de Bobina entre nodos 3, 2: -2.00001e-15 - 1.00002e-07 i

Transitorio 1 0.998185 0.0907441 -0.00907441 -0.00907441 -0.00907441 0 1 0.996703 0.255599 -0.0164855 -0.0164855 -0.0164855 1e-06 1 0.995657 0.472744 -0.0217146 -0.0217146 -0.0217146 2e-06 1 0.995102 0.717637 -0.0244892 -0.0244892 -0.0244892 3e-06 1 0.995043 0.965485 -0.0247848 -0.0247848 -0.0247848 4e-06 1 0.995439 1.19352 -0.022804 -0.022804 -0.022804 5e-06 1 0.996213 1.3829 -0.0189371 -0.0189371 -0.0189371 6e-06 1 0.997258 1.51999 -0.0137098 -0.0137098 -0.0137098 7e-06 1 0.998456 1.59722 -0.00772218 -0.00772218 -0.00772218 8e-06

8.2. Solu iones

1 0.999682 1.6131 -0.00158804 -0.00158804 -0.00158804 9e-06 1 1.00082 1.57187 0.00412243 0.00412243 0.00412243 1e-05 1 1.00179 1.48257 0.00893026 0.00893026 0.00893026 1.1e-05 1 1.0025 1.35774 0.0124827 0.0124827 0.0124827 1.2e-05 1 1.00291 1.21201 0.0145736 0.0145736 0.0145736 1.3e-05 1 1.00303 1.06052 0.0151485 0.0151485 0.0151485 1.4e-05 1 1.00286 0.917565 0.0142956 0.0142956 0.0142956 1.5e-05 1 1.00244 0.795321 0.0122243 0.0122243 0.0122243 1.6e-05 1 1.00185 0.702966 0.00923553 0.00923553 0.00923553 1.7e-05 1 1.00114 0.646113 0.00568529 0.00568529 0.00568529 1.8e-05 1 1.00039 0.626635 0.00194775 0.00194775 0.00194775 1.9e-05 1 0.999676 0.642841 -0.0016206 -0.0016206 -0.0016206 2e-05 1 0.999058 0.689957 -0.0047116 -0.0047116 -0.0047116 2.1e-05 1 0.998582 0.760847 -0.00708895 -0.00708895 -0.00708895 2.2e-05 1 0.998279 0.846877 -0.00860298 -0.00860298 -0.00860298 2.3e-05 1 0.998161 0.938839 -0.0091962 -0.0091962 -0.0091962 2.4e-05 1 0.99822 1.02784 -0.00890001 -0.00890001 -0.00890001 2.5e-05 1 0.998435 1.10607 -0.00782361 -0.00782361 -0.00782361 2.6e-05 1 0.998773 1.16744 -0.0061369 -0.0061369 -0.0061369 2.7e-05 1 0.99919 1.20794 -0.00404942 -0.00404942 -0.00404942 2.8e-05 1 0.999642 1.22582 -0.00178769 -0.00178769 -0.00178769 2.9e-05 1 1.00009 1.22155 0.000426912 0.000426912 0.000426912 3e-05 1 1.00048 1.19757 0.0023978 0.0023978 0.0023978 3.1e-05 1 1.00079 1.15788 0.00396867 0.00396867 0.00396867 3.2e-05 1 1.00101 1.10754 0.00503402 0.00503402 0.00503402 3.3e-05 1 1.00111 1.0521 0.00554394 0.00554394 0.00554394 3.4e-05 1 1.0011 0.997066 0.00550359 0.00550359 0.00550359 3.5e-05 1 1.00099 0.94739 0.00496756 0.00496756 0.00496756 3.6e-05 1 1.00081 0.907086 0.00403037 0.00403037 0.00403037 3.7e-05 1 1.00056 0.878945 0.00281418 0.00281418 0.00281418 3.8e-05 1 1.00029 0.864393 0.0014552 0.0014552 0.0014552 3.9e-05 1 1.00002 0.863493 8.99512e-05 8.99512e-05 8.99512e-05 4e-05 1 0.999769 0.875064 -0.00115709 -0.00115709 -0.00115709 4.1e-05 1 0.999563 0.896901 -0.00218371 -0.00218371 -0.00218371 4.2e-05 1 0.999417 0.926073 -0.00291715 -0.00291715 -0.00291715 4.3e-05 1 0.999336 0.959253 -0.00331799 -0.00331799 -0.00331799 4.4e-05 1 0.999324 0.993059 -0.00338064 -0.00338064 -0.00338064 4.5e-05 1 0.999374 1.02437 -0.00313071 -0.00313071 -0.00313071 4.6e-05 1 0.999476 1.05056 -0.00261983 -0.00261983 -0.00261983 4.7e-05 1 0.999616 1.06975 -0.0019185 -0.0019185 -0.0019185 4.8e-05 1 0.999778 1.08083 -0.00110799 -0.00110799 -0.00110799 4.9e-05 1 0.999946 1.08355 -0.000271956 -0.000271956 -0.000271956 5e-05 1 1.0001 1.07844 0.000511373 0.000511373 0.000511373 5.1e-05 1 1.00024 1.06668 0.00117579 0.00117579 0.00117579 5.2e-05 1 1.00033 1.04996 0.00167202 0.00167202 0.00167202 5.3e-05 1 1.00039 1.03025 0.00197059 0.00197059 0.00197059 5.4e-05 1 1.00041 1.00962 0.00206271 0.00206271 0.00206271 5.5e-05 1 1.00039 0.990033 0.00195912 0.00195912 0.00195912 5.6e-05 1 1.00034 0.97316 0.00168734 0.00168734 0.00168734 5.7e-05 1 1.00026 0.960284 0.0012876 0.0012876 0.0012876 5.8e-05 1 1.00016 0.952203 0.000808016 0.000808016 0.000808016 5.9e-05 1 1.00006 0.949208 0.000299501 0.000299501 0.000299501 6e-05 1 0.999962 0.9511 -0.000189125 -0.000189125 -0.000189125 6.1e-05 1 0.999877 0.957253 -0.000615361 -0.000615361 -0.000615361 6.2e-05

8. Cir uito RLC serie.

1 0.999811 0.966716 -0.000946306 -0.000946306 -0.000946306 6.3e-05 1 0.999768 0.978324 -0.00116075 -0.00116075 -0.00116075 6.4e-05 1 0.99975 0.990824 -0.00125001 -0.00125001 -0.00125001 6.5e-05 1 0.999756 1.003 -0.00121758 -0.00121758 -0.00121758 6.6e-05 1 0.999784 1.01378 -0.00107766 -0.00107766 -0.00107766 6.7e-05 1 0.999829 1.02231 -0.000852901 -0.000852901 -0.000852901 6.8e-05 1 0.999886 1.02802 -0.000571551 -0.000571551 -0.000571551 6.9e-05 1 0.999947 1.03066 -0.000264377 -0.000264377 -0.000264377 7e-05 1 1.00001 1.03028 3.83557e-05 3.83557e-05 3.83557e-05 7.1e-05 1 1.00006 1.02719 0.000309587 0.000309587 0.000309587 7.2e-05 1 1.00011 1.02191 0.000527621 0.000527621 0.000527621 7.3e-05 1 1.00014 1.01513 0.000677595 0.000677595 0.000677595 7.4e-05 1 1.00015 1.00761 0.000752199 0.000752199 0.000752199 7.5e-05 1 1.00015 1.00009 0.000751641 0.000751641 0.000751641 7.6e-05 1 1.00014 0.993265 0.000682928 0.000682928 0.000682928 7.7e-05 1 1.00011 0.987679 0.000558603 0.000558603 0.000558603 7.8e-05 1 1.00008 0.983728 0.000395095 0.000395095 0.000395095 7.9e-05 1 1.00004 0.98162 0.000210869 0.000210869 0.000210869 8e-05 1 1 0.981374 2.45595e-05 2.45595e-05 2.45595e-05 8.1e-05 1 0.999971 0.982841 -0.000146734 -0.000146734 -0.000146734 8.2e-05 1 0.999942 0.98573 -0.000288857 -0.000288857 -0.000288857 8.3e-05 1 0.999922 0.989646 -0.000391614 -0.000391614 -0.000391614 8.4e-05 1 0.99991 0.994139 -0.000449323 -0.000449323 -0.000449323 8.5e-05 1 0.999908 0.998748 -0.000460917 -0.000460917 -0.000460917 8.6e-05 1 0.999914 1.00304 -0.000429612 -0.000429612 -0.000429612 8.7e-05 1 0.999928 1.00667 -0.00036222 -0.00036222 -0.00036222 8.8e-05 1 0.999946 1.00935 -0.000268197 -0.000268197 -0.000268197 8.9e-05 1 0.999968 1.01093 -0.000158539 -0.000158539 -0.000158539 9e-05 1 0.999991 1.01138 -4.46441e-05 -4.46441e-05 -4.46441e-05 9.1e-05 1 1.00001 1.01075 6.27598e-05 6.27598e-05 6.27598e-05 9.2e-05 1 1.00003 1.00921 0.000154527 0.000154527 0.000154527 9.3e-05 1 1.00004 1.00697 0.000223779 0.000223779 0.000223779 9.4e-05 1 1.00005 1.00431 0.000266313 0.000266313 0.000266313 9.5e-05 1 1.00006 1.0015 0.000280745 0.000280745 0.000280745 9.6e-05 1 1.00005 0.998816 0.000268365 0.000268365 0.000268365 9.7e-05 1 1.00005 0.996488 0.000232778 0.000232778 0.000232778 9.8e-05 1 1.00004 0.994694 0.000179362 0.000179362 0.000179362 9.9e-05

set terminal png set output ' /home/ ayose / Programa ion /AVALON/debug / s r / o l e i o n / G r a f i o s / o l e i o n p r o b l e m a s /4b/ e j e m p l o 0 4 _ g r a f i a . png '

using 7 : 2 t i t l e 'V en nodo 2 ' with l i n e s , ' /home/ ayose / Programa ion

/AVALON/debug / s r / o l e i o n / G r a f i o s / o l e i o n p r o b l e m a s /4b/ ejemplo04_x_trans . data ' using 7 : 3 t i t l e 'V en nodo 3 ' with l i n e s , ' /home/ ayose / Programa ion /AVALON/debug / s r / o l e i o n / G r a f i o s /

8.2. Solu iones

o l e i o n p r o b l e m a s /4b/ ejemplo04_x_trans . data ' using 7 : 4 t i t l e ' I R e s i s t e n i a e n t r e nodos 2 , 1 ' with l i n e s , ' /home/ ayose / Programa ion /AVALON/debug / s r / o l e i o n / G r a f i o s / o l e i o n p r o b l e m a s /4b/ ejemplo04_x_trans . data ' using 7 : 5 t i t l e ' I de Fuente t e n s i o n e n t r e nodos 1 , 0 ' with l i n e s , ' /home/ ayose / Programa ion /AVALON/debug / s r / o l e i o n / G r a f i o s / o l e i o n p r o b l e m a s /4b/ ejemplo04_x_trans . data ' using 7 : 6 t i t l e ' I de Bobina e n t r e nodos 3 , 2 ' with l i n e s

Gr谩 o de salida.

Como la intensidad posee una amplitud mu ho menor que la onda de tensi贸n representaremos ahora por separado la intensidad del ir uito, on esto onseguiremos una visualiza i贸n de la variable mu ho mejor en su evolu i贸n temporal.

8. Cir uito RLC serie.

Capítulo 9 Cir uito RLC sin ex ita ión.

Cir uito de segundo orden, RLC serie on ondi iones ini iales y análisis de su respuesta transitoria y esta ionaria. 1

9.1.

Datos Generales.

Ar hivo *.sp ∗ SPICE i r u i t <ejemplo09> from XCir uit v3 . 6 rev 135

2 1 0 1 1 0 0 0 ,000001 3 1 0 2 0 2 0 0 ,0001 1 1 0 2 2 1 0 0 ,2 . end Tipo de análisis realizado Análisis esta ionario Análisis transitorio

Datos generales del ir uito Elementos del Cto: 3 EA: 0 Nodos: 2 A2: 2 No nulos: 9 Densidad: 0.5625 Dispersion: 0.4375 65

⊠ ⊠

9. Cir uito RLC sin ex ita ión.

Los valores dados al ir uito son: Elemento Resisten ia Bobina Condensador

Magnitud 0, 2 Ω 0, 0001 H 10−6 F

Matriz T. row 0: (0, row 1: (2, row 2: (1, row 3: (0,

9.2.

9.2.1.

0 + 1e-06 i) (3, -1) -1) (3, 1) -1) (2, -0 - 0.0001 i) -1) (1, 1) (3, -0.2)

Solu iones

Primer análisis Tiempo Ini ial Tiempo Final Paso de Tiempo Theta

0 0, 0006 0, 0000012

Esta ionario Resultados sistema esta ionario: Tensión en nodo 1: 0 Tensión en nodo 2: 0 I de Bobina entre nodos 0, 2: 0 I Resisten ia entre nodos 2, 1: 0

Transitorio 1.97168 1.96696 -0.0236035 -0.0236035 0 1.9159 1.9066 -0.0464827 -0.0464827 1.2e-06 1.83391 1.82024 -0.0683256 -0.0683256 2.4e-06 1.7273 1.70953 -0.0888399 -0.0888399 3.6e-06 1.59799 1.57644 -0.107757 -0.107757 4.8e-06 1.44819 1.42322 -0.124836 -0.124836 6e-06 1.28035 1.25238 -0.139864 -0.139864 7.2e-06 1.09715 1.06662 -0.152664 -0.152664 8.4e-06 0.901445 0.868827 -0.16309 -0.16309 9.6e-06 0.696205 0.661998 -0.171034 -0.171034 1.08e-05 0.484496 0.449211 -0.176424 -0.176424 1.2e-05 0.269423 0.233578 -0.179227 -0.179227 1.32e-05 0.0540885 0.0181994 -0.179446 -0.179446 1.44e-05 -0.158454 -0.193878 -0.177119 -0.177119 1.56e-05 -0.365241 -0.399706 -0.172323 -0.172323 1.68e-05

1 (Euler)

9.2. Solu iones

-0.563439 -0.596472 -0.165165 -0.165165 1.8e-05 -0.750383 -0.78154 -0.155786 -0.155786 1.92e-05 -0.923611 -0.952482 -0.144357 -0.144357 2.04e-05 -1.0809 -1.10711 -0.131071 -0.131071 2.16e-05 -1.22028 -1.24351 -0.116149 -0.116149 2.28e-05 -1.34007 -1.36004 -0.0998288 -0.0998288 2.4e-05 -1.43891 -1.45538 -0.0823642 -0.0823642 2.52e-05 -1.51573 -1.52854 -0.0640218 -0.0640218 2.64e-05 -1.56982 -1.57884 -0.0450757 -0.0450757 2.76e-05 -1.60079 -1.60595 -0.0258043 -0.0258043 2.88e-05 -1.60857 -1.60987 -0.00648587 -0.00648587 3e-05 -1.59345 -1.59092 0.0126052 0.0126052 3.12e-05 -1.556 -1.54976 0.0312024 0.0312024 3.24e-05 -1.49714 -1.48733 0.0490504 0.0490504 3.36e-05 -1.41805 -1.40487 0.0659088 0.0659088 3.48e-05 -1.32019 -1.30387 0.0815553 0.0815553 3.6e-05 -1.20524 -1.18608 0.0957883 0.0957883 3.72e-05 -1.07512 -1.05344 0.10843 0.10843 3.84e-05 -0.931932 -0.908067 0.119326 0.119326 3.96e-05 -0.777909 -0.752238 0.128353 0.128353 4.08e-05 -0.615413 -0.58833 0.135413 0.135413 4.2e-05 -0.446886 -0.418799 0.140439 0.140439 4.32e-05 -0.274815 -0.246137 0.143392 0.143392 4.44e-05 -0.101696 -0.0728423 0.144267 0.144267 4.56e-05 0.070004 0.0986206 0.143083 0.143083 4.68e-05 0.237875 0.265854 0.139893 0.139893 4.8e-05 0.399604 0.426559 0.134774 0.134774 4.92e-05 0.553002 0.578568 0.127831 0.127831 5.04e-05 0.696033 0.719872 0.119193 0.119193 5.16e-05 0.826844 0.848646 0.109009 0.109009 5.28e-05 0.943784 0.963274 0.0974498 0.0974498 5.4e-05 1.04543 1.06237 0.0847014 0.0847014 5.52e-05 1.13058 1.14478 0.0709641 0.0709641 5.64e-05 1.19832 1.20961 0.0564488 0.0564488 5.76e-05 1.24797 1.25624 0.0413738 0.0413738 5.88e-05 1.27912 1.28432 0.025962 0.025962 6e-05 1.29165 1.29374 0.0104372 0.0104372 6.12e-05 1.28567 1.28468 -0.00497894 -0.00497894 6.24e-05 1.26159 1.25758 -0.0200699 -0.0200699 6.36e-05 1.22004 1.21311 -0.0346272 -0.0346272 6.48e-05 1.16189 1.1522 -0.0484536 -0.0484536 6.60001e-05 1.08825 1.07598 -0.0613654 -0.0613654 6.72001e-05 1.00042 0.985782 -0.0731948 -0.0731948 6.84001e-05 0.89987 0.883112 -0.0837921 -0.0837921 6.96001e-05 0.788237 0.769631 -0.0930277 -0.0930277 7.08001e-05 0.667285 0.647126 -0.100793 -0.100793 7.20001e-05 0.538882 0.517481 -0.107003 -0.107003 7.32001e-05 0.404968 0.382649 -0.111595 -0.111595 7.44001e-05 0.267531 0.244625 -0.11453 -0.11453 7.56001e-05 0.128577 0.105418 -0.115795 -0.115795 7.68001e-05 -0.00990236 -0.0329823 -0.1154 -0.1154 7.80001e-05 -0.145954 -0.168629 -0.113376 -0.113376 7.92001e-05 -0.27769 -0.299646 -0.10978 -0.10978 8.04001e-05 -0.403317 -0.424255 -0.104689 -0.104689 8.16001e-05

9. Cir uito RLC sin ex ita i贸n.

-0.521156 -0.540796 -0.0981996 -0.0981996 8.28001e-05 -0.629668 -0.647754 -0.0904266 -0.0904266 8.40001e-05 -0.72747 -0.74377 -0.0815013 -0.0815013 8.52001e-05 -0.813353 -0.827667 -0.0715693 -0.0715693 8.64001e-05 -0.886298 -0.898456 -0.0607879 -0.0607879 8.76001e-05 -0.945487 -0.955352 -0.0493236 -0.0493236 8.88001e-05 -0.990307 -0.997777 -0.0373503 -0.0373503 9.00001e-05 -1.02036 -1.02537 -0.0250459 -0.0250459 9.12001e-05 -1.03547 -1.03799 -0.01259 -0.01259 9.24001e-05 -1.03566 -1.0357 -0.000161634 -0.000161634 9.36001e-05 -1.02119 -1.01878 0.0120637 0.0120637 9.48001e-05 -0.992488 -0.987705 0.0239161 0.0239161 9.60001e-05 -0.950208 -0.943161 0.0352341 0.0352341 9.72001e-05 -0.895168 -0.885995 0.045866 0.045866 9.84001e-05 -0.828361 -0.817227 0.0556727 0.0556727 9.96001e-05 -0.750926 -0.738021 0.064529 0.064529 0.0001008 -0.664136 -0.649671 0.072325 0.072325 0.000102 -0.569375 -0.553581 0.078968 0.078968 0.0001032 -0.468115 -0.451239 0.0843829 0.0843829 0.0001044 -0.361899 -0.344197 0.0885132 0.0885132 0.0001056 -0.252313 -0.234049 0.0913218 0.0913218 0.0001068 -0.140964 -0.122406 0.0927907 0.0927907 0.000108 -0.029459 -0.0108747 0.0929212 0.0929212 0.0001092 0.0806213 0.098968 0.0917336 0.0917336 0.0001104 0.187741 0.205594 0.0892664 0.0892664 0.0001116 0.290432 0.307547 0.0855759 0.0855759 0.0001128 0.387313 0.40346 0.0807343 0.0807343 0.000114 0.477109 0.492074 0.0748294 0.0748294 0.0001152 0.558663 0.572256 0.0679624 0.0679624 0.0001164 0.630959 0.643008 0.0602463 0.0602463 0.0001176 0.693124 0.703485 0.0518045 0.0518045 0.0001188 0.744446 0.753 0.0427685 0.0427685 0.00012 0.784378 0.791033 0.0332761 0.0332761 0.0001212 0.812541 0.817235 0.0234692 0.0234692 0.0001224 0.828731 0.83143 0.0134921 0.0134921 0.0001236 0.832918 0.833615 0.0034887 0.0034887 0.0001248 0.825239 0.823959 -0.00639882 -0.00639882 0.000126 0.806 0.802794 -0.0160323 -0.0160323 0.0001272 0.775665 0.770609 -0.0252797 -0.0252797 0.0001284 0.734845 0.728042 -0.0340162 -0.0340162 0.0001296 0.684294 0.675868 -0.0421266 -0.0421266 0.0001308 0.624886 0.614985 -0.0495064 -0.0495064 0.000132 0.55761 0.546397 -0.0560632 -0.0560632 0.0001332 0.483549 0.471205 -0.0617176 -0.0617176 0.0001344 0.403863 0.390582 -0.0664046 -0.0664046 0.0001356 0.319775 0.30576 -0.0700737 -0.0700737 0.0001368 0.232547 0.218009 -0.0726898 -0.0726898 0.000138 0.143467 0.12862 -0.0742333 -0.0742333 0.0001392 0.0538272 0.0388872 -0.0746999 -0.0746999 0.0001404 -0.035094 -0.0499142 -0.074101 -0.074101 0.0001416 -0.122049 -0.136541 -0.0724625 -0.0724625 0.0001428 -0.205839 -0.219804 -0.0698248 -0.0698248 0.000144 -0.285329 -0.298577 -0.0662419 -0.0662419 0.0001452 -0.359465 -0.371821 -0.06178 -0.06178 0.0001464

9.2. Solu iones

-0.427285 -0.438589 -0.056517 -0.056517 0.0001476 -0.487934 -0.498042 -0.0505405 -0.0505405 0.0001488 -0.54067 -0.54946 -0.043947 -0.043947 0.00015 -0.584878 -0.592246 -0.03684 -0.03684 0.0001512 -0.620073 -0.625939 -0.0293287 -0.0293287 0.0001524 -0.645904 -0.65021 -0.0215262 -0.0215262 0.0001536 -0.662162 -0.664871 -0.0135478 -0.0135478 0.0001548 -0.668773 -0.669875 -0.00550927 -0.00550927 0.000156 -0.665803 -0.665309 0.00247443 0.00247443 0.0001572 -0.653454 -0.651396 0.0102912 0.0102912 0.0001584 -0.632054 -0.628488 0.017833 0.017833 0.0001596 -0.602057 -0.597058 0.0249977 0.0249977 0.0001608 -0.564029 -0.557691 0.03169 0.03169 0.000162 -0.518642 -0.511077 0.0378229 0.0378229 0.0001632 -0.466659 -0.457995 0.0433189 0.0433189 0.0001644 -0.408926 -0.399304 0.0481105 0.0481105 0.0001656 -0.346356 -0.335928 0.0521417 0.0521417 0.0001668 -0.279915 -0.268841 0.0553678 0.0553678 0.000168 -0.210607 -0.199056 0.0577564 0.0577564 0.0001692 -0.139462 -0.127604 0.0592877 0.0592877 0.0001704 -0.0675171 -0.0555263 0.059954 0.059954 0.0001716 0.00419514 0.0161472 0.0597602 0.0597602 0.0001728 0.0746632 0.0864078 0.0587233 0.0587233 0.000174 0.142909 0.154284 0.0568719 0.0568719 0.0001752 0.208004 0.218853 0.0542457 0.0542457 0.0001764 0.269078 0.279257 0.0508946 0.0508946 0.0001776 0.325332 0.334707 0.0468781 0.0468781 0.0001788 0.376049 0.384501 0.0422641 0.0422641 0.00018 0.420602 0.428027 0.0371278 0.0371278 0.0001812 0.458462 0.464773 0.0315505 0.0315505 0.0001824 0.489205 0.494328 0.0256186 0.0256186 0.0001836 0.512511 0.516395 0.0194218 0.0194218 0.0001848 0.528174 0.530784 0.0130524 0.0130524 0.000186 0.536098 0.537419 0.00660339 0.00660339 0.0001872 0.536299 0.536332 0.000167401 0.000167401 0.0001884 0.528901 0.527668 -0.00616462 -0.00616462 0.0001896 0.514136 0.511675 -0.0123047 -0.0123047 0.0001908 0.492333 0.488699 -0.0181691 -0.0181691 0.000192 0.463918 0.459182 -0.0236793 -0.0236793 0.0001932 0.429402 0.423649 -0.0287631 -0.0287631 0.0001944 0.389375 0.382704 -0.0333555 -0.0333555 0.0001956 0.344496 0.337016 -0.0373997 -0.0373997 0.0001968 0.295479 0.287309 -0.0408474 -0.0408474 0.000198 0.243087 0.234355 -0.0436597 -0.0436597 0.0001992 0.188118 0.178957 -0.0458072 -0.0458072 0.0002004 0.131394 0.12194 -0.0472704 -0.0472704 0.0002016 0.0737458 0.0641378 -0.0480401 -0.0480401 0.0002028 0.0160058 0.00638243 -0.0481167 -0.0481167 0.000204 -0.0410069 -0.050509 -0.0475106 -0.0475106 0.0002052 -0.0964969 -0.105745 -0.0462416 -0.0462416 0.0002064 -0.149703 -0.158571 -0.0443388 -0.0443388 0.0002076 -0.199911 -0.208279 -0.0418394 -0.0418394 0.0002088 -0.246457 -0.254215 -0.0387889 -0.0387889 0.00021 -0.288745 -0.295792 -0.0352393 -0.0352393 0.0002112

9. Cir uito RLC sin ex ita i贸n.

-0.326244 -0.332494 -0.0312494 -0.0312494 0.0002124 -0.358503 -0.36388 -0.0268829 -0.0268829 0.0002136 -0.385153 -0.389594 -0.0222077 -0.0222077 0.0002148 -0.405907 -0.409366 -0.0172953 -0.0172953 0.000216 -0.42057 -0.423014 -0.0122192 -0.0122192 0.0002172 -0.429035 -0.430445 -0.00705383 -0.00705383 0.0002184 -0.431283 -0.431658 -0.00187393 -0.00187393 0.0002196 -0.427387 -0.426738 0.00324692 0.00324692 0.0002208 -0.417502 -0.415855 0.00823718 0.00823718 0.000222 -0.401868 -0.399263 0.0130283 0.0130283 0.0002232 -0.380801 -0.37729 0.0175558 0.0175558 0.0002244 -0.35469 -0.350338 0.0217599 0.0217599 0.0002256 -0.323986 -0.318869 0.0255863 0.0255863 0.0002268 -0.289201 -0.283404 0.0289871 0.0289871 0.000228 -0.250896 -0.244512 0.0319213 0.0319213 0.0002292 -0.20967 -0.202799 0.0343549 0.0343549 0.0002304 -0.166156 -0.158904 0.0362617 0.0362617 0.0002316 -0.121008 -0.113483 0.0376235 0.0376235 0.0002328 -0.0748918 -0.0672058 0.03843 0.03843 0.000234 -0.0284771 -0.0207414 0.0386789 0.0386789 0.0002352 0.0175739 0.0252491 0.0383759 0.0383759 0.0002364 0.0626152 0.0701221 0.0375344 0.0375344 0.0002376 0.106026 0.113261 0.0361753 0.0361753 0.0002388 0.147217 0.154082 0.0343263 0.0343263 0.00024 0.185643 0.192048 0.0320217 0.0320217 0.0002412 0.220805 0.226666 0.0293017 0.0293017 0.0002424 0.252259 0.257502 0.0262117 0.0262117 0.0002436 0.279621 0.284182 0.0228015 0.0228015 0.0002448 0.302571 0.306396 0.0191248 0.0191248 0.000246 0.320857 0.323904 0.0152379 0.0152379 0.0002472 0.334296 0.336536 0.0111995 0.0111995 0.0002484 0.342779 0.344193 0.0070692 0.0070692 0.0002496 0.346267 0.346849 0.00290701 0.00290701 0.0002508 0.344794 0.344549 -0.00122757 -0.00122757 0.000252 0.338463 0.337407 -0.00527646 -0.00527646 0.0002532 0.327442 0.325605 -0.00918373 -0.00918373 0.0002544 0.311966 0.309387 -0.0128964 -0.0128964 0.0002556 0.292328 0.289055 -0.016365 -0.016365 0.0002568 0.268875 0.264966 -0.0195446 -0.0195446 0.000258 0.242001 0.237522 -0.0223949 -0.0223949 0.0002592 0.212144 0.207168 -0.0248809 -0.0248809 0.0002604 0.179776 0.174381 -0.0269735 -0.0269735 0.0002616 0.145396 0.139666 -0.0286495 -0.0286495 0.0002628 0.109526 0.103548 -0.029892 -0.029892 0.000264 0.072697 0.0665589 -0.0306908 -0.0306908 0.0002652 0.0354471 0.0292388 -0.0310416 -0.0310416 0.0002664 -0.00168941 -0.00787883 -0.0309471 -0.0309471 0.0002676 -0.0381884 -0.0442716 -0.0304158 -0.0304158 0.0002688 -0.0735435 -0.079436 -0.0294626 -0.0294626 0.00027 -0.107273 -0.112894 -0.0281078 -0.0281078 0.0002712 -0.138926 -0.144201 -0.0263774 -0.0263774 0.0002724 -0.168088 -0.172949 -0.024302 -0.024302 0.0002736 -0.194388 -0.198772 -0.0219168 -0.0219168 0.0002748 -0.217501 -0.221353 -0.0192605 -0.0192605 0.000276

9.2. Solu iones

-0.237152 -0.240427 -0.0163754 -0.0163754 0.0002772 -0.253119 -0.25578 -0.0133061 -0.0133061 0.0002784 -0.265238 -0.267257 -0.010099 -0.010099 0.0002796 -0.2734 -0.27476 -0.00680185 -0.00680185 0.0002808 -0.277555 -0.278248 -0.00346288 -0.00346288 0.000282 -0.277711 -0.277737 -0.00013003 -0.00013003 0.0002832 -0.273932 -0.273302 0.00314959 0.00314959 0.0002844 -0.266335 -0.265069 0.00633042 0.00633042 0.0002856 -0.255092 -0.253219 0.00936905 0.00936905 0.0002868 -0.240423 -0.237978 0.0122248 0.0122248 0.000288 -0.222591 -0.219618 0.0148602 0.0148602 0.0002892 -0.201901 -0.198452 0.0172416 0.0172416 0.0002904 -0.178693 -0.174825 0.0193395 0.0193395 0.0002916 -0.153338 -0.149113 0.0211289 0.0211289 0.0002928 -0.126231 -0.121713 0.0225894 0.0225894 0.000294 -0.097784 -0.0930428 0.023706 0.023706 0.0002952 -0.068422 -0.0635283 0.0244683 0.0244683 0.0002964 -0.0385762 -0.0336019 0.0248715 0.0248715 0.0002976 -0.00867716 -0.00369399 0.0249158 0.0249158 0.0002988 0.0208507 0.0257721 0.0246066 0.0246066 0.0003 0.0495955 0.0543863 0.0239539 0.0239539 0.0003012 0.0771629 0.0817575 0.0229729 0.0229729 0.0003024 0.103182 0.107519 0.0216826 0.0216826 0.0003036 0.12731 0.131331 0.0201067 0.0201067 0.0003048 0.149236 0.152891 0.018272 0.018272 0.000306 0.168687 0.171929 0.0162088 0.0162088 0.0003072 0.185427 0.188217 0.0139502 0.0139502 0.0003084 0.199265 0.201571 0.0115314 0.0115314 0.0003096 0.210052 0.21185 0.00898916 0.00898916 0.0003108 0.217686 0.218958 0.00636167 0.00636167 0.000312 0.222111 0.222848 0.00368748 0.00368748 0.0003132 0.223317 0.223518 0.00100527 0.00100527 0.0003144 0.221341 0.221012 -0.00164687 -0.00164687 0.0003156 0.216263 0.215416 -0.00423187 -0.00423187 0.0003168 0.208206 0.206863 -0.00671422 -0.00671422 0.000318 0.197333 0.195521 -0.00906047 -0.00906047 0.0003192 0.183845 0.181598 -0.0112396 -0.0112396 0.0003204 0.167977 0.165332 -0.0132236 -0.0132236 0.0003216 0.149992 0.146995 -0.0149876 -0.0149876 0.0003228 0.13018 0.126878 -0.0165101 -0.0165101 0.000324 0.108852 0.105297 -0.0177737 -0.0177737 0.0003252 0.086334 0.082581 -0.0187646 -0.0187646 0.0003264 0.0629658 0.0590711 -0.0194735 -0.0194735 0.0003276 0.039092 0.035113 -0.0198948 -0.0198948 0.0003288 0.015059 0.0110535 -0.0200275 -0.0200275 0.00033 -0.0087902 -0.0127651 -0.0198743 -0.0198743 0.0003312 -0.0321208 -0.0360093 -0.0194422 -0.0194422 0.0003324 -0.0546111 -0.0583595 -0.0187419 -0.0187419 0.0003336 -0.0759564 -0.0795139 -0.0177877 -0.0177877 0.0003348 -0.0958732 -0.0991927 -0.0165974 -0.0165974 0.000336 -0.114103 -0.117142 -0.0151917 -0.0151917 0.0003372 -0.130416 -0.133135 -0.0135941 -0.0135941 0.0003384 -0.144613 -0.146979 -0.0118303 -0.0118303 0.0003396 -0.156526 -0.158512 -0.00992819 -0.00992819 0.0003408

9. Cir uito RLC sin ex ita i贸n.

-0.166027 -0.16761 -0.00791687 -0.00791687 0.000342 -0.173019 -0.174184 -0.00582667 -0.00582667 0.0003432 -0.177445 -0.178183 -0.00368848 -0.00368848 0.0003444 -0.179285 -0.179592 -0.00153338 -0.00153338 0.0003456 -0.178555 -0.178434 0.000607831 0.000607831 0.0003468 -0.175309 -0.174768 0.00270505 0.00270505 0.000348 -0.169634 -0.168688 0.00472931 0.00472931 0.0003492 -0.16165 -0.16032 0.00665315 0.00665315 0.0003504 -0.151509 -0.149819 0.00845098 0.00845098 0.0003516 -0.13939 -0.13737 0.0100994 0.0100994 0.0003528 -0.125497 -0.123181 0.0115776 0.0115776 0.000354 -0.110056 -0.107483 0.0128674 0.0128674 0.0003552 -0.0933116 -0.0905209 0.0139536 0.0139536 0.0003564 -0.0755224 -0.0725576 0.0148243 0.0148243 0.0003576 -0.0569576 -0.0538635 0.0154707 0.0154707 0.0003588 -0.0378929 -0.0347154 0.0158873 0.0158873 0.00036 -0.0186065 -0.0153921 0.016072 0.016072 0.0003612 0.000624729 0.00382993 0.016026 0.016026 0.0003624 0.0195294 0.0226801 0.0157539 0.0157539 0.0003636 0.0378451 0.0408977 0.0152631 0.0152631 0.000364801 0.0553222 0.058235 0.0145643 0.0145643 0.000366001 0.0717271 0.0744612 0.0136707 0.0136707 0.000367201 0.0868451 0.0893648 0.0125984 0.0125984 0.000368401 0.100483 0.102756 0.0113653 0.0113653 0.000369601 0.112473 0.114472 0.00999162 0.00999162 0.000370801 0.122672 0.124372 0.00849915 0.00849915 0.000372001 0.130966 0.132348 0.00691098 0.00691098 0.000373201 0.137267 0.138317 0.00525117 0.00525117 0.000374401 0.14152 0.142229 0.00354442 0.00354442 0.000375601 0.143699 0.144062 0.00181568 0.00181568 0.000376801 0.143807 0.143825 8.97796e-05 8.97796e-05 0.000378001 0.141876 0.141554 -0.00160887 -0.00160887 0.000379201 0.137968 0.137317 -0.00325667 -0.00325667 0.000380401 0.132171 0.131205 -0.00483113 -0.00483113 0.000381601 0.124597 0.123335 -0.00631115 -0.00631115 0.000382801 0.115385 0.113849 -0.00767734 -0.00767734 0.000384001 0.10469 0.102907 -0.00891223 -0.00891223 0.000385201 0.0926893 0.0906892 -0.0100005 -0.0100005 0.000386401 0.0795743 0.0773885 -0.0109292 -0.0109292 0.000387601 0.0655491 0.0632115 -0.0116877 -0.0116877 0.000388801 0.0508273 0.0483736 -0.0122682 -0.0122682 0.000390001 0.0356289 0.0330958 -0.0126653 -0.0126653 0.000391201 0.020177 0.0176017 -0.0128766 -0.0128766 0.000392401 0.00469467 0.00211429 -0.0129019 -0.0129019 0.000393601 -0.0105983 -0.0131472 -0.0127442 -0.0127442 0.000394801 -0.0254885 -0.0279702 -0.0124085 -0.0124085 0.000396001 -0.0397718 -0.0421523 -0.0119027 -0.0119027 0.000397201 -0.0532558 -0.0555031 -0.0112367 -0.0112367 0.000398401 -0.0657627 -0.0678472 -0.0104225 -0.0104225 0.000399601 -0.0771317 -0.0790266 -0.00947417 -0.00947417 0.000400801 -0.0872206 -0.088902 -0.00840734 -0.00840734 0.000402001 -0.0959074 -0.0973553 -0.00723908 -0.00723908 0.000403201 -0.103093 -0.10429 -0.0059876 -0.0059876 0.000404401 -0.108699 -0.109633 -0.004672 -0.004672 0.000405601

9.2. Solu iones

-0.112673 -0.113336 -0.00331197 -0.00331197 0.000406801 -0.114986 -0.115372 -0.00192751 -0.00192751 0.000408001 -0.115633 -0.11574 -0.000538623 -0.000538623 0.000409201 -0.114631 -0.114464 0.000834942 0.000834942 0.000410401 -0.112022 -0.111587 0.00217399 0.00217399 0.000411601 -0.10787 -0.107178 0.00346012 0.00346012 0.000412801 -0.102259 -0.101323 0.004676 0.004676 0.000414001 -0.0952919 -0.0941308 0.00580557 0.00580557 0.000415201 -0.0870908 -0.085724 0.00683426 0.00683426 0.000416401 -0.0777918 -0.076242 0.00774916 0.00774916 0.000417601 -0.0675448 -0.0658369 0.00853921 0.00853921 0.000418801 -0.0565105 -0.0546714 0.00919526 0.00919526 0.000420001 -0.0448581 -0.0429161 0.00971026 0.00971026 0.000421201 -0.0327631 -0.0307472 0.0100792 0.0100792 0.000422401 -0.0204039 -0.018344 0.0102994 0.0102994 0.000423601 -0.00795987 -0.00588588 0.01037 0.01037 0.000424801 0.00439123 0.00644975 0.0102926 0.0102926 0.000426001 0.0164761 0.0184902 0.0100707 0.0100707 0.000427201 0.0281279 0.0300699 0.00970986 0.00970986 0.000428401 0.0391889 0.0410324 0.00921748 0.00921748 0.000429601 0.0495121 0.0512326 0.00860268 0.00860268 0.000430801 0.0589636 0.0605388 0.00787622 0.00787622 0.000432001 0.0674238 0.0688339 0.00705021 0.00705021 0.000433201 0.0747894 0.076017 0.00613801 0.00613801 0.000434401 0.0809742 0.082005 0.00515395 0.00515395 0.000435601 0.08591 0.0867326 0.00411316 0.00411316 0.000436801 0.0895475 0.0901538 0.00303131 0.00303131 0.000438001 0.0918568 0.0922417 0.00192441 0.00192441 0.000439201 0.0928271 0.0929888 0.000808545 0.000808545 0.000440401 0.0924667 0.0924066 -0.000300334 -0.000300334 0.000441601 0.0908027 0.0905254 -0.00138664 -0.00138664 0.000442801 0.0878803 0.0873932 -0.00243536 -0.00243536 0.000444001 0.0837616 0.0830751 -0.00343226 -0.00343226 0.000445201 0.0785247 0.0776519 -0.00436408 -0.00436408 0.000446401 0.0722622 0.0712185 -0.0052187 -0.0052187 0.000447601 0.0650799 0.0638828 -0.0059853 -0.0059853 0.000448801 0.0570945 0.0557636 -0.00665446 -0.00665446 0.000450001 0.0484325 0.0469889 -0.00721833 -0.00721833 0.000451201 0.0392277 0.0376936 -0.00767065 -0.00767065 0.000452401 0.0296195 0.0280181 -0.00800687 -0.00800687 0.000453601 0.0197505 0.0181057 -0.00822414 -0.00822414 0.000454801 0.00976493 0.00810066 -0.00832134 -0.00832134 0.000456001 -0.000193987 -0.00185381 -0.0082991 -0.0082991 0.000457201 -0.00998561 -0.0116176 -0.00815969 -0.00815969 0.000458401 -0.019474 -0.0210554 -0.00790702 -0.00790702 0.000459601 -0.0285299 -0.0300392 -0.00754655 -0.00754655 0.000460801 -0.0370321 -0.0384491 -0.00708516 -0.00708516 0.000462001 -0.0448694 -0.0461756 -0.00653106 -0.00653106 0.000463201 -0.0519417 -0.0531204 -0.00589361 -0.00589361 0.000464401 -0.0581616 -0.0591982 -0.00518323 -0.00518323 0.000465601 -0.063455 -0.0643372 -0.00441118 -0.00441118 0.000466801 -0.0677623 -0.0684802 -0.00358942 -0.00358942 0.000468001 -0.0710388 -0.0715849 -0.0027304 -0.0027304 0.000469201 -0.0732551 -0.0736245 -0.00184691 -0.00184691 0.000470401

9. Cir uito RLC sin ex ita i贸n.

-0.0743973 -0.0745877 -0.000951858 -0.000951858 0.000471601 -0.0744671 -0.0744787 -5.81142e-05 -5.81142e-05 0.000472801 -0.073481 -0.0733167 0.000821686 0.000821686 0.000474001 -0.0714707 -0.0711356 0.00167531 0.00167531 0.000475201 -0.0684813 -0.0679831 0.00249111 0.00249111 0.000476401 -0.0645715 -0.0639199 0.00325815 0.00325815 0.000477601 -0.0598119 -0.0590186 0.00396637 0.00396637 0.000478801 -0.0542838 -0.0533625 0.00460672 0.00460672 0.000480001 -0.0480783 -0.0470441 0.00517125 0.00517125 0.000481201 -0.0412945 -0.0401638 0.00565322 0.00565322 0.000482401 -0.0340379 -0.0328284 0.00604716 0.00604716 0.000483601 -0.0264191 -0.0251493 0.00634895 0.00634895 0.000484801 -0.0185521 -0.017241 0.00655584 0.00655584 0.000486001 -0.0105524 -0.00921906 0.00666647 0.00666647 0.000487201 -0.00253532 -0.00119915 0.00668086 0.00668086 0.000488401 0.00538516 0.00670523 0.0066004 0.0066004 0.000489601 0.0130985 0.0143841 0.00642779 0.00642779 0.000490801 0.0204989 0.0217323 0.006167 0.006167 0.000492001 0.0274867 0.0286514 0.00582319 0.00582319 0.000493201 0.0339698 0.0350503 0.00540258 0.00540258 0.000494401 0.0398647 0.0408472 0.00491241 0.00491241 0.000495602 0.0450977 0.0459698 0.00436078 0.00436078 0.000496802 0.0496054 0.0503567 0.0037565 0.0037565 0.000498002 0.0533362 0.053958 0.003109 0.003109 0.000499202 0.0562501 0.0567357 0.00242817 0.00242817 0.000500402 0.0583191 0.0586639 0.0017242 0.0017242 0.000501602 0.059528 0.0597295 0.00100745 0.00100745 0.000502802 0.059874 0.0599316 0.00028827 0.00028827 0.000504002 0.0593662 0.0592816 -0.000423109 -0.000423109 0.000505202 0.0580261 0.0578028 -0.00111674 -0.00111674 0.000506402 0.0558864 0.0555298 -0.0017831 -0.0017831 0.000507602 0.0529906 0.0525079 -0.0024132 -0.0024132 0.000508802 0.0493921 0.0487924 -0.0029987 -0.0029987 0.000510002 0.0451537 0.0444472 -0.00353207 -0.00353207 0.000511202 0.0403457 0.0395444 -0.0040066 -0.0040066 0.000512402 0.0350459 0.0341625 -0.00441655 -0.00441655 0.000513602 0.0293372 0.0283858 -0.00475718 -0.00475718 0.000514802 0.0233075 0.0223025 -0.00502481 -0.00502481 0.000516002 0.0170472 0.0160039 -0.00521686 -0.00521686 0.000517202 0.010649 0.00958263 -0.00533185 -0.00533185 0.000518402 0.00420568 0.0031318 -0.00536943 -0.00536943 0.000519602 -0.00219074 -0.00325681 -0.00533035 -0.00533035 0.000520802 -0.00845045 -0.00949374 -0.00521643 -0.00521643 0.000522002 -0.0144871 -0.0154932 -0.00503051 -0.00503051 0.000523202 -0.0202188 -0.0211741 -0.00477642 -0.00477642 0.000524402 -0.0255694 -0.0264612 -0.00445889 -0.00445889 0.000525602 -0.0304696 -0.0312863 -0.00408345 -0.00408345 0.000526802 -0.0348572 -0.0355885 -0.00365639 -0.00365639 0.000528002 -0.0386788 -0.0393157 -0.0031846 -0.0031846 0.000529202 -0.0418894 -0.0424245 -0.00267551 -0.00267551 0.000530402 -0.0444537 -0.0448811 -0.00213693 -0.00213693 0.000531602 -0.0463461 -0.0466615 -0.001577 -0.001577 0.000532802 -0.0475509 -0.0477517 -0.00100398 -0.00100398 0.000534002 -0.0480623 -0.0481475 -0.000426206 -0.000426206 0.000535202

9.2. Solu iones

-0.0478846 -0.047855 0.000148055 0.000148055 0.000536402 -0.0470318 -0.0468896 0.00071073 0.00071073 0.000537602 -0.0455269 -0.0452761 0.00125404 0.00125404 0.000538802 -0.0434022 -0.043048 0.00177062 0.00177062 0.000540002 -0.0406979 -0.0402471 0.00225359 0.00225359 0.000541202 -0.0374619 -0.0369225 0.00269666 0.00269666 0.000542402 -0.0337488 -0.03313 0.00309422 0.00309422 0.000543602 -0.0296192 -0.0289309 0.00344139 0.00344139 0.000544802 -0.0251383 -0.0243914 0.00373408 0.00373408 0.000546002 -0.0203754 -0.0195816 0.00396906 0.00396906 0.000547202 -0.0154026 -0.0145739 0.00414395 0.00414395 0.000548402 -0.0102939 -0.00944248 0.00425726 0.00425726 0.000549602 -0.00512384 -0.00426216 0.0043084 0.0043084 0.000550802 3.33823e-05 0.00089292 0.00429769 0.00429769 0.000552002 0.00510493 0.00595018 0.00422629 0.00422629 0.000553202 0.0100204 0.0108396 0.00409621 0.00409621 0.000554402 0.0147127 0.0154948 0.00391027 0.00391027 0.000555602 0.0191191 0.0198536 0.00367203 0.00367203 0.000556802 0.023182 0.0238592 0.00338572 0.00338572 0.000558002 0.0268494 0.0274607 0.00305619 0.00305619 0.000559202 0.030076 0.0306138 0.00268883 0.00268883 0.000560402 0.0328234 0.0332813 0.00228945 0.00228945 0.000561602 0.0350605 0.0354333 0.00186425 0.00186425 0.000562802 0.0367641 0.037048 0.00141968 0.00141968 0.000564002 0.0379189 0.0381114 0.00096234 0.00096234 0.000565202 0.0385176 0.0386174 0.000498931 0.000498931 0.000566402 0.038561 0.0385682 3.61125e-05 3.61125e-05 0.000567602 0.0380575 0.0379736 -0.00041957 -0.00041957 0.000568802 0.0370233 0.036851 -0.000861782 -0.000861782 0.000570002 0.035482 0.0352251 -0.00128448 -0.00128448 0.000571202 0.0334635 0.0331271 -0.00168201 -0.00168201 0.000572402 0.0310046 0.0305947 -0.00204915 -0.00204915 0.000573602 0.0281471 0.0276709 -0.0023812 -0.0023812 0.000574802 0.0249383 0.0244035 -0.00267404 -0.00267404 0.000576002 0.0214293 0.0208445 -0.00292417 -0.00292417 0.000577202 0.0176748 0.017049 -0.00312876 -0.00312876 0.000578402 0.013732 0.0130749 -0.00328566 -0.00328566 0.000579602 0.00965987 0.00898118 -0.00339343 -0.00339343 0.000580802 0.00551822 0.00482795 -0.00345137 -0.00345137 0.000582002 0.00136686 0.00067497 -0.00345947 -0.00345947 0.000583202 -0.00273526 -0.00341895 -0.00341844 -0.00341844 0.000584402 -0.00673088 -0.00739681 -0.00332968 -0.00332968 0.000585602 -0.0105652 -0.0112042 -0.00319523 -0.00319523 0.000586802 -0.0141864 -0.01479 -0.00301775 -0.00301775 0.000588002 -0.017547 -0.0181071 -0.00280046 -0.00280046 0.000589202 -0.0206035 -0.021113 -0.00254711 -0.00254711 0.000590402 -0.0233178 -0.0237701 -0.00226187 -0.00226187 0.000591602 -0.0256569 -0.0260468 -0.0019493 -0.0019493 0.000592802 -0.0275941 -0.027917 -0.0016143 -0.0016143 0.000594002 -0.0291085 -0.0293609 -0.00126197 -0.00126197 0.000595202 -0.0301856 -0.0303651 -0.000897589 -0.000897589 0.000596402 -0.0308174 -0.0309227 -0.000526517 -0.000526517 0.000597602 -0.0310023 -0.0310332 -0.000154119 -0.000154119 0.0006

9. Cir uito RLC sin ex ita i贸n.

set terminal png set output ' /home/ ayose / Programa ion /AVALON/debug / s r / o l e i o n / G r a f i o s / o l e i o n p r o b l e m a s /9/ e j e m p l o 0 9 _ g r a f i a . png '

using 5 : 2 t i t l e 'V en nodo 2 ' with l i n e s , ' /home/ ayose / Programa ion

/AVALON/debug / s r / o l e i o n / G r a f i o s / o l e i o n p r o b l e m a s /9/ ejemplo09_x_trans . data ' using 5 : 3 t i t l e ' I de Bobina e n t r e nodos 0 , 2 ' with l i n e s , ' /home/ ayose / Programa ion /AVALON/debug / s r / o l e i o n / G r a f i o s / o l e i o n p r o b l e m a s /9/ ejemplo09_x_trans . data ' using 5 : 4 t i t l e ' I R e s i s t e n i a e n t r e nodos 2 , 1 ' with l i n e s

Gr谩 o de salida.

Ve谩mos por separado la tensi贸n del nudo 1, la del 2 y la intensidad de la malla

9.2. Solu iones

Podríamos pensar que las tensiones en los nudos 1 y 2 son iguales pero esto no es así, tal y omo puede verse en los datos de salida. Sus valores son similares debido a la po a aída de tensión existente en la misma debido a su redu ido valor de 0, 2 Ω

9. Cir uito RLC sin ex ita i贸n.

Capítulo 10 Cir uito RLC paralelo.

Cir uitos de segundo orden, RLC paralelo on ex ita ión de fuente de intensidad.

10.1.

Datos Generales.

Ar hivo *.sp ∗ SPICE i r u i t <ejemplo010> from XCir uit v3 . 6 rev 135

2 3 1 5

1 1 1 1

0 0 0 0

1 2 2 3

1 1 1 1

0 0 0 0

0 ,000002 0 ,0001 10 1 rho f a b A B C D

. end Tipo de análisis realizado Análisis esta ionario Análisis transitorio

Datos generales del ir uito Elementos del Cto: 4 EA: 0 Nodos: 1 A2: 2 No nulos: 7 Densidad: 0.777778 Dispersion: 0.2222222222 79

⊠ ⊠

10. Cir uito RLC paralelo.

Los valores dados al ir uito son: Elemento Resisten ia Bobina Condensador

Magnitud 10 Ω 0, 0001 H 2 · 10−6 F

Matriz T. row 0: (0, 0 + 2e-06 i) (1, 1) (2, 1) row 1: (0, 1) (1, -10) row 2: (0, 1) (2, -0 - 0.0001 i)

10.2.

10.2.1.

Solu iones

Primer análisis Tiempo Ini ial Tiempo Final Paso de Tiempo Theta

Esta ionario Resultados sistema esta ionario: Tensión en nodo 1: -1e-10 - 1e-05 i I Resisten ia entre nodos 1, 0: 0.1 - 1e-06 i I de Bobina entre nodos 1, 0: -0.1 + 1e-06 i

Transitorio -0.982143 0.00178571 0.980357 0 -1.84152 -0.0841518 0.943527 2e-06 -2.57593 -0.157593 0.892008 4e-06 -3.18566 -0.218566 0.828295 6e-06 -3.67318 -0.267318 0.754831 8e-06 -4.04286 -0.304286 0.673974 1e-05 -4.30075 -0.330075 0.587959 1.2e-05 -4.4542 -0.34542 0.498875 1.4e-05 -4.51168 -0.351168 0.408642 1.6e-05 -4.48243 -0.348243 0.318993 1.8e-05 -4.37627 -0.337627 0.231468 2e-05 -4.20334 -0.320334 0.147401 2.2e-05 -3.97387 -0.297387 0.0679236 2.4e-05 -3.69803 -0.269803 -0.00603705 2.6e-05 -3.38571 -0.238571 -0.0737512 2.8e-05 -3.04639 -0.204639 -0.134679 3e-05 -2.68903 -0.168903 -0.18846 3.2e-05

0 0, 00064 0, 000002

1 (Euler)

10.2. Solu iones

-2.32194 -0.132194 -0.234898 3.4e-05 -1.95271 -0.0952713 -0.273953 3.6e-05 -1.58818 -0.0588179 -0.305716 3.8e-05 -1.23434 -0.0234341 -0.330403 4e-05 -0.896374 0.0103626 -0.34833 4.2e-05 -0.57861 0.042139 -0.359903 4.4e-05 -0.28456 0.071544 -0.365594 4.6e-05 -0.0169341 0.0983066 -0.365933 4.8e-05 0.22232 0.122232 -0.361486 5e-05 0.43197 0.143197 -0.352847 5.2e-05 0.611443 0.161144 -0.340618 5.4e-05 0.760769 0.176077 -0.325403 5.6e-05 0.88051 0.188051 -0.307792 5.8e-05 0.971699 0.19717 -0.288358 6e-05 1.03577 0.203577 -0.267643 6.2e-05 1.07447 0.207447 -0.246154 6.4e-05 1.08984 0.208984 -0.224357 6.6e-05 1.08411 0.208411 -0.202675 6.8e-05 1.05963 0.205963 -0.181482 7e-05 1.01885 0.201885 -0.161105 7.2e-05 0.964243 0.196424 -0.14182 7.4e-05 0.898271 0.189827 -0.123855 7.6e-05 0.823327 0.182333 -0.107388 7.8e-05 0.74171 0.174171 -0.0925541 8e-05 0.655593 0.165559 -0.0794422 8.2e-05 0.566995 0.1567 -0.0681023 8.4e-05 0.477766 0.147777 -0.058547 8.6e-05 0.389565 0.138956 -0.0507557 8.8e-05 0.303858 0.130386 -0.0446785 9e-05 0.221907 0.122191 -0.0402404 9.2e-05 0.144775 0.114477 -0.0373449 9.4e-05 0.0733211 0.107332 -0.0358785 9.6e-05 0.00821392 0.100821 -0.0357142 9.8e-05 -0.0500642 0.0949936 -0.0367155 0.0001 -0.101204 0.0898796 -0.0387396 0.000102 -0.145058 0.0854942 -0.0416407 0.000104 -0.181622 0.0818378 -0.0452732 0.000106 -0.211026 0.0788974 -0.0494937 0.000108 -0.233511 0.0766489 -0.0541639 0.00011 -0.249417 0.0750583 -0.0591522 0.000112 -0.259165 0.0740835 -0.0643355 0.000114 -0.263241 0.0736759 -0.0696004 0.000116 -0.262179 0.0737821 -0.0748439 0.000118 -0.256549 0.0743451 -0.0799749 0.00012 -0.246941 0.0753059 -0.0849137 0.000122 -0.233953 0.0766047 -0.0895928 0.000124 -0.218179 0.0781821 -0.0939564 0.000126 -0.200199 0.0799801 -0.0979603 0.000128 -0.18057 0.081943 -0.101572 0.00013 -0.15982 0.084018 -0.104768 0.000132 -0.138439 0.0861561 -0.107537 0.000134 -0.116877 0.0883123 -0.109874 0.000136 -0.0955378 0.0904462 -0.111785 0.000138 -0.0747791 0.0925221 -0.113281 0.00014

10. Cir uito RLC paralelo.

-0.0549092 0.0945091 -0.114379 0.000142 -0.0361877 0.0963812 -0.115103 0.000144 -0.0188259 0.0981174 -0.115479 0.000146 -0.00298807 0.0997012 -0.115539 0.000148 0.0112062 0.101121 -0.115315 0.00015 0.0236795 0.102368 -0.114841 0.000152 0.0343936 0.103439 -0.114153 0.000154 0.0433456 0.104335 -0.113287 0.000156 0.0505643 0.105056 -0.112275 0.000158 0.0561068 0.105611 -0.111153 0.00016 0.0600534 0.106005 -0.109952 0.000162 0.0625049 0.10625 -0.108702 0.000164 0.0635775 0.106358 -0.10743 0.000166 0.0633999 0.10634 -0.106162 0.000168 0.0621092 0.106211 -0.10492 0.00017 0.0598476 0.105985 -0.103723 0.000172 0.0567597 0.105676 -0.102588 0.000174 0.0529891 0.105299 -0.101528 0.000176 0.0486762 0.104868 -0.100555 0.000178 0.0439562 0.104396 -0.0996756 0.00018 0.038957 0.103896 -0.0988965 0.000182 0.0337977 0.10338 -0.0982205 0.000184 0.0285877 0.102859 -0.0976488 0.000186 0.0234254 0.102343 -0.0971803 0.000188 0.0183979 0.10184 -0.0968123 0.00019 0.0135806 0.101358 -0.0965407 0.000192 0.00903684 0.100904 -0.09636 0.000194 0.00481857 0.100482 -0.0962636 0.000196 0.000966203 0.100097 -0.0962443 0.000198 -0.00249066 0.0997509 -0.0962941 0.0002 -0.00553267 0.0994467 -0.0964047 0.000202 -0.00814995 0.099185 -0.0965677 0.000204 -0.0103413 0.0989659 -0.0967745 0.000206 -0.0121131 0.0987887 -0.0970168 0.000208 -0.0134789 0.0986521 -0.0972864 0.00021 -0.0144576 0.0985542 -0.0975755 0.000212 -0.0150732 0.0984927 -0.097877 0.000214 -0.0153538 0.0984646 -0.0981841 0.000216 -0.0153301 0.098467 -0.0984907 0.000218 -0.0150352 0.0984965 -0.0987914 0.00022 -0.0145034 0.0985497 -0.0990815 0.000222 -0.0137696 0.098623 -0.0993568 0.000224 -0.0128685 0.0987131 -0.0996142 0.000226 -0.0118342 0.0988166 -0.0998509 0.000228 -0.0106994 0.0989301 -0.100065 0.00023 -0.00949508 0.0990505 -0.100255 0.000232 -0.00825026 0.099175 -0.10042 0.000234 -0.00699148 0.0993009 -0.10056 0.000236 -0.00574273 0.0994257 -0.100674 0.000238 -0.00452523 0.0995475 -0.100765 0.00024 -0.00335736 0.0996643 -0.100832 0.000242 -0.00225467 0.0997745 -0.100877 0.000244 -0.00122986 0.099877 -0.100902 0.000246 -0.000292892 0.0999707 -0.100908 0.000248

10.2. Solu iones

0.000548917 0.100055 -0.100897 0.00025 0.00129073 0.100129 -0.100871 0.000252 0.00193001 0.100193 -0.100832 0.000254 0.00246634 0.100247 -0.100783 0.000256 0.00290116 0.10029 -0.100725 0.000258 0.00323759 0.100324 -0.10066 0.00026 0.00348015 0.100348 -0.100591 0.000262 0.00363458 0.100363 -0.100518 0.000264 0.00370756 0.100371 -0.100444 0.000266 0.00370652 0.100371 -0.10037 0.000268 0.0036394 0.100364 -0.100297 0.00027 0.00351448 0.100351 -0.100227 0.000272 0.00334019 0.100334 -0.10016 0.000274 0.00312492 0.100312 -0.100097 0.000276 0.00287692 0.100288 -0.10004 0.000278 0.00260412 0.10026 -0.0999876 0.00028 0.00231404 0.100231 -0.0999413 0.000282 0.00201372 0.100201 -0.0999011 0.000284 0.00170962 0.100171 -0.0998669 0.000286 0.00140757 0.100141 -0.0998387 0.000288 0.00111275 0.100111 -0.0998165 0.00029 0.000829643 0.100083 -0.0997999 0.000292 0.000562057 0.100056 -0.0997886 0.000294 0.000313104 0.100031 -0.0997824 0.000296 8.52329e-05 0.100009 -0.0997807 0.000298 -0.000119745 0.099988 -0.099783 0.0003 -0.000300623 0.0999699 -0.0997891 0.000302 -0.000456753 0.0999543 -0.0997982 0.000304 -0.000587998 0.0999412 -0.09981 0.000306 -0.000694681 0.0999305 -0.0998238 0.000308 -0.000777529 0.0999222 -0.0998394 0.00031 -0.000837616 0.0999162 -0.0998562 0.000312 -0.000876308 0.0999124 -0.0998737 0.000314 -0.000895206 0.0999105 -0.0998916 0.000316 -0.000896093 0.0999104 -0.0999095 0.000318 -0.000880883 0.0999119 -0.0999271 0.00032 -0.000851573 0.0999148 -0.0999442 0.000322 -0.000810197 0.099919 -0.0999604 0.000324 -0.000758786 0.0999241 -0.0999755 0.000326 -0.000699334 0.0999301 -0.0999895 0.000327999 -0.000633763 0.0999366 -0.100002 0.000329999 -0.000563901 0.0999436 -0.100013 0.000331999 -0.000491454 0.0999509 -0.100023 0.000333999 -0.000417993 0.0999582 -0.100032 0.000335999 -0.000344939 0.0999655 -0.100039 0.000337999 -0.000273553 0.0999726 -0.100044 0.000339999 -0.00020493 0.0999795 -0.100048 0.000341999 -0.000140001 0.099986 -0.100051 0.000343999 -7.95275e-05 0.099992 -0.100053 0.000345999 -2.41136e-05 0.0999976 -0.100053 0.000347999 2.57937e-05 0.100003 -0.100052 0.000349999 6.98932e-05 0.100007 -0.100051 0.000351999 0.00010802 0.100011 -0.100049 0.000353999 0.000140132 0.100014 -0.100046 0.000355999

10. Cir uito RLC paralelo.

0.000166302 0.100017 -0.100043 0.000357999 0.000186698 0.100019 -0.100039 0.000359999 0.000201575 0.10002 -0.100035 0.000361999 0.000211258 0.100021 -0.100031 0.000363999 0.000216131 0.100022 -0.100026 0.000365999 0.000216623 0.100022 -0.100022 0.000367999 0.000213194 0.100021 -0.100018 0.000369999 0.000206325 0.100021 -0.100014 0.000371999 0.000196508 0.10002 -0.10001 0.000373999 0.000184233 0.100018 -0.100006 0.000375999 0.000169984 0.100017 -0.100003 0.000377999 0.000154226 0.100015 -0.0999997 0.000379999 0.000137402 0.100014 -0.0999969 0.000381999 0.000119928 0.100012 -0.0999945 0.000383999 0.000102184 0.10001 -0.0999925 0.000385999 8.45161e-05 0.100008 -0.0999908 0.000387999 6.72323e-05 0.100007 -0.0999894 0.000389999 5.05997e-05 0.100005 -0.0999884 0.000391999 3.48457e-05 0.100003 -0.0999877 0.000393999 2.01573e-05 0.100002 -0.0999873 0.000395999 6.68271e-06 0.100001 -0.0999872 0.000397999 -5.4675e-06 0.0999995 -0.0999873 0.000399999 -1.62183e-05 0.0999984 -0.0999876 0.000401999 -2.55275e-05 0.0999974 -0.0999881 0.000403999 -3.33835e-05 0.0999967 -0.0999888 0.000405999 -3.98017e-05 0.099996 -0.0999896 0.000407999 -4.48215e-05 0.0999955 -0.0999905 0.000409999 -4.8503e-05 0.0999951 -0.0999915 0.000411999 -5.0924e-05 0.0999949 -0.0999925 0.000413999 -5.21762e-05 0.0999948 -0.0999935 0.000415999 -5.23625e-05 0.0999948 -0.0999946 0.000417999 -5.15938e-05 0.0999948 -0.0999956 0.000419999 -4.99862e-05 0.099995 -0.0999966 0.000421999 -4.76582e-05 0.0999952 -0.0999976 0.000423999 -4.47286e-05 0.0999955 -0.0999985 0.000425999 -4.13142e-05 0.0999959 -0.0999993 0.000427999 -3.75278e-05 0.0999962 -0.1 0.000429999 -3.3477e-05 0.0999967 -0.100001 0.000431999 -2.92624e-05 0.0999971 -0.100001 0.000433999 -2.49768e-05 0.0999975 -0.100002 0.000435999 -2.07043e-05 0.0999979 -0.100002 0.000437999 -1.65199e-05 0.0999983 -0.100003 0.000439999 -1.24889e-05 0.0999988 -0.100003 0.000441999 -8.6667e-06 0.0999991 -0.100003 0.000443999 -5.09928e-06 0.0999995 -0.100003 0.000445999 -1.82303e-06 0.0999998 -0.100003 0.000447999 1.13476e-06 0.1 -0.100003 0.000449999 3.75537e-06 0.1 -0.100003 0.000451999 6.02815e-06 0.100001 -0.100003 0.000453999 7.94976e-06 0.100001 -0.100003 0.000455999 9.52353e-06 0.100001 -0.100003 0.000457999 1.07586e-05 0.100001 -0.100002 0.000459999 1.16693e-05 0.100001 -0.100002 0.000461999 1.2274e-05 0.100001 -0.100002 0.000463999

10.2. Solu iones

1.25947e-05 0.100001 -0.100002 0.000465999 1.26561e-05 0.100001 -0.100001 0.000467999 1.2485e-05 0.100001 -0.100001 0.000469999 1.21093e-05 0.100001 -0.100001 0.000471999 1.15575e-05 0.100001 -0.100001 0.000473998 1.08585e-05 0.100001 -0.1 0.000475998 1.00405e-05 0.100001 -0.1 0.000477998 9.13089e-06 0.100001 -0.1 0.000479998 8.15565e-06 0.100001 -0.0999998 0.000481998 7.13926e-06 0.100001 -0.0999997 0.000483998 6.10428e-06 0.100001 -0.0999996 0.000485998 5.07119e-06 0.100001 -0.0999995 0.000487998 4.05823e-06 0.1 -0.0999994 0.000489998 3.08133e-06 0.1 -0.0999993 0.000491998 2.15408e-06 0.1 -0.0999993 0.000493998 1.28771e-06 0.1 -0.0999993 0.000495998 4.91166e-07 0.1 -0.0999993 0.000497998 -2.28802e-07 0.1 -0.0999993 0.000499998 -8.67544e-07 0.0999999 -0.0999993 0.000501998 -1.42236e-06 0.0999999 -0.0999993 0.000503998 -1.89233e-06 0.0999998 -0.0999993 0.000505998 -2.27815e-06 0.0999998 -0.0999994 0.000507999 -2.58196e-06 0.0999997 -0.0999994 0.000509999 -2.8071e-06 0.0999997 -0.0999995 0.000511999 -2.958e-06 0.0999997 -0.0999996 0.000513999 -3.03991e-06 0.0999997 -0.0999996 0.000515999 -3.05876e-06 0.0999997 -0.0999997 0.000517999 -3.02097e-06 0.0999997 -0.0999997 0.000519999 -2.93328e-06 0.0999997 -0.0999998 0.000521999 -2.80261e-06 0.0999997 -0.0999999 0.000523999 -2.63589e-06 0.0999997 -0.0999999 0.000525999 -2.43996e-06 0.0999998 -0.1 0.000527999 -2.22146e-06 0.0999998 -0.1 0.000529999 -1.9867e-06 0.0999998 -0.1 0.000531999 -1.74161e-06 0.0999998 -0.1 0.000533999 -1.49168e-06 0.0999999 -0.1 0.000535999 -1.2419e-06 0.0999999 -0.1 0.000537999 -9.96699e-07 0.0999999 -0.1 0.000539999 -7.59972e-07 0.0999999 -0.1 0.000541999 -5.35037e-07 0.0999999 -0.1 0.000543999 -3.24649e-07 0.1 -0.1 0.000545999 -1.31005e-07 0.1 -0.1 0.000547999 4.42307e-08 0.1 -0.1 0.000549999 1.99901e-07 0.1 -0.1 0.000551999 3.35324e-07 0.1 -0.1 0.000553999 4.50248e-07 0.1 -0.1 0.000555999 5.44819e-07 0.1 -0.1 0.000557999 6.19529e-07 0.1 -0.1 0.000559999 6.75171e-07 0.1 -0.1 0.000561999 7.12795e-07 0.1 -0.1 0.000563999 7.33659e-07 0.1 -0.1 0.000565999 7.39186e-07 0.1 -0.1 0.000567999 7.30922e-07 0.1 -0.1 0.000569999 7.10491e-07 0.1 -0.1 0.000571999

10. Cir uito RLC paralelo.

6.79562e-07 0.1 -0.1 0.000573999 6.39811e-07 0.1 -0.1 0.000575999 5.92894e-07 0.1 -0.1 0.000577999 5.40417e-07 0.1 -0.1 0.000579999 4.83912e-07 0.1 -0.1 0.000581999 4.2482e-07 0.1 -0.1 0.000583999 3.64473e-07 0.1 -0.1 0.000585999 3.04083e-07 0.1 -0.1 0.000587999 2.44733e-07 0.1 -0.1 0.000589999 1.87373e-07 0.1 -0.1 0.000591999 1.32812e-07 0.1 -0.1 0.000593999 8.1725e-08 0.1 -0.1 0.000595999 3.46525e-08 0.1 -0.1 0.0006

set terminal png set output ' /home/ ayose / Programa ion /AVALON/debug / s r / o l e i o n / G r a f i o s / o l e i o n p r o b l e m a s /10/ e j e m p l o 0 1 0 _ g r af i a . png '

using 4 : 2 t i t l e ' I R e s i s t e n i a e n t r e nodos 1 , 0 ' with l i n e s , ' /home

/ ayose / Programa ion /AVALON/debug / s r / o l e i o n / G r a f i o s / o l e i o n p r o b l e m a s /10/ ejemplo010_x_trans . data ' using 4 : 3 t i t l e ' I de Bobina e n t r e nodos 1 , 0 ' with l i n e s

Grรก o de salida.

10.2. Solu iones

Ve谩mos por separado la tensi贸n del nudo 1,y las intensidades de la resisten ia y bobina. Podr铆amos obtener la intensidad del ondensador indi ando al programa que este es e ua i贸n adi ional.

10. Cir uito RLC paralelo.

Capítulo 11 Cir uito RLC paralelo sin ex ita ión.

Cir uitos de segundo orden, RLC paralelo on ondi iones ini iales. 1

11.1.

Datos Generales.

Ar hivo *.sp ∗ SPICE i r u i t <ejemplo011> from XCir uit v3 . 6 rev 135

2 1 0 1 1 0 0 0 ,000002 3 1 0 2 1 0 0 0 ,0001 1 1 0 2 1 0 0 10 . end Tipo de análisis realizado Análisis esta ionario Análisis transitorio

⊠ ⊠

Datos generales del ir uito Elementos del Cto: 3 EA: 0 Nodos: 1 A2: 2 No nulos: 7 Densidad: 0.777778 Dispersion: 0.2222222222

Los valores dados al ir uito son: Elemento Resisten ia Bobina Condensador

Magnitud 10 Ω 0, 0001 H 2 · 10−6 F

Condi iones Ini iales V nodo 1 I Resisten ia entre nodos 0, 1 I Bobina entre nodos 1, 0 89

Valor 0 0 0, 1

11. Cir uito RLC paralelo sin ex ita i贸n.

Matriz T. row 0: (0, 0 + 2e-06 i) (1, 1) (2, 1) row 1: (0, 1) (1, -0 - 0.0001 i) row 2: (0, 1) (2, -10)

11.2.

11.2.1.

Solu iones

Primer an谩lisis Tiempo Ini ial Tiempo Final Paso de Tiempo Theta

Esta ionario Resultados sistema esta ionario: Tensi贸n en nodo 1: 0 I de Bobina entre nodos 1, 0: 0 I Resisten ia entre nodos 1, 0: 0

Transitorio -0.0892857 0.0982143 -0.00892857 0 -0.167411 0.0948661 -0.0167411 2e-06 -0.234176 0.0901826 -0.0234176 4e-06 -0.289606 0.0843904 -0.0289606 6e-06 -0.333925 0.0777119 -0.0333925 8e-06 -0.367533 0.0703613 -0.0367533 1e-05 -0.390977 0.0625417 -0.0390977 1.2e-05 -0.404927 0.0544432 -0.0404927 1.4e-05 -0.410152 0.0462401 -0.0410152 1.6e-05 -0.407493 0.0380903 -0.0407493 1.8e-05 -0.397843 0.0301334 -0.0397843 2e-05 -0.382121 0.022491 -0.0382121 2.2e-05 -0.361261 0.0152658 -0.0361261 2.4e-05 -0.336185 0.00854209 -0.0336185 2.6e-05 -0.307792 0.00238625 -0.0307792 2.8e-05 -0.276945 -0.00315264 -0.0276945 3e-05 -0.244457 -0.00804178 -0.0244457 3.2e-05 -0.211085 -0.0122635 -0.0211085 3.4e-05 -0.177519 -0.0158139 -0.0177519 3.6e-05 -0.14438 -0.0187015 -0.014438 3.8e-05 -0.112213 -0.0209457 -0.0112213 4e-05 -0.0814885 -0.0225755 -0.00814885 4.2e-05 -0.0526009 -0.0236275 -0.00526009 4.4e-05 -0.0258691 -0.0241449 -0.00258691 4.6e-05

0 0, 0004 0, 000002

1 (Euler)

11.2. Solu iones

-0.00153946 -0.0241757 -0.000153946 4.8e-05 0.0202109 -0.0237715 0.00202109 5e-05 0.03927 -0.0229861 0.003927 5.2e-05 0.0555858 -0.0218744 0.00555858 5.4e-05 0.0691608 -0.0204911 0.00691608 5.6e-05 0.0800464 -0.0188902 0.00800464 5.8e-05 0.0883363 -0.0171235 0.00883363 6e-05 0.0941605 -0.0152403 0.00941605 6.2e-05 0.0976792 -0.0132867 0.00976792 6.4e-05 0.0990767 -0.0113052 0.00990767 6.6e-05 0.0985553 -0.00933405 0.00985553 6.8e-05 0.0963297 -0.00740746 0.00963297 7e-05 0.0926225 -0.00555501 0.00926225 7.2e-05 0.0876585 -0.00380184 0.00876585 7.4e-05 0.081661 -0.00216862 0.0081661 7.6e-05 0.0748479 -0.000671659 0.00748479 7.8e-05 0.0674282 0.000676904 0.00674282 8e-05 0.0595993 0.00186889 0.00595993 8.2e-05 0.051545 0.00289979 0.0051545 8.4e-05 0.0434333 0.00376846 0.00434333 8.6e-05 0.035415 0.00447676 0.0035415 8.8e-05 0.0276234 0.00502922 0.00276234 9e-05 0.0201734 0.00543269 0.00201734 9.2e-05 0.0131613 0.00569592 0.00131613 9.4e-05 0.00666556 0.00582923 0.000666556 9.6e-05 0.00074672 0.00584417 7.4672e-05 9.8e-05 -0.00455129 0.00575314 -0.000455129 0.0001 -0.00920038 0.00556913 -0.000920038 0.000102 -0.0131871 0.00530539 -0.00131871 0.000104 -0.0165111 0.00497517 -0.00165111 0.000106 -0.0191842 0.00459148 -0.00191842 0.000108 -0.0212283 0.00416692 -0.00212283 0.00011 -0.0226743 0.00371343 -0.00226743 0.000112 -0.0235605 0.00324222 -0.00235605 0.000114 -0.023931 0.0027636 -0.0023931 0.000116 -0.0238344 0.00228692 -0.00238344 0.000118 -0.0233226 0.00182046 -0.00233226 0.00012 -0.0224492 0.00137148 -0.00224492 0.000122 -0.0212685 0.00094611 -0.00212685 0.000124 -0.0198344 0.000549421 -0.00198344 0.000126 -0.0181999 0.000185423 -0.00181999 0.000128 -0.0164154 -0.000142886 -0.00164154 0.00013 -0.0145291 -0.000433467 -0.00145291 0.000132 -0.0125854 -0.000685174 -0.00125854 0.000134 -0.0106252 -0.000897678 -0.00106252 0.000136 -0.00868526 -0.00107138 -0.000868526 0.000138 -0.0067981 -0.00120734 -0.00067981 0.00014 -0.00499175 -0.00130718 -0.000499175 0.000142 -0.00328979 -0.00137298 -0.000328979 0.000144 -0.00171144 -0.0014072 -0.000171144 0.000146 -0.000271643 -0.00141264 -2.71643e-05 0.000148 0.00101875 -0.00139226 0.000101875 0.00015 0.00215269 -0.00134921 0.000215269 0.000152 0.00312669 -0.00128667 0.000312669 0.000154

11. Cir uito RLC paralelo sin ex ita i贸n.

0.00394051 -0.00120786 0.000394051 0.000156 0.00459676 -0.00111593 0.000459676 0.000158 0.00510061 -0.00101392 0.000510061 0.00016 0.0054594 -0.000904729 0.00054594 0.000162 0.00568226 -0.000791084 0.000568226 0.000164 0.00577977 -0.000675489 0.000577977 0.000166 0.00576363 -0.000560216 0.000576363 0.000168 0.00564629 -0.00044729 0.000564629 0.00017 0.00544069 -0.000338476 0.000544069 0.000172 0.00515997 -0.000235277 0.000515997 0.000174 0.00481719 -0.000138933 0.000481719 0.000176 0.00442511 -5.04309e-05 0.000442511 0.000178 0.00399602 2.94894e-05 0.000399602 0.00018 0.00354154 0.00010032 0.000354154 0.000182 0.00307252 0.000161771 0.000307252 0.000184 0.00259888 0.000213748 0.000259888 0.000186 0.00212958 0.00025634 0.000212958 0.000188 0.00167254 0.000289791 0.000167254 0.00019 0.0012346 0.000314483 0.00012346 0.000192 0.000821531 0.000330913 8.21531e-05 0.000194 0.000438051 0.000339674 4.38051e-05 0.000196 8.78367e-05 0.000341431 8.78367e-06 0.000198 -0.000226424 0.000336903 -2.26424e-05 0.0002 -0.00050297 0.000326843 -5.0297e-05 0.000202 -0.000740905 0.000312025 -7.40905e-05 0.000204 -0.000940116 0.000293223 -9.40116e-05 0.000206 -0.0011012 0.000271199 -0.00011012 0.000208 -0.00122535 0.000246692 -0.000122535 0.00021 -0.00131432 0.000220405 -0.000131432 0.000212 -0.0013703 0.000193 -0.00013703 0.000214 -0.0013958 0.000165084 -0.00013958 0.000216 -0.00139364 0.000137211 -0.000139364 0.000218 -0.00136684 0.000109874 -0.000136684 0.00022 -0.00131849 8.35041e-05 -0.000131849 0.000222 -0.00125178 5.84685e-05 -0.000125178 0.000224 -0.00116987 3.50712e-05 -0.000116987 0.000226 -0.00107584 1.35545e-05 -0.000107584 0.000228 -0.00097267 -5.89892e-06 -9.7267e-05 0.00023 -0.000863189 -2.31627e-05 -8.63189e-05 0.000232 -0.000750023 -3.81632e-05 -7.50023e-05 0.000234 -0.000635589 -5.0875e-05 -6.35589e-05 0.000236 -0.000522066 -6.13163e-05 -5.22066e-05 0.000238 -0.000411384 -6.9544e-05 -4.11384e-05 0.00024 -0.000305214 -7.56483e-05 -3.05214e-05 0.000242 -0.00020497 -7.97476e-05 -2.0497e-05 0.000244 -0.000111805 -8.19838e-05 -1.11805e-05 0.000246 -2.66265e-05 -8.25163e-05 -2.66265e-06 0.000248 4.99016e-05 -8.15183e-05 4.99016e-06 0.00025 0.000117339 -7.91715e-05 1.17339e-05 0.000252 0.000175456 -7.56624e-05 1.75456e-05 0.000254 0.000224213 -7.11781e-05 2.24213e-05 0.000256 0.000263742 -6.59033e-05 2.63742e-05 0.000258 0.000294326 -6.00167e-05 2.94326e-05 0.00026 0.000316377 -5.36892e-05 3.16377e-05 0.000262

11.2. Solu iones

0.000330417 -4.70809e-05 3.30417e-05 0.000264 0.000337051 -4.03398e-05 3.37051e-05 0.000266 0.000336956 -3.36007e-05 3.36956e-05 0.000268 0.000330855 -2.69836e-05 3.30855e-05 0.00027 0.000319498 -2.05937e-05 3.19498e-05 0.000272 0.000303654 -1.45206e-05 3.03654e-05 0.000274 0.000284084 -8.8389e-06 2.84084e-05 0.000276 0.000261538 -3.60813e-06 2.61538e-05 0.000278 0.000236738 1.12663e-06 2.36738e-05 0.00028 0.000210367 5.33397e-06 2.10367e-05 0.000282 0.000183065 8.99528e-06 1.83065e-05 0.000284 0.00015542 1.21037e-05 1.5542e-05 0.000286 0.000127961 1.46629e-05 1.27961e-05 0.000288 0.000101159 1.66861e-05 1.01159e-05 0.00029 7.54221e-05 1.81945e-05 7.54221e-06 0.000292 5.10961e-05 1.92164e-05 5.10961e-06 0.000294 2.8464e-05 1.97857e-05 2.8464e-06 0.000296 7.74844e-06 1.99407e-05 7.74844e-07 0.000298 -1.08859e-05 1.9723e-05 -1.08859e-06 0.0003 -2.73294e-05 1.91764e-05 -2.73294e-06 0.000302 -4.1523e-05 1.83459e-05 -4.1523e-06 0.000304 -5.34544e-05 1.72768e-05 -5.34544e-06 0.000306 -6.31529e-05 1.60138e-05 -6.31529e-06 0.000308 -7.06845e-05 1.46001e-05 -7.06845e-06 0.00031 -7.61469e-05 1.30771e-05 -7.61469e-06 0.000312 -7.96644e-05 1.14839e-05 -7.96644e-06 0.000314 -8.13823e-05 9.85621e-06 -8.13823e-06 0.000316 -8.1463e-05 8.22695e-06 -8.1463e-06 0.000318 -8.00803e-05 6.62534e-06 -8.00803e-06 0.00032 -7.74158e-05 5.07703e-06 -7.74158e-06 0.000322 -7.36543e-05 3.60394e-06 -7.36543e-06 0.000324 -6.89805e-05 2.22433e-06 -6.89805e-06 0.000326 -6.35758e-05 9.52816e-07 -6.35758e-06 0.000327999 -5.76148e-05 -1.9948e-07 -5.76148e-06 0.000329999 -5.12637e-05 -1.22475e-06 -5.12637e-06 0.000331999 -4.46776e-05 -2.11831e-06 -4.46776e-06 0.000333999 -3.79994e-05 -2.87829e-06 -3.79994e-06 0.000335999 -3.13581e-05 -3.50546e-06 -3.13581e-06 0.000337999 -2.48685e-05 -4.00283e-06 -2.48685e-06 0.000339999 -1.863e-05 -4.37543e-06 -1.863e-06 0.000341999 -1.27273e-05 -4.62997e-06 -1.27273e-06 0.000343999 -7.22977e-06 -4.77457e-06 -7.22977e-07 0.000345999 -2.19215e-06 -4.81841e-06 -2.19215e-07 0.000347999 2.34488e-06 -4.77151e-06 2.34488e-07 0.000349999 6.35392e-06 -4.64444e-06 6.35392e-07 0.000351999 9.81996e-06 -4.44804e-06 9.81996e-07 0.000353999 1.27393e-05 -4.19325e-06 1.27393e-06 0.000355999 1.51183e-05 -3.89088e-06 1.51183e-06 0.000357999 1.69725e-05 -3.55143e-06 1.69725e-06 0.000359999 1.8325e-05 -3.18493e-06 1.8325e-06 0.000361999 1.92053e-05 -2.80083e-06 1.92053e-06 0.000363999 1.96483e-05 -2.40786e-06 1.96483e-06 0.000365999 1.9693e-05 -2.014e-06 1.9693e-06 0.000367999 1.93813e-05 -1.62638e-06 1.93813e-06 0.000369999

11. Cir uito RLC paralelo sin ex ita i贸n.

1.87568e-05 -1.25124e-06 1.87568e-06 0.000371999 1.78643e-05 -8.93956e-07 1.78643e-06 0.000373999 1.67485e-05 -5.58986e-07 1.67485e-06 0.000375999 1.54531e-05 -2.49924e-07 1.54531e-06 0.000377999 1.40205e-05 3.04866e-08 1.40205e-06 0.000379999 1.24911e-05 2.80309e-07 1.24911e-06 0.000381999 1.09025e-05 4.98359e-07 1.09025e-06 0.000383999 9.28942e-06 6.84148e-07 9.28942e-07 0.000385999 7.68328e-06 8.37814e-07 7.68328e-07 0.000387999 6.11203e-06 9.60054e-07 6.11203e-07 0.000389999 4.59997e-06 1.05205e-06 4.59997e-07 0.000391999 3.16779e-06 1.11541e-06 3.16779e-07 0.000393999 1.83248e-06 1.15206e-06 1.83248e-07 0.000395999 6.07519e-07 1.16421e-06 6.07519e-08 0.0004

set terminal png set output ' /home/ ayose / Programa ion /AVALON/debug / s r / o l e i o n / G r a f i o s / o l e i o n p r o b l e m a s /11/ e j e m p l o 0 1 1 _ g r af i a . png '

using 4 : 2 t i t l e ' I de Bobina e n t r e nodos 1 , 0 ' with l i n e s , ' /home/ ayose / Programa ion /AVALON/debug / s r / o l e i o n / G r a f i o s / o l e i o n p r o b l e m a s /11/ ejemplo011_x_trans . data ' using 4 : 3 t i t l e ' I R e s i s t e n i a e n t r e nodos 1 , 0 ' with l i n e s

Gr谩 o de salida.

11.2. Solu iones

Ve谩mos por separado la tensi贸n del nudo 1, la intensidad en la bobina y la de la resisten ia.

11. Cir uito RLC paralelo sin ex ita i贸n.

Capítulo 12 Cir uito RLC paralelo sin ex ita ión on EA.

Ya que hasta el momento no se había pedido al programa añadir más variables que las que al ula por defe to pro ederemos a añadir al problema anterior el ál ulo de la intensidad del ondensador a través de una e ua ión adi ional EA. Para ello simplemente, una vez argado el ir uito le indi amos en la tabla MDG (Matriz de Datos Generales) que el ondensador tiene una EA poniendo un 1 en la olumna orrespondiente a este tipo de valores. Re ordemos que el ondensador se ensambla en el sistema omo elemento del tipo A1, lo que se tradu e en que su intensidad no es al ulada por defe to, a no ser que se le indique al programa que pro eda de otra forma. Tomando el ejemplo anterior: 1

12.1.

Datos Generales.

Ar hivo *.sp ∗ SPICE i r u i t <ejemplo011> from XCir uit v3 . 6 rev 135

2 1 1 1 1 0 0 0 ,000002 3 1 0 2 1 0 0 0 ,0001 1 1 0 2 1 0 0 10 . end Tipo de análisis realizado Análisis esta ionario Análisis transitorio

Datos generales del ir uito Elementos del Cto: 3 EA: 1 Nodos: 1 97

⊠ ⊠

12. Cir uito RLC paralelo sin ex ita ión on EA.

A2: 2 No nulos: 9 Densidad: 0.5625 Dispersion: 0.4375

Los valores dados al ir uito son: Elemento Resisten ia Bobina Condensador

Magnitud 10 Ω 0, 0001 H 2 · 10−6 F

Condi iones Ini iales V nodo 1 I Resisten ia entre nodos 0, 1 I Bobina entre nodos 1, 0 I de Condensador 1, 0

Matriz T. row 0: (1, row 1: (0, row 2: (0, row 3: (0,

12.2.

12.2.1.

1) (2, 1) (3, 1) 1) (1, -0 - 0.0001 i) 1) (2, -10) 0 + 2e-06 i) (3, -1)

Solu iones

Primer análisis Tiempo Ini ial Tiempo Final Paso de Tiempo Theta

0 0, 0004 0, 000002

1 (Euler)

Esta ionario Resultados sistema esta ionario: Tensión en nodo 1: 0 I de Bobina entre nodos 1, 0: 0 I Resisten ia entre nodos 1, 0: 0 Intensidad de Condensador entre nodos 1, 0: 0

Transitorio -0.0892857 0.0982143 -0.00892857 -0.0892857 0 -0.167411 0.0948661 -0.0167411 -0.078125 2e-06 -0.234176 0.0901826 -0.0234176 -0.066765 4e-06 -0.289606 0.0843904 -0.0289606 -0.0554299 6e-06 -0.333925 0.0777119 -0.0333925 -0.0443194 8e-06 -0.367533 0.0703613 -0.0367533 -0.033608 1e-05 -0.390977 0.0625417 -0.0390977 -0.023444 1.2e-05 -0.404927 0.0544432 -0.0404927 -0.0139504 1.4e-05 -0.410152 0.0462401 -0.0410152 -0.00522491 1.6e-05

Valor 0 0 0, 1 0

12.2. Solu iones

-0.407493 0.0380903 -0.0407493 0.00265906 1.8e-05 -0.397843 0.0301334 -0.0397843 0.00965082 2e-05 -0.382121 0.022491 -0.0382121 0.0157211 2.2e-05 -0.361261 0.0152658 -0.0361261 0.0208603 2.4e-05 -0.336185 0.00854209 -0.0336185 0.0250764 2.6e-05 -0.307792 0.00238625 -0.0307792 0.0283929 2.8e-05 -0.276945 -0.00315264 -0.0276945 0.0308471 3e-05 -0.244457 -0.00804178 -0.0244457 0.0324875 3.2e-05 -0.211085 -0.0122635 -0.0211085 0.033372 3.4e-05 -0.177519 -0.0158139 -0.0177519 0.0335658 3.6e-05 -0.14438 -0.0187015 -0.014438 0.0331395 3.8e-05 -0.112213 -0.0209457 -0.0112213 0.032167 4e-05 -0.0814885 -0.0225755 -0.00814885 0.0307244 4.2e-05 -0.0526009 -0.0236275 -0.00526009 0.0288876 4.4e-05 -0.0258691 -0.0241449 -0.00258691 0.0267318 4.6e-05 -0.00153946 -0.0241757 -0.000153946 0.0243296 4.8e-05 0.0202109 -0.0237715 0.00202109 0.0217504 5e-05 0.03927 -0.0229861 0.003927 0.0190591 5.2e-05 0.0555858 -0.0218744 0.00555858 0.0163158 5.4e-05 0.0691608 -0.0204911 0.00691608 0.0135751 5.6e-05 0.0800464 -0.0188902 0.00800464 0.0108856 5.8e-05 0.0883363 -0.0171235 0.00883363 0.00828986 6e-05 0.0941605 -0.0152403 0.00941605 0.00582423 6.2e-05 0.0976792 -0.0132867 0.00976792 0.00351877 6.4e-05 0.0990767 -0.0113052 0.00990767 0.00139748 6.6e-05 0.0985553 -0.00933405 0.00985553 -0.000521475 6.8e-05 0.0963297 -0.00740746 0.00963297 -0.00222552 7e-05 0.0926225 -0.00555501 0.00926225 -0.00370724 7.2e-05 0.0876585 -0.00380184 0.00876585 -0.00496401 7.4e-05 0.081661 -0.00216862 0.0081661 -0.00599748 7.6e-05 0.0748479 -0.000671659 0.00748479 -0.00681313 7.8e-05 0.0674282 0.000676904 0.00674282 -0.00741972 8e-05 0.0595993 0.00186889 0.00595993 -0.00782882 8.2e-05 0.051545 0.00289979 0.0051545 -0.00805429 8.4e-05 0.0434333 0.00376846 0.00434333 -0.00811178 8.6e-05 0.035415 0.00447676 0.0035415 -0.00801826 8.8e-05 0.0276234 0.00502922 0.00276234 -0.00779157 9e-05 0.0201734 0.00543269 0.00201734 -0.00745003 9.2e-05 0.0131613 0.00569592 0.00131613 -0.00701205 9.4e-05 0.00666556 0.00582923 0.000666556 -0.00649579 9.6e-05 0.00074672 0.00584417 7.4672e-05 -0.00591884 9.8e-05 -0.00455129 0.00575314 -0.000455129 -0.00529801 0.0001 -0.00920038 0.00556913 -0.000920038 -0.00464909 0.000102 -0.0131871 0.00530539 -0.00131871 -0.00398668 0.000104 -0.0165111 0.00497517 -0.00165111 -0.00332406 0.000106 -0.0191842 0.00459148 -0.00191842 -0.00267307 0.000108 -0.0212283 0.00416692 -0.00212283 -0.00204409 0.00011 -0.0226743 0.00371343 -0.00226743 -0.001446 0.000112 -0.0235605 0.00324222 -0.00235605 -0.000886178 0.000114 -0.023931 0.0027636 -0.0023931 -0.000370507 0.000116 -0.0238344 0.00228692 -0.00238344 9.65285e-05 0.000118 -0.0233226 0.00182046 -0.00233226 0.000511801 0.00012 -0.0224492 0.00137148 -0.00224492 0.000873441 0.000122 -0.0212685 0.00094611 -0.00212685 0.00118074 0.000124

100

12. Cir uito RLC paralelo sin ex ita i贸n on EA.

-0.0198344 0.000549421 -0.00198344 0.00143402 0.000126 -0.0181999 0.000185423 -0.00181999 0.00163456 0.000128 -0.0164154 -0.000142886 -0.00164154 0.00178443 0.00013 -0.0145291 -0.000433467 -0.00145291 0.00188637 0.000132 -0.0125854 -0.000685174 -0.00125854 0.00194371 0.000134 -0.0106252 -0.000897678 -0.00106252 0.00196019 0.000136 -0.00868526 -0.00107138 -0.000868526 0.00193991 0.000138 -0.0067981 -0.00120734 -0.00067981 0.00188715 0.00014 -0.00499175 -0.00130718 -0.000499175 0.00180635 0.000142 -0.00328979 -0.00137298 -0.000328979 0.00170195 0.000144 -0.00171144 -0.0014072 -0.000171144 0.00157835 0.000146 -0.000271643 -0.00141264 -2.71643e-05 0.0014398 0.000148 0.00101875 -0.00139226 0.000101875 0.00129039 0.00015 0.00215269 -0.00134921 0.000215269 0.00113394 0.000152 0.00312669 -0.00128667 0.000312669 0.000974006 0.000154 0.00394051 -0.00120786 0.000394051 0.000813814 0.000156 0.00459676 -0.00111593 0.000459676 0.000656254 0.000158 0.00510061 -0.00101392 0.000510061 0.000503856 0.00016 0.0054594 -0.000904729 0.00054594 0.000358789 0.000162 0.00568226 -0.000791084 0.000568226 0.000222858 0.000164 0.00577977 -0.000675489 0.000577977 9.75113e-05 0.000166 0.00576363 -0.000560216 0.000576363 -1.61466e-05 0.000168 0.00564629 -0.00044729 0.000564629 -0.000117339 0.00017 0.00544069 -0.000338476 0.000544069 -0.000205593 0.000172 0.00515997 -0.000235277 0.000515997 -0.000280721 0.000174 0.00481719 -0.000138933 0.000481719 -0.000342786 0.000176 0.00442511 -5.04309e-05 0.000442511 -0.00039208 0.000178 0.00399602 2.94894e-05 0.000399602 -0.000429091 0.00018 0.00354154 0.00010032 0.000354154 -0.000454475 0.000182 0.00307252 0.000161771 0.000307252 -0.000469023 0.000184 0.00259888 0.000213748 0.000259888 -0.000473637 0.000186 0.00212958 0.00025634 0.000212958 -0.000469299 0.000188 0.00167254 0.000289791 0.000167254 -0.000457045 0.00019 0.0012346 0.000314483 0.00012346 -0.000437943 0.000192 0.000821531 0.000330913 8.21531e-05 -0.000413066 0.000194 0.000438051 0.000339674 4.38051e-05 -0.00038348 0.000196 8.78367e-05 0.000341431 8.78367e-06 -0.000350215 0.000198 -0.000226424 0.000336903 -2.26424e-05 -0.00031426 0.0002 -0.00050297 0.000326843 -5.0297e-05 -0.000276546 0.000202 -0.000740905 0.000312025 -7.40905e-05 -0.000237935 0.000204 -0.000940116 0.000293223 -9.40116e-05 -0.000199211 0.000206 -0.0011012 0.000271199 -0.00011012 -0.000161079 0.000208 -0.00122535 0.000246692 -0.000122535 -0.000124157 0.00021 -0.00131432 0.000220405 -0.000131432 -8.89729e-05 0.000212 -0.0013703 0.000193 -0.00013703 -5.597e-05 0.000214 -0.0013958 0.000165084 -0.00013958 -2.55037e-05 0.000216 -0.00139364 0.000137211 -0.000139364 2.15384e-06 0.000218 -0.00136684 0.000109874 -0.000136684 2.68096e-05 0.00022 -0.00131849 8.35041e-05 -0.000131849 4.83449e-05 0.000222 -0.00125178 5.84685e-05 -0.000125178 6.67096e-05 0.000224 -0.00116987 3.50712e-05 -0.000116987 8.19153e-05 0.000226 -0.00107584 1.35545e-05 -0.000107584 9.40291e-05 0.000228 -0.00097267 -5.89892e-06 -9.7267e-05 0.000103166 0.00023 -0.000863189 -2.31627e-05 -8.63189e-05 0.000109482 0.000232

12.2. Solu iones

-0.000750023 -3.81632e-05 -7.50023e-05 0.000113165 0.000234 -0.000635589 -5.0875e-05 -6.35589e-05 0.000114434 0.000236 -0.000522066 -6.13163e-05 -5.22066e-05 0.000113523 0.000238 -0.000411384 -6.9544e-05 -4.11384e-05 0.000110682 0.00024 -0.000305214 -7.56483e-05 -3.05214e-05 0.00010617 0.000242 -0.00020497 -7.97476e-05 -2.0497e-05 0.000100245 0.000244 -0.000111805 -8.19838e-05 -1.11805e-05 9.31643e-05 0.000246 -2.66265e-05 -8.25163e-05 -2.66265e-06 8.51789e-05 0.000248 4.99016e-05 -8.15183e-05 4.99016e-06 7.65281e-05 0.00025 0.000117339 -7.91715e-05 1.17339e-05 6.74376e-05 0.000252 0.000175456 -7.56624e-05 1.75456e-05 5.81168e-05 0.000254 0.000224213 -7.11781e-05 2.24213e-05 4.87568e-05 0.000256 0.000263742 -6.59033e-05 2.63742e-05 3.95291e-05 0.000258 0.000294326 -6.00167e-05 2.94326e-05 3.05842e-05 0.00026 0.000316377 -5.36892e-05 3.16377e-05 2.20515e-05 0.000262 0.000330417 -4.70809e-05 3.30417e-05 1.40392e-05 0.000264 0.000337051 -4.03398e-05 3.37051e-05 6.63471e-06 0.000266 0.000336956 -3.36007e-05 3.36956e-05 -9.49285e-08 0.000268 0.000330855 -2.69836e-05 3.30855e-05 -6.10184e-06 0.00027 0.000319498 -2.05937e-05 3.19498e-05 -1.13562e-05 0.000272 0.000303654 -1.45206e-05 3.03654e-05 -1.58448e-05 0.000274 0.000284084 -8.8389e-06 2.84084e-05 -1.95695e-05 0.000276 0.000261538 -3.60813e-06 2.61538e-05 -2.25457e-05 0.000278 0.000236738 1.12663e-06 2.36738e-05 -2.48004e-05 0.00028 0.000210367 5.33397e-06 2.10367e-05 -2.63707e-05 0.000282 0.000183065 8.99528e-06 1.83065e-05 -2.73018e-05 0.000284 0.00015542 1.21037e-05 1.5542e-05 -2.76457e-05 0.000286 0.000127961 1.46629e-05 1.27961e-05 -2.7459e-05 0.000288 0.000101159 1.66861e-05 1.01159e-05 -2.6802e-05 0.00029 7.54221e-05 1.81945e-05 7.54221e-06 -2.57367e-05 0.000292 5.10961e-05 1.92164e-05 5.10961e-06 -2.4326e-05 0.000294 2.8464e-05 1.97857e-05 2.8464e-06 -2.26321e-05 0.000296 7.74844e-06 1.99407e-05 7.74844e-07 -2.07155e-05 0.000298 -1.08859e-05 1.9723e-05 -1.08859e-06 -1.86344e-05 0.0003 -2.73294e-05 1.91764e-05 -2.73294e-06 -1.64434e-05 0.000302 -4.1523e-05 1.83459e-05 -4.1523e-06 -1.41936e-05 0.000304 -5.34544e-05 1.72768e-05 -5.34544e-06 -1.19314e-05 0.000306 -6.31529e-05 1.60138e-05 -6.31529e-06 -9.69849e-06 0.000308 -7.06845e-05 1.46001e-05 -7.06845e-06 -7.53163e-06 0.00031 -7.61469e-05 1.30771e-05 -7.61469e-06 -5.46245e-06 0.000312 -7.96644e-05 1.14839e-05 -7.96644e-06 -3.51742e-06 0.000314 -8.13823e-05 9.85621e-06 -8.13823e-06 -1.71798e-06 0.000316 -8.1463e-05 8.22695e-06 -8.1463e-06 -8.06504e-08 0.000318 -8.00803e-05 6.62534e-06 -8.00803e-06 1.38269e-06 0.00032 -7.74158e-05 5.07703e-06 -7.74158e-06 2.66455e-06 0.000322 -7.36543e-05 3.60394e-06 -7.36543e-06 3.76148e-06 0.000324 -6.89805e-05 2.22433e-06 -6.89805e-06 4.67372e-06 0.000326 -6.35758e-05 9.52816e-07 -6.35758e-06 5.40476e-06 0.000327999 -5.76148e-05 -1.9948e-07 -5.76148e-06 5.96096e-06 0.000329999 -5.12637e-05 -1.22475e-06 -5.12637e-06 6.35112e-06 0.000331999 -4.46776e-05 -2.11831e-06 -4.46776e-06 6.58607e-06 0.000333999 -3.79994e-05 -2.87829e-06 -3.79994e-06 6.67823e-06 0.000335999 -3.13581e-05 -3.50546e-06 -3.13581e-06 6.64127e-06 0.000337999 -2.48685e-05 -4.00283e-06 -2.48685e-06 6.48967e-06 0.000339999

101

102

12. Cir uito RLC paralelo sin ex ita i贸n on EA.

-1.863e-05 -4.37543e-06 -1.863e-06 6.23843e-06 0.000341999 -1.27273e-05 -4.62997e-06 -1.27273e-06 5.90271e-06 0.000343999 -7.22977e-06 -4.77457e-06 -7.22977e-07 5.49755e-06 0.000345999 -2.19215e-06 -4.81841e-06 -2.19215e-07 5.03763e-06 0.000347999 2.34488e-06 -4.77151e-06 2.34488e-07 4.53703e-06 0.000349999 6.35392e-06 -4.64444e-06 6.35392e-07 4.00904e-06 0.000351999 9.81996e-06 -4.44804e-06 9.81996e-07 3.46604e-06 0.000353999 1.27393e-05 -4.19325e-06 1.27393e-06 2.91932e-06 0.000355999 1.51183e-05 -3.89088e-06 1.51183e-06 2.37905e-06 0.000357999 1.69725e-05 -3.55143e-06 1.69725e-06 1.85418e-06 0.000359999 1.8325e-05 -3.18493e-06 1.8325e-06 1.35244e-06 0.000361999 1.92053e-05 -2.80083e-06 1.92053e-06 8.80303e-07 0.000363999 1.96483e-05 -2.40786e-06 1.96483e-06 4.43034e-07 0.000365999 1.9693e-05 -2.014e-06 1.9693e-06 4.47037e-08 0.000367999 1.93813e-05 -1.62638e-06 1.93813e-06 -3.11747e-07 0.000369999 1.87568e-05 -1.25124e-06 1.87568e-06 -6.24439e-07 0.000371999 1.78643e-05 -8.93956e-07 1.78643e-06 -8.92478e-07 0.000373999 1.67485e-05 -5.58986e-07 1.67485e-06 -1.11586e-06 0.000375999 1.54531e-05 -2.49924e-07 1.54531e-06 -1.29538e-06 0.000377999 1.40205e-05 3.04866e-08 1.40205e-06 -1.43254e-06 0.000379999 1.24911e-05 2.80309e-07 1.24911e-06 -1.52942e-06 0.000381999 1.09025e-05 4.98359e-07 1.09025e-06 -1.58861e-06 0.000383999 9.28942e-06 6.84148e-07 9.28942e-07 -1.61309e-06 0.000385999 7.68328e-06 8.37814e-07 7.68328e-07 -1.60614e-06 0.000387999 6.11203e-06 9.60054e-07 6.11203e-07 -1.57126e-06 0.000389999 4.59997e-06 1.05205e-06 4.59997e-07 -1.51205e-06 0.000391999 3.16779e-06 1.11541e-06 3.16779e-07 -1.43219e-06 0.000393999 1.83248e-06 1.15206e-06 1.83248e-07 -1.33531e-06 0.000395999 6.07519e-07 1.16421e-06 6.07519e-08 -1.22496e-06 0.0004

set terminal png set output ' /home/ ayose / Programa ion /AVALON/debug / s r / o l e i o n / G r a f i o s / o l e i o n p r o b l e m a s /12/ e j e m p l o 0 1 2 _ g r af i a . png '

using 5 : 2 t i t l e ' I de Bobina e n t r e nodos 1 , 0 ' with l i n e s , ' /home/

ayose / Programa ion /AVALON/debug / s r / o l e i o n / G r a f i o s / o l e i o n p r o b l e m a s /12/ ejemplo012_x_trans . data ' using 5 : 3 t i t l e ' I R e s i s t e n i a e n t r e nodos 1 , 0 ' with l i n e s , ' /home/ ayose / Programa ion /AVALON/debug / s r / o l e i o n / G r a f i o s / o l e i o n p r o b l e m a s /12/ ejemplo012_x_trans . data ' using 5 : 4 t i t l e ' I n t e n s i d a d de Condensador e n t r e nodos 1 , 0 ' with l i n e s

Gr谩 o de salida.

12.2. Solu iones

Veรกmos la nueva grรก a de la evolu iรณn temporal de la intensidad del ondensador

103

Capítulo 13 Cir uito on a oplamiento magnéti o simple.

Ahora pasaremos al análsis de ir uitos on elementos bipuertos o uatripolos, el primero que vamos a analizar será un ir uito on ex ita ión es alón y unas bobinas a opladas. 1

13.1.

Datos Generales.

Ar hivo *.sp ∗ SPICE i r u i t <ejemplo013> from XCir uit v3 . 6 rev 135

1 1 0 2 0 3 0 1 1 2 0 2 2 1 0 1 12 1 0 2 2 0 3 0 0 0 0 0 0 0 2 3 1 4 1 0 2 1 0 4 Cte rho f 0 b 0 1 C D . end Tipo de análisis realizado Análisis esta ionario Análisis transitorio

Datos generales del ir uito Elementos del Cto: 4 EA: 0 Nodos: 3 A2: 5 No nulos: 18 Densidad: 0.28125 Dispersion: 0.71875 105

⊠ ⊠

106

13. Cir uito on a oplamiento magnéti o simple.

Los valores dados al ir uito son: Elemento Resisten ias Bobinas a opladas Fuente de tensión, ex ita ión es alón unidad

Magnitud 1Ω L1 = 2, L2 = 3, M = 1 1V

Matriz T. row 0: (5, row 1: (3, row 2: (4, row 3: (1, row 4: (2, row 5: (0, row 6: (2, row 7: (0,

13.2.

13.2.1.

1) (7, -1) 1) (7, 1) 1) (6, -1) 1) (3, -0 - 2 i) (4, -0 - 1 i) 1) (3, -0 - 1 i) (4, -0 - 3 i) 1) -1) (6, -1) -1) (1, 1) (7, -1)

Solu iones

Primer análisis Tiempo Ini ial Tiempo Final Paso de Tiempo Theta

0 20 0, 13

1 (Euler)

Esta ionario Resultados sistema esta ionario: Tensión en nodo 1: 1.26117e-44 - 4.70372e-61 i Tensión en nodo 2: 9.22806e-45 + 5.22924e-45 i Tensión en nodo 3: 1.53801e-45 - 1.23041e-45 i I de Bobinas A opladas entre nodos 2, 0: 3.38362e-45 - 5.22924e-45 i I de Bobinas A opladas entre nodos 3, 0: -1.53801e-45 + 1.23041e-45 i I de Fuente tension entre nodos 1, 0: -3.38362e-45 + 5.22924e-45 i I Resisten ia entre nodos 0, 3: -1.53801e-45 + 1.23041e-45 i I Resisten ia entre nodos 2, 1: -3.38362e-45 + 5.22924e-45 i

Transitorio 1 0.928197 0.0229402 0.0718029 -0.0229402 -0.0718029 -0.0229402 -0.0718029 0 1 0.862076 0.0431124 0.137924 -0.0431124 -0.137924 -0.0431124 -0.137924 0.13 1 0.801165 0.060782 0.198835 -0.060782 -0.198835 -0.060782 -0.198835 0.26 1 0.745034 0.076191 0.254966 -0.076191 -0.254966 -0.076191 -0.254966 0.39 1 0.693286 0.0895593 0.306714 -0.0895593 -0.306714 -0.0895593 -0.306714 0.52 1 0.645561 0.101087 0.354439 -0.101087 -0.354439 -0.101087 -0.354439 0.65 1 0.601526 0.110957 0.398474 -0.110957 -0.398474 -0.110957 -0.398474 0.78

13.2. Solu iones

1 0.56088 0.119335 0.43912 -0.119335 -0.43912 -0.119335 -0.43912 0.91 1 0.523345 0.12637 0.476655 -0.12637 -0.476655 -0.12637 -0.476655 1.04 1 0.488666 0.132201 0.511334 -0.132201 -0.511334 -0.132201 -0.511334 1.17 1 0.456611 0.136952 0.543389 -0.136952 -0.543389 -0.136952 -0.543389 1.3 1 0.426967 0.140735 0.573033 -0.140735 -0.573033 -0.140735 -0.573033 1.43 1 0.399538 0.143653 0.600462 -0.143653 -0.600462 -0.143653 -0.600462 1.56 1 0.374146 0.145799 0.625854 -0.145799 -0.625854 -0.145799 -0.625854 1.69 1 0.350625 0.147258 0.649375 -0.147258 -0.649375 -0.147258 -0.649375 1.82 1 0.328828 0.148106 0.671172 -0.148106 -0.671172 -0.148106 -0.671172 1.95 1 0.308614 0.148412 0.691386 -0.148412 -0.691386 -0.148412 -0.691386 2.08 1 0.28986 0.14824 0.71014 -0.14824 -0.71014 -0.14824 -0.71014 2.21 1 0.272448 0.147646 0.727552 -0.147646 -0.727552 -0.147646 -0.727552 2.34 1 0.256272 0.146682 0.743728 -0.146682 -0.743728 -0.146682 -0.743728 2.47 1 0.241236 0.145394 0.758764 -0.145394 -0.758764 -0.145394 -0.758764 2.6 1 0.22725 0.143823 0.77275 -0.143823 -0.77275 -0.143823 -0.77275 2.73 1 0.214232 0.142009 0.785768 -0.142009 -0.785768 -0.142009 -0.785768 2.86 1 0.202107 0.139984 0.797893 -0.139984 -0.797893 -0.139984 -0.797893 2.99 1 0.190807 0.137781 0.809193 -0.137781 -0.809193 -0.137781 -0.809193 3.12 1 0.180267 0.135426 0.819733 -0.135426 -0.819733 -0.135426 -0.819733 3.25 1 0.17043 0.132944 0.82957 -0.132944 -0.82957 -0.132944 -0.82957 3.38 1 0.161242 0.130357 0.838758 -0.130357 -0.838758 -0.130357 -0.838758 3.51 1 0.152655 0.127687 0.847345 -0.127687 -0.847345 -0.127687 -0.847345 3.64 1 0.144623 0.12495 0.855377 -0.12495 -0.855377 -0.12495 -0.855377 3.77 1 0.137105 0.122162 0.862895 -0.122162 -0.862895 -0.122162 -0.862895 3.9 1 0.130063 0.119338 0.869937 -0.119338 -0.869937 -0.119338 -0.869937 4.03 1 0.123462 0.11649 0.876538 -0.11649 -0.876538 -0.11649 -0.876538 4.16 1 0.117269 0.113631 0.882731 -0.113631 -0.882731 -0.113631 -0.882731 4.29 1 0.111456 0.110769 0.888544 -0.110769 -0.888544 -0.110769 -0.888544 4.42 1 0.105994 0.107913 0.894006 -0.107913 -0.894006 -0.107913 -0.894006 4.55 1 0.100859 0.105071 0.899141 -0.105071 -0.899141 -0.105071 -0.899141 4.68 1 0.0960271 0.102251 0.903973 -0.102251 -0.903973 -0.102251 -0.903973 4.81 1 0.0914777 0.0994577 0.908522 -0.0994577 -0.908522 -0.0994577 -0.908522 4.94 1 0.0871909 0.0966965 0.912809 -0.0966965 -0.912809 -0.0966965 -0.912809 5.07 1 0.0831486 0.0939718 0.916851 -0.0939718 -0.916851 -0.0939718 -0.916851 5.2 1 0.079334 0.0912876 0.920666 -0.0912876 -0.920666 -0.0912876 -0.920666 5.33 1 0.0757318 0.0886469 0.924268 -0.0886469 -0.924268 -0.0886469 -0.924268 5.46 1 0.0723276 0.0860527 0.927672 -0.0860527 -0.927672 -0.0860527 -0.927672 5.59 1 0.0691083 0.0835072 0.930892 -0.0835072 -0.930892 -0.0835072 -0.930892 5.72 1 0.0660618 0.0810121 0.933938 -0.0810121 -0.933938 -0.0810121 -0.933938 5.85 1 0.0631768 0.0785691 0.936823 -0.0785691 -0.936823 -0.0785691 -0.936823 5.98 1 0.0604429 0.0761793 0.939557 -0.0761793 -0.939557 -0.0761793 -0.939557 6.11 1 0.0578505 0.0738436 0.942149 -0.0738436 -0.942149 -0.0738436 -0.942149 6.24 1 0.0553907 0.0715625 0.944609 -0.0715625 -0.944609 -0.0715625 -0.944609 6.37 1 0.0530551 0.0693364 0.946945 -0.0693364 -0.946945 -0.0693364 -0.946945 6.5 1 0.0508362 0.0671656 0.949164 -0.0671656 -0.949164 -0.0671656 -0.949164 6.63 1 0.0487268 0.0650499 0.951273 -0.0650499 -0.951273 -0.0650499 -0.951273 6.76 1 0.0467203 0.0629892 0.95328 -0.0629892 -0.95328 -0.0629892 -0.95328 6.89 1 0.0448107 0.0609831 0.955189 -0.0609831 -0.955189 -0.0609831 -0.955189 7.02 1 0.0429921 0.0590313 0.957008 -0.0590313 -0.957008 -0.0590313 -0.957008 7.15 1 0.0412593 0.0571331 0.958741 -0.0571331 -0.958741 -0.0571331 -0.958741 7.28 1 0.0396074 0.0552879 0.960393 -0.0552879 -0.960393 -0.0552879 -0.960393 7.41 1 0.0380318 0.053495 0.961968 -0.053495 -0.961968 -0.053495 -0.961968 7.54 1 0.0365282 0.0517536 0.963472 -0.0517536 -0.963472 -0.0517536 -0.963472 7.67 1 0.0350926 0.0500627 0.964907 -0.0500627 -0.964907 -0.0500627 -0.964907 7.8

107

108

13. Cir uito on a oplamiento magnĂŠti o simple.

1 0.0337213 0.0484215 0.966279 -0.0484215 -0.966279 -0.0484215 -0.966279 7.93001 1 0.0324108 0.0468291 0.967589 -0.0468291 -0.967589 -0.0468291 -0.967589 8.06001 1 0.0311579 0.0452844 0.968842 -0.0452844 -0.968842 -0.0452844 -0.968842 8.19001 1 0.0299595 0.0437865 0.97004 -0.0437865 -0.97004 -0.0437865 -0.97004 8.32001 1 0.0288128 0.0423342 0.971187 -0.0423342 -0.971187 -0.0423342 -0.971187 8.45001 1 0.0277151 0.0409266 0.972285 -0.0409266 -0.972285 -0.0409266 -0.972285 8.58001 1 0.026664 0.0395626 0.973336 -0.0395626 -0.973336 -0.0395626 -0.973336 8.71001 1 0.025657 0.0382412 0.974343 -0.0382412 -0.974343 -0.0382412 -0.974343 8.84001 1 0.024692 0.0369612 0.975308 -0.0369612 -0.975308 -0.0369612 -0.975308 8.97001 1 0.0237669 0.0357216 0.976233 -0.0357216 -0.976233 -0.0357216 -0.976233 9.10001 1 0.0228799 0.0345214 0.97712 -0.0345214 -0.97712 -0.0345214 -0.97712 9.23001 1 0.022029 0.0333594 0.977971 -0.0333594 -0.977971 -0.0333594 -0.977971 9.36001 1 0.0212125 0.0322348 0.978788 -0.0322348 -0.978788 -0.0322348 -0.978788 9.49001 1 0.0204288 0.0311463 0.979571 -0.0311463 -0.979571 -0.0311463 -0.979571 9.62001 1 0.0196765 0.030093 0.980324 -0.030093 -0.980324 -0.030093 -0.980324 9.75001 1 0.018954 0.029074 0.981046 -0.029074 -0.981046 -0.029074 -0.981046 9.88001 1 0.01826 0.0280882 0.98174 -0.0280882 -0.98174 -0.0280882 -0.98174 10.01 1 0.0175932 0.0271346 0.982407 -0.0271346 -0.982407 -0.0271346 -0.982407 10.14 1 0.0169525 0.0262123 0.983048 -0.0262123 -0.983048 -0.0262123 -0.983048 10.27 1 0.0163366 0.0253204 0.983663 -0.0253204 -0.983663 -0.0253204 -0.983663 10.4 1 0.0157444 0.024458 0.984256 -0.024458 -0.984256 -0.024458 -0.984256 10.53 1 0.015175 0.0236241 0.984825 -0.0236241 -0.984825 -0.0236241 -0.984825 10.66 1 0.0146273 0.0228178 0.985373 -0.0228178 -0.985373 -0.0228178 -0.985373 10.79 1 0.0141005 0.0220384 0.9859 -0.0220384 -0.9859 -0.0220384 -0.9859 10.92 1 0.0135936 0.0212851 0.986406 -0.0212851 -0.986406 -0.0212851 -0.986406 11.05 1 0.0131058 0.0205569 0.986894 -0.0205569 -0.986894 -0.0205569 -0.986894 11.18 1 0.0126364 0.019853 0.987364 -0.019853 -0.987364 -0.019853 -0.987364 11.31 1 0.0121845 0.0191728 0.987816 -0.0191728 -0.987816 -0.0191728 -0.987816 11.44 1 0.0117494 0.0185155 0.988251 -0.0185155 -0.988251 -0.0185155 -0.988251 11.57 1 0.0113305 0.0178803 0.988669 -0.0178803 -0.988669 -0.0178803 -0.988669 11.7 1 0.0109271 0.0172666 0.989073 -0.0172666 -0.989073 -0.0172666 -0.989073 11.83 1 0.0105386 0.0166736 0.989461 -0.0166736 -0.989461 -0.0166736 -0.989461 11.96 1 0.0101644 0.0161006 0.989836 -0.0161006 -0.989836 -0.0161006 -0.989836 12.09 1 0.00980394 0.0155471 0.990196 -0.0155471 -0.990196 -0.0155471 -0.990196 12.22 1 0.00945664 0.0150123 0.990543 -0.0150123 -0.990543 -0.0150123 -0.990543 12.35 1 0.00912201 0.0144957 0.990878 -0.0144957 -0.990878 -0.0144957 -0.990878 12.48 1 0.00879956 0.0139967 0.9912 -0.0139967 -0.9912 -0.0139967 -0.9912 12.61 1 0.00848881 0.0135146 0.991511 -0.0135146 -0.991511 -0.0135146 -0.991511 12.74 1 0.00818932 0.013049 0.991811 -0.013049 -0.991811 -0.013049 -0.991811 12.87 1 0.00790065 0.0125992 0.992099 -0.0125992 -0.992099 -0.0125992 -0.992099 13 1 0.00762239 0.0121648 0.992378 -0.0121648 -0.992378 -0.0121648 -0.992378 13.13 1 0.00735414 0.0117453 0.992646 -0.0117453 -0.992646 -0.0117453 -0.992646 13.26 1 0.00709553 0.0113401 0.992904 -0.0113401 -0.992904 -0.0113401 -0.992904 13.39 1 0.0068462 0.0109488 0.993154 -0.0109488 -0.993154 -0.0109488 -0.993154 13.52 1 0.00660579 0.0105708 0.993394 -0.0105708 -0.993394 -0.0105708 -0.993394 13.65 1 0.00637397 0.0102058 0.993626 -0.0102058 -0.993626 -0.0102058 -0.993626 13.78 1 0.00615042 0.00985338 0.99385 -0.00985338 -0.99385 -0.00985338 -0.99385 13.91 1 0.00593485 0.00951301 0.994065 -0.00951301 -0.994065 -0.00951301 -0.994065 14.04 1 0.00572694 0.00918433 0.994273 -0.00918433 -0.994273 -0.00918433 -0.994273 14.17 1 0.00552642 0.00886693 0.994474 -0.00886693 -0.994474 -0.00886693 -0.994474 14.3 1 0.00533301 0.00856045 0.994667 -0.00856045 -0.994667 -0.00856045 -0.994667 14.43 1 0.00514647 0.0082645 0.994854 -0.0082645 -0.994854 -0.0082645 -0.994854 14.56 1 0.00496652 0.00797874 0.995033 -0.00797874 -0.995033 -0.00797874 -0.995033 14.69 1 0.00479295 0.00770281 0.995207 -0.00770281 -0.995207 -0.00770281 -0.995207 14.82

13.2. Solu iones

109

1 0.0046255 0.00743638 0.995374 -0.00743638 -0.995374 -0.00743638 -0.995374 14.95 1 0.00446397 0.00717913 0.995536 -0.00717913 -0.995536 -0.00717913 -0.995536 15.08 1 0.00430814 0.00693074 0.995692 -0.00693074 -0.995692 -0.00693074 -0.995692 15.21 1 0.00415779 0.00669092 0.995842 -0.00669092 -0.995842 -0.00669092 -0.995842 15.34 1 0.00401274 0.00645936 0.995987 -0.00645936 -0.995987 -0.00645936 -0.995987 15.47 1 0.00387279 0.00623579 0.996127 -0.00623579 -0.996127 -0.00623579 -0.996127 15.6 1 0.00373777 0.00601994 0.996262 -0.00601994 -0.996262 -0.00601994 -0.996262 15.73 1 0.00360748 0.00581153 0.996393 -0.00581153 -0.996393 -0.00581153 -0.996393 15.86 1 0.00348177 0.00561032 0.996518 -0.00561032 -0.996518 -0.00561032 -0.996518 15.99 1 0.00336047 0.00541606 0.99664 -0.00541606 -0.99664 -0.00541606 -0.99664 16.12 1 0.00324343 0.00522851 0.996757 -0.00522851 -0.996757 -0.00522851 -0.996757 16.25 1 0.00313048 0.00504743 0.99687 -0.00504743 -0.99687 -0.00504743 -0.99687 16.38 1 0.00302149 0.00487262 0.996979 -0.00487262 -0.996979 -0.00487262 -0.996979 16.51 1 0.00291632 0.00470384 0.997084 -0.00470384 -0.997084 -0.00470384 -0.997084 16.64 1 0.00281483 0.0045409 0.997185 -0.0045409 -0.997185 -0.0045409 -0.997185 16.77 1 0.00271688 0.00438359 0.997283 -0.00438359 -0.997283 -0.00438359 -0.997283 16.9 1 0.00262236 0.00423172 0.997378 -0.00423172 -0.997378 -0.00423172 -0.997378 17.03 1 0.00253115 0.00408511 0.997469 -0.00408511 -0.997469 -0.00408511 -0.997469 17.16 1 0.00244312 0.00394356 0.997557 -0.00394356 -0.997557 -0.00394356 -0.997557 17.29 1 0.00235816 0.00380692 0.997642 -0.00380692 -0.997642 -0.00380692 -0.997642 17.42 1 0.00227617 0.003675 0.997724 -0.003675 -0.997724 -0.003675 -0.997724 17.55 1 0.00219704 0.00354764 0.997803 -0.00354764 -0.997803 -0.00354764 -0.997803 17.68 1 0.00212067 0.0034247 0.997879 -0.0034247 -0.997879 -0.0034247 -0.997879 17.81 1 0.00204696 0.003306 0.997953 -0.003306 -0.997953 -0.003306 -0.997953 17.94 1 0.00197582 0.00319142 0.998024 -0.00319142 -0.998024 -0.00319142 -0.998024 18.07 1 0.00190717 0.00308081 0.998093 -0.00308081 -0.998093 -0.00308081 -0.998093 18.2 1 0.0018409 0.00297402 0.998159 -0.00297402 -0.998159 -0.00297402 -0.998159 18.33 1 0.00177694 0.00287093 0.998223 -0.00287093 -0.998223 -0.00287093 -0.998223 18.46 1 0.00171521 0.00277141 0.998285 -0.00277141 -0.998285 -0.00277141 -0.998285 18.59 1 0.00165563 0.00267534 0.998344 -0.00267534 -0.998344 -0.00267534 -0.998344 18.72 1 0.00159813 0.0025826 0.998402 -0.0025826 -0.998402 -0.0025826 -0.998402 18.85 1 0.00154262 0.00249307 0.998457 -0.00249307 -0.998457 -0.00249307 -0.998457 18.98 1 0.00148905 0.00240664 0.998511 -0.00240664 -0.998511 -0.00240664 -0.998511 19.11 1 0.00143734 0.0023232 0.998563 -0.0023232 -0.998563 -0.0023232 -0.998563 19.24 1 0.00138743 0.00224266 0.998613 -0.00224266 -0.998613 -0.00224266 -0.998613 19.37 1 0.00133925 0.0021649 0.998661 -0.0021649 -0.998661 -0.0021649 -0.998661 19.5 1 0.00129276 0.00208984 0.998707 -0.00208984 -0.998707 -0.00208984 -0.998707 19.63 1 0.00124787 0.00201738 0.998752 -0.00201738 -0.998752 -0.00201738 -0.998752 19.76

set terminal png set output ' /home/ ayose / Programa ion /AVALON/debug / s r / o l e i o n / G r a f i o s / o l e i o n p r o b l e m a s /13/ e j e m p l o 0 1 3 _ g r af i a . png '

using 9 : 2 t i t l e 'V en nodo 2 ' with l i n e s , ' /home/ ayose / Programa ion

/AVALON/debug / s r / o l e i o n / G r a f i o s / o l e i o n p r o b l e m a s /13/ ejemplo013_x_trans . data ' using 9 : 3 t i t l e 'V en nodo 3 ' with l i n e s ,

110

13. Cir uito on a oplamiento magnĂŠti o simple.

' /home/ ayose / Programa ion /AVALON/debug / s r / o l e i o n / G r a f i o s / o l e i o n p r o b l e m a s /13/ ejemplo013_x_trans . data ' using 9 : 4 t i t l e ' I de Bobinas A opladas e n t r e nodos 2 , 0 ' with l i n e s , ' /home/ ayose / Programa ion /AVALON/debug / s r / o l e i o n / G r a f i o s / o l e i o n p r o b l e m a s /13/ ejemplo013_x_trans . data ' using 9 : 5 t i t l e ' I de Bobinas A opladas e n t r e nodos 3 , 0 ' with l i n e s , ' /home/ ayose / Programa ion / AVALON/debug / s r / o l e i o n / G r a f i o s / o l e i o n p r o b l e m a s /13/ ejemplo013_x_trans . data ' using 9 : 6 t i t l e ' I de Fuente t e n s i o n e n t r e nodos 1 , 0 ' with l i n e s , ' /home/ ayose / Programa ion /AVALON/debug / s r / o l e i o n / G r a f i o s / o l e i o n p r o b l e m a s /13/ ejemplo013_x_trans . data ' using 9 : 7 t i t l e ' I R e s i s t e n i a e n t r e nodos 0 , 3 ' with l i n e s , ' /home / ayose / Programa ion /AVALON/debug / s r / o l e i o n / G r a f i o s / o l e i o n p r o b l e m a s /13/ ejemplo013_x_trans . data ' using 9 : 8 t i t l e ' I R e s i s t e n i a e n t r e nodos 2 , 1 ' with l i n e s

GrĂĄ o de salida.

VeĂĄmos las intensidades de las bobinas a opladas on mayor detalle.

13.2. Solu iones

111

Capítulo 14 Cir uito on a oplamiento magnéti o.

Ahora se pro ederá al análsis de un ir uito on bobinas a opladas un po o más ompli ado que el anterior. 2

1 0

14.1.

Datos Generales.

Ar hivo *.sp ∗ SPICE i r u i t <ejemplo014> from XCir uit v3 . 6 rev 135

1 1 0 2 0 3 0 1 2 1 0 1 0 3 0 2 2 2 0 1 2 0 0 1 1 2 0 2 2 1 0 1 12 1 0 2 2 0 3 0 0 0 0 0 0 0 1 3 1 0 4 1 0 2 1 0 0 1 rho f a b A B C D . end Tipo de análisis realizado Análisis esta ionario Análisis transitorio

Datos generales del ir uito Elementos del Cto: 6 EA: 0 Nodos: 3 A2: 5 No nulos: 20 113

⊠ ⊠

114

14. Cir uito on a oplamiento magnéti o.

Densidad: 0.3125 Dispersion: 0.6875

Los valores dados al ir uito son: Elemento Resisten ias Condensador entre nodos 2, 0 Condensador entre nodos 3, 0 Bobinas a opladas Fuente de tensión

Magnitud 1Ω 1F 2F L1 = 1, L2 = 3, M = 1 1V

Matriz T. row 0: (5, row 1: (1, row 2: (2, row 3: (1, row 4: (2, row 5: (0, row 6: (2, row 7: (0,

14.2.

14.2.1.

1) (7, -1) 0 + 1 i) (3, 1) (7, 1) 0 + 2 i) (4, 1) (6, -1) 1) (3, -0 - 1 i) (4, -0 - 1 i) 1) (3, -0 - 1 i) (4, -0 - 3 i) 1) -1) (6, -1) -1) (1, 1) (7, -1)

Solu iones

Primer análisis Tiempo Ini ial Tiempo Final Paso de Tiempo Theta

0 20 0, 05

1 (Euler)

Esta ionario Resultados sistema esta ionario: Tensión en nodo 1: 1 + 5.0307e-17 i Tensión en nodo 2: 0.7 + 0.4 i Tensión en nodo 3: -0.1 - 0.2 i I de Bobinas A opladas entre nodos 2, 0: 0.7 - 1.1 i I de Bobinas A opladas entre nodos 3, 0: -0.3 + 0.4 i I de Fuente tension entre nodos 1, 0: -0.3 + 0.4 i I Resisten ia entre nodos 0, 3: 0.1 + 0.2 i I Resisten ia entre nodos 2, 1: -0.3 + 0.4 i

14.2. Solu iones

Transitorio 1 0.0474496 2.89151e-05 0.003558 -0.00118552 -0.95255 -2.89151e-05 -0.95255 0 1 0.0923102 0.000113342 0.0104784 -0.00349044 -0.90769 -0.000113342 -0.90769 0.05 1 0.134554 0.000277587 0.0205631 -0.00684736 -0.865446 -0.000277587 -0.865446 0.1 1 0.174165 0.000543692 0.0336119 -0.0111879 -0.825835 -0.000543692 -0.825835 0.15 1 0.211137 0.000931481 0.0494239 -0.016443 -0.788863 -0.000931481 -0.788863 0.2 1 0.245474 0.0014586 0.067798 -0.0225434 -0.754526 -0.0014586 -0.754526 0.25 1 0.277188 0.00214058 0.0885335 -0.0294196 -0.722812 -0.00214058 -0.722812 0.3 1 0.306301 0.00299087 0.111431 -0.0370024 -0.693699 -0.00299087 -0.693699 0.35 1 0.332844 0.00402092 0.136294 -0.0452229 -0.667156 -0.00402092 -0.667156 0.4 1 0.356855 0.00524024 0.162927 -0.0540133 -0.643145 -0.00524024 -0.643145 0.45 1 0.378379 0.00665649 0.191139 -0.0633064 -0.621621 -0.00665649 -0.621621 0.5 1 0.397469 0.00827551 0.220743 -0.0730362 -0.602531 -0.00827551 -0.602531 0.55 1 0.414182 0.0101014 0.251554 -0.0831382 -0.585818 -0.0101014 -0.585818 0.6 1 0.428583 0.0121367 0.283394 -0.0935494 -0.571417 -0.0121367 -0.571417 0.65 1 0.440741 0.0143824 0.31609 -0.104208 -0.559259 -0.0143824 -0.559259 0.7 1 0.450731 0.0168378 0.349474 -0.115056 -0.549269 -0.0168378 -0.549269 0.75 1 0.45863 0.0195012 0.383384 -0.126034 -0.54137 -0.0195012 -0.54137 0.8 1 0.464521 0.0223691 0.417664 -0.137088 -0.535479 -0.0223691 -0.535479 0.85 1 0.468489 0.0254373 0.452164 -0.148164 -0.531511 -0.0254373 -0.531511 0.9 1 0.47062 0.0287001 0.486743 -0.159212 -0.52938 -0.0287001 -0.52938 0.95 1 0.471007 0.0321509 0.521265 -0.170183 -0.528993 -0.0321509 -0.528993 1 1 0.46974 0.0357822 0.555601 -0.181032 -0.53026 -0.0357822 -0.53026 1.05 1 0.466913 0.0395854 0.58963 -0.191716 -0.533087 -0.0395854 -0.533087 1.1 1 0.46262 0.0435514 0.623237 -0.202192 -0.53738 -0.0435514 -0.53738 1.15 1 0.456956 0.0476703 0.656317 -0.212424 -0.543044 -0.0476703 -0.543044 1.2 1 0.450017 0.0519314 0.68877 -0.222377 -0.549983 -0.0519314 -0.549983 1.25 1 0.441897 0.0563237 0.720505 -0.232016 -0.558103 -0.0563237 -0.558103 1.3 1 0.43269 0.0608356 0.751435 -0.241312 -0.56731 -0.0608356 -0.56731 1.35 1 0.422492 0.0654552 0.781486 -0.250238 -0.577508 -0.0654552 -0.577508 1.4 1 0.411393 0.0701702 0.810586 -0.258769 -0.588607 -0.0701702 -0.588607 1.45 1 0.399485 0.074968 0.838673 -0.266882 -0.600515 -0.074968 -0.600515 1.5 1 0.386857 0.079836 0.865692 -0.274557 -0.613143 -0.079836 -0.613143 1.55 1 0.373598 0.0847614 0.891592 -0.281778 -0.626402 -0.0847614 -0.626402 1.6 1 0.359792 0.0897314 0.916333 -0.28853 -0.640208 -0.0897314 -0.640208 1.65 1 0.345521 0.0947331 0.939879 -0.294799 -0.654479 -0.0947331 -0.654479 1.7 1 0.330868 0.0997536 0.962201 -0.300577 -0.669132 -0.0997536 -0.669132 1.75 1 0.315909 0.104781 0.983274 -0.305855 -0.684091 -0.104781 -0.684091 1.8 1 0.300719 0.109801 1.00308 -0.310628 -0.699281 -0.109801 -0.699281 1.85 1 0.28537 0.114803 1.02162 -0.314892 -0.71463 -0.114803 -0.71463 1.9 1 0.26993 0.119775 1.03887 -0.318646 -0.73007 -0.119775 -0.73007 1.95 1 0.254465 0.124705 1.05483 -0.32189 -0.745535 -0.124705 -0.745535 2 1 0.239037 0.129581 1.06952 -0.324627 -0.760963 -0.129581 -0.760963 2.05 1 0.223705 0.134393 1.08294 -0.326859 -0.776295 -0.134393 -0.776295 2.1 1 0.208523 0.139129 1.0951 -0.328594 -0.791477 -0.139129 -0.791477 2.15 1 0.193545 0.143781 1.10602 -0.329838 -0.806455 -0.143781 -0.806455 2.2 1 0.178818 0.148337 1.11572 -0.3306 -0.821182 -0.148337 -0.821182 2.25 1 0.164387 0.15279 1.12423 -0.33089 -0.835613 -0.15279 -0.835613 2.3 1 0.150293 0.15713 1.13158 -0.330719 -0.849707 -0.15713 -0.849707 2.35 1 0.136575 0.161348 1.13779 -0.3301 -0.863425 -0.161348 -0.863425 2.4 1 0.123267 0.165439 1.1429 -0.329046 -0.876733 -0.165439 -0.876733 2.45 1 0.1104 0.169393 1.14694 -0.327571 -0.8896 -0.169393 -0.8896 2.5 1 0.0980018 0.173205 1.14996 -0.325691 -0.901998 -0.173205 -0.901998 2.55

115

116

14. Cir uito on a oplamiento magnĂŠti o.

1 0.0860971 0.176869 1.152 -0.323422 -0.913903 -0.176869 -0.913903 2.6 1 0.0747072 0.180379 1.15309 -0.32078 -0.925293 -0.180379 -0.925293 2.65 1 0.0638504 0.18373 1.15329 -0.317783 -0.93615 -0.18373 -0.93615 2.7 1 0.0535418 0.186919 1.15263 -0.314448 -0.946458 -0.186919 -0.946458 2.75 1 0.0437939 0.18994 1.15116 -0.310795 -0.956206 -0.18994 -0.956206 2.8 1 0.034616 0.192791 1.14894 -0.30684 -0.965384 -0.192791 -0.965384 2.85 1 0.026015 0.19547 1.14601 -0.302604 -0.973985 -0.19547 -0.973985 2.9 1 0.0179949 0.197973 1.14241 -0.298105 -0.982005 -0.197973 -0.982005 2.95 1 0.0105575 0.200299 1.13819 -0.293361 -0.989442 -0.200299 -0.989442 3 1 0.00370208 0.202448 1.13341 -0.288392 -0.996298 -0.202448 -0.996298 3.05 1 -0.00257436 0.204418 1.1281 -0.283218 -1.00257 -0.204418 -1.00257 3.1 1 -0.00827689 0.206209 1.12233 -0.277855 -1.00828 -0.206209 -1.00828 3.15 1 -0.0134126 0.207822 1.11613 -0.272325 -1.01341 -0.207822 -1.01341 3.2 1 -0.0179903 0.209256 1.10955 -0.266643 -1.01799 -0.209256 -1.01799 3.25 1 -0.0220208 0.210514 1.10263 -0.26083 -1.02202 -0.210514 -1.02202 3.3 1 -0.0255163 0.211597 1.09543 -0.254902 -1.02552 -0.211597 -1.02552 3.35 1 -0.0284907 0.212506 1.08798 -0.248877 -1.02849 -0.212506 -1.02849 3.4 1 -0.030959 0.213244 1.08032 -0.242772 -1.03096 -0.213244 -1.03096 3.45 1 -0.0329375 0.213814 1.07251 -0.236603 -1.03294 -0.213814 -1.03294 3.5 1 -0.0344439 0.214218 1.06457 -0.230387 -1.03444 -0.214218 -1.03444 3.55 1 -0.0354964 0.21446 1.05655 -0.224138 -1.0355 -0.21446 -1.0355 3.6 1 -0.0361144 0.214543 1.04847 -0.217872 -1.03611 -0.214543 -1.03611 3.65 1 -0.0363179 0.214472 1.04039 -0.211602 -1.03632 -0.214472 -1.03632 3.7 1 -0.0361277 0.214249 1.03232 -0.205342 -1.03613 -0.214249 -1.03613 3.75 1 -0.0355649 0.21388 1.02431 -0.199106 -1.03556 -0.21388 -1.03556 3.8 1 -0.0346511 0.213368 1.01638 -0.192906 -1.03465 -0.213368 -1.03465 3.85 1 -0.0334083 0.212719 1.00855 -0.186753 -1.03341 -0.212719 -1.03341 3.9 1 -0.0318585 0.211937 1.00086 -0.180658 -1.03186 -0.211937 -1.03186 3.95 1 -0.0300242 0.211027 0.993337 -0.174631 -1.03002 -0.211027 -1.03002 4 1 -0.0279274 0.209994 0.985992 -0.168683 -1.02793 -0.209994 -1.02793 4.05 1 -0.0255905 0.208844 0.978852 -0.162823 -1.02559 -0.208844 -1.02559 4.1 1 -0.0230354 0.207581 0.971935 -0.157057 -1.02304 -0.207581 -1.02304 4.15 1 -0.0202841 0.20621 0.965258 -0.151395 -1.02028 -0.20621 -1.02028 4.2 1 -0.0173581 0.204738 0.958838 -0.145842 -1.01736 -0.204738 -1.01736 4.25 1 -0.0142786 0.203169 0.952688 -0.140406 -1.01428 -0.203169 -1.01428 4.3 1 -0.0110662 0.201508 0.94682 -0.135092 -1.01107 -0.201508 -1.01107 4.35 1 -0.00774144 0.199762 0.941245 -0.129904 -1.00774 -0.199762 -1.00774 4.4 1 -0.00432388 0.197935 0.935973 -0.124848 -1.00432 -0.197935 -1.00432 4.45 1 -0.000832711 0.196032 0.931009 -0.119926 -1.00083 -0.196032 -1.00083 4.5 1 0.00271354 0.194059 0.926361 -0.115142 -0.997286 -0.194059 -0.997286 4.55 1 0.00629703 0.192021 0.922033 -0.110499 -0.993703 -0.192021 -0.993703 4.6 1 0.00990062 0.189923 0.918028 -0.105999 -0.990099 -0.189923 -0.990099 4.65 1 0.0135079 0.18777 0.914346 -0.101642 -0.986492 -0.18777 -0.986492 4.7 1 0.0171032 0.185567 0.91099 -0.0974307 -0.982897 -0.185567 -0.982897 4.75 1 0.0206718 0.183318 0.907958 -0.0933645 -0.979328 -0.183318 -0.979328 4.8 1 0.0241995 0.181028 0.905247 -0.0894438 -0.975801 -0.181028 -0.975801 4.85 1 0.0276731 0.178702 0.902855 -0.0856681 -0.972327 -0.178702 -0.972327 4.9 1 0.0310802 0.176345 0.900777 -0.0820365 -0.96892 -0.176345 -0.96892 4.95 1 0.0344093 0.173959 0.899009 -0.0785477 -0.965591 -0.173959 -0.965591 5 1 0.0376496 0.17155 0.897544 -0.0752002 -0.96235 -0.17155 -0.96235 5.05 1 0.0407913 0.169122 0.896375 -0.0719919 -0.959209 -0.169122 -0.959209 5.1 1 0.0438253 0.166678 0.895495 -0.0689206 -0.956175 -0.166678 -0.956175 5.15 1 0.0467434 0.164222 0.894895 -0.0659836 -0.953257 -0.164222 -0.953257 5.2 1 0.0495381 0.161758 0.894567 -0.0631782 -0.950462 -0.161758 -0.950462 5.25

14.2. Solu iones

1 0.052203 0.159288 0.8945 -0.060501 -0.947797 -0.159288 -0.947797 5.3 1 0.0547322 0.156816 0.894684 -0.0579489 -0.945268 -0.156816 -0.945268 5.35 1 0.0571207 0.154346 0.89511 -0.0555183 -0.942879 -0.154346 -0.942879 5.4 1 0.0593642 0.151879 0.895765 -0.0532054 -0.940636 -0.151879 -0.940636 5.45 1 0.0614593 0.149419 0.896639 -0.0510064 -0.938541 -0.149419 -0.938541 5.5 1 0.0634032 0.146967 0.89772 -0.0489173 -0.936597 -0.146967 -0.936597 5.55 1 0.0651937 0.144528 0.898996 -0.046934 -0.934806 -0.144528 -0.934806 5.6 1 0.0668294 0.142101 0.900456 -0.0450522 -0.933171 -0.142101 -0.933171 5.65 1 0.0683096 0.139691 0.902087 -0.0432677 -0.93169 -0.139691 -0.93169 5.7 1 0.069634 0.137298 0.903877 -0.0415761 -0.930366 -0.137298 -0.930366 5.75 1 0.0708032 0.134924 0.905814 -0.0399731 -0.929197 -0.134924 -0.929197 5.8 1 0.071818 0.132571 0.907886 -0.0384542 -0.928182 -0.132571 -0.928182 5.85 1 0.0726799 0.13024 0.910081 -0.0370152 -0.92732 -0.13024 -0.92732 5.9 1 0.073391 0.127933 0.912387 -0.0356517 -0.926609 -0.127933 -0.926609 5.95 1 0.0739537 0.125651 0.914792 -0.0343592 -0.926046 -0.125651 -0.926046 6 1 0.0743709 0.123395 0.917285 -0.0331336 -0.925629 -0.123395 -0.925629 6.05 1 0.0746458 0.121165 0.919855 -0.0319707 -0.925354 -0.121165 -0.925354 6.10001 1 0.0747823 0.118962 0.922489 -0.0308662 -0.925218 -0.118962 -0.925218 6.15001 1 0.0747841 0.116788 0.925178 -0.0298161 -0.925216 -0.116788 -0.925216 6.20001 1 0.0746558 0.114642 0.927912 -0.0288164 -0.925344 -0.114642 -0.925344 6.25001 1 0.0744018 0.112526 0.930679 -0.0278633 -0.925598 -0.112526 -0.925598 6.30001 1 0.0740269 0.110439 0.93347 -0.026953 -0.925973 -0.110439 -0.925973 6.35001 1 0.0735364 0.108381 0.936275 -0.0260819 -0.926464 -0.108381 -0.926464 6.40001 1 0.0729353 0.106353 0.939087 -0.0252464 -0.927065 -0.106353 -0.927065 6.45001 1 0.0722291 0.104356 0.941895 -0.0244433 -0.927771 -0.104356 -0.927771 6.50001 1 0.0714233 0.102388 0.944692 -0.0236692 -0.928577 -0.102388 -0.928577 6.55001 1 0.0705236 0.100449 0.94747 -0.022921 -0.929476 -0.100449 -0.929476 6.60001 1 0.0695358 0.0985409 0.950222 -0.0221959 -0.930464 -0.0985409 -0.930464 6.65001 1 0.0684655 0.0966616 0.95294 -0.021491 -0.931535 -0.0966616 -0.931535 6.70001 1 0.0673186 0.0948114 0.955619 -0.0208037 -0.932681 -0.0948114 -0.932681 6.75001 1 0.066101 0.0929899 0.958251 -0.0201314 -0.933899 -0.0929899 -0.933899 6.80001 1 0.0648184 0.0911968 0.960833 -0.019472 -0.935182 -0.0911968 -0.935182 6.85001 1 0.0634767 0.0894316 0.963358 -0.0188231 -0.936523 -0.0894316 -0.936523 6.90001 1 0.0620815 0.0876938 0.965822 -0.0181828 -0.937918 -0.0876938 -0.937918 6.95001 1 0.0606386 0.085983 0.96822 -0.0175492 -0.939361 -0.085983 -0.939361 7.00001 1 0.0591535 0.0842985 0.970549 -0.0169206 -0.940847 -0.0842985 -0.940847 7.05001 1 0.0576316 0.0826399 0.972805 -0.0162954 -0.942368 -0.0826399 -0.942368 7.10001 1 0.0560784 0.0810066 0.974986 -0.0156722 -0.943922 -0.0810066 -0.943922 7.15001 1 0.054499 0.0793979 0.977089 -0.0150497 -0.945501 -0.0793979 -0.945501 7.20001 1 0.0528986 0.0778132 0.979111 -0.0144268 -0.947101 -0.0778132 -0.947101 7.25001 1 0.051282 0.076252 0.98105 -0.0138026 -0.948718 -0.076252 -0.948718 7.30001 1 0.0496539 0.0747135 0.982907 -0.0131761 -0.950346 -0.0747135 -0.950346 7.35001 1 0.0480191 0.0731973 0.984678 -0.0125466 -0.951981 -0.0731973 -0.951981 7.40001 1 0.0463818 0.0717025 0.986364 -0.0119136 -0.953618 -0.0717025 -0.953618 7.45001 1 0.0447462 0.0702287 0.987965 -0.0112765 -0.955254 -0.0702287 -0.955254 7.50001 1 0.0431165 0.0687752 0.989479 -0.0106351 -0.956884 -0.0687752 -0.956884 7.55001 1 0.0414963 0.0673414 0.990908 -0.00998894 -0.958504 -0.0673414 -0.958504 7.60001 1 0.0398892 0.0659267 0.992251 -0.00933801 -0.960111 -0.0659267 -0.960111 7.65001 1 0.0382988 0.0645305 0.99351 -0.00868222 -0.961701 -0.0645305 -0.961701 7.70001 1 0.0367281 0.0631522 0.994686 -0.00802161 -0.963272 -0.0631522 -0.963272 7.75001 1 0.0351801 0.0617913 0.99578 -0.00735633 -0.96482 -0.0617913 -0.96482 7.80001 1 0.0336576 0.0604473 0.996793 -0.00668659 -0.966342 -0.0604473 -0.966342 7.85001 1 0.0321631 0.0591197 0.997727 -0.00601267 -0.967837 -0.0591197 -0.967837 7.90001 1 0.0306989 0.0578078 0.998584 -0.00533495 -0.969301 -0.0578078 -0.969301 7.95001

117

118

14. Cir uito on a oplamiento magnĂŠti o.

1 0.0292672 0.0565114 0.999367 -0.00465384 -0.970733 -0.0565114 -0.970733 8.00001 1 0.0278699 0.0552299 1.00008 -0.00396985 -0.97213 -0.0552299 -0.97213 8.05001 1 0.0265087 0.0539629 1.00072 -0.00328349 -0.973491 -0.0539629 -0.973491 8.10001 1 0.0251851 0.05271 1.00129 -0.00259537 -0.974815 -0.05271 -0.974815 8.15001 1 0.0239005 0.0514709 1.00179 -0.00190611 -0.976099 -0.0514709 -0.976099 8.20001 1 0.022656 0.0502452 1.00224 -0.00121638 -0.977344 -0.0502452 -0.977344 8.25001 1 0.0214524 0.0490326 1.00262 -0.000526874 -0.978548 -0.0490326 -0.978548 8.30001 1 0.0202907 0.0478327 1.00294 0.000161676 -0.979709 -0.0478327 -0.979709 8.35001 1 0.0191713 0.0466454 1.00322 0.000848527 -0.980829 -0.0466454 -0.980829 8.40001 1 0.0180948 0.0454703 1.00344 0.00153291 -0.981905 -0.0454703 -0.981905 8.45001 1 0.0170613 0.0443072 1.00361 0.00221406 -0.982939 -0.0443072 -0.982939 8.50001 1 0.016071 0.0431561 1.00373 0.00289119 -0.983929 -0.0431561 -0.983929 8.55001 1 0.0151239 0.0420166 1.00382 0.00356351 -0.984876 -0.0420166 -0.984876 8.60001 1 0.0142198 0.0408886 1.00386 0.00423023 -0.98578 -0.0408886 -0.98578 8.65001 1 0.0133583 0.039772 1.00387 0.00489057 -0.986642 -0.039772 -0.986642 8.70002 1 0.0125392 0.0386668 1.00384 0.00554376 -0.987461 -0.0386668 -0.987461 8.75002 1 0.0117617 0.0375727 1.00379 0.00618903 -0.988238 -0.0375727 -0.988238 8.80002 1 0.0110254 0.0364898 1.0037 0.00682565 -0.988975 -0.0364898 -0.988975 8.85002 1 0.0103294 0.0354181 1.00359 0.00745286 -0.989671 -0.0354181 -0.989671 8.90002 1 0.00967285 0.0343574 1.00346 0.00806998 -0.990327 -0.0343574 -0.990327 8.95002 1 0.00905492 0.0333078 1.0033 0.0086763 -0.990945 -0.0333078 -0.990945 9.00002 1 0.00847456 0.0322693 1.00313 0.00927116 -0.991525 -0.0322693 -0.991525 9.05002 1 0.0079307 0.0312419 1.00295 0.00985394 -0.992069 -0.0312419 -0.992069 9.10002 1 0.00742222 0.0302256 1.00275 0.010424 -0.992578 -0.0302256 -0.992578 9.15002 1 0.00694792 0.0292206 1.00254 0.0109808 -0.993052 -0.0292206 -0.993052 9.20002 1 0.00650657 0.0282268 1.00232 0.0115239 -0.993493 -0.0282268 -0.993493 9.25002 1 0.0060969 0.0272444 1.0021 0.0120525 -0.993903 -0.0272444 -0.993903 9.30002 1 0.0057176 0.0262734 1.00187 0.0125664 -0.994282 -0.0262734 -0.994282 9.35002 1 0.00536732 0.0253139 1.00164 0.0130651 -0.994633 -0.0253139 -0.994633 9.40002 1 0.00504472 0.0243661 1.00141 0.0135481 -0.994955 -0.0243661 -0.994955 9.45002 1 0.00474841 0.0234299 1.00118 0.0140152 -0.995252 -0.0234299 -0.995252 9.50002 1 0.00447701 0.0225057 1.00095 0.0144659 -0.995523 -0.0225057 -0.995523 9.55002 1 0.00422914 0.0215933 1.00073 0.0149 -0.995771 -0.0215933 -0.995771 9.60002 1 0.00400341 0.0206931 1.00051 0.0153172 -0.995997 -0.0206931 -0.995997 9.65002 1 0.00379844 0.019805 1.0003 0.0157174 -0.996202 -0.019805 -0.996202 9.70002 1 0.00361286 0.0189293 1.0001 0.0161003 -0.996387 -0.0189293 -0.996387 9.75002 1 0.00344532 0.018066 0.999905 0.0164658 -0.996555 -0.018066 -0.996555 9.80002 1 0.00329449 0.0172152 0.999722 0.0168138 -0.996706 -0.0172152 -0.996706 9.85002 1 0.00315906 0.0163772 0.99955 0.0171443 -0.996841 -0.0163772 -0.996841 9.90002 1 0.00303774 0.015552 0.999389 0.0174572 -0.996962 -0.015552 -0.996962 9.95002 1 0.00292928 0.0147397 0.99924 0.0177524 -0.997071 -0.0147397 -0.997071 10 1 0.00283247 0.0139404 0.999104 0.0180301 -0.997168 -0.0139404 -0.997168 10.05 1 0.00274611 0.0131543 0.998981 0.0182903 -0.997254 -0.0131543 -0.997254 10.1 1 0.00266908 0.0123814 0.998872 0.0185331 -0.997331 -0.0123814 -0.997331 10.15 1 0.00260027 0.0116219 0.998776 0.0187587 -0.9974 -0.0116219 -0.9974 10.2 1 0.00253861 0.0108758 0.998695 0.0189671 -0.997461 -0.0108758 -0.997461 10.25 1 0.0024831 0.0101433 0.998627 0.0191586 -0.997517 -0.0101433 -0.997517 10.3 1 0.00243276 0.00942435 0.998574 0.0193334 -0.997567 -0.00942435 -0.997567 10.35 1 0.00238667 0.00871908 0.998535 0.0194917 -0.997613 -0.00871908 -0.997613 10.4 1 0.00234397 0.00802755 0.99851 0.0196338 -0.997656 -0.00802755 -0.997656 10.45 1 0.00230382 0.00734981 0.998499 0.0197599 -0.997696 -0.00734981 -0.997696 10.5 1 0.00226545 0.0066859 0.998502 0.0198705 -0.997735 -0.0066859 -0.997735 10.55 1 0.00222813 0.00603586 0.998518 0.0199656 -0.997772 -0.00603586 -0.997772 10.6 1 0.0021912 0.00539972 0.998548 0.0200459 -0.997809 -0.00539972 -0.997809 10.65

14.2. Solu iones

1 0.00215401 0.0047775 0.99859 0.0201114 -0.997846 -0.0047775 -0.997846 10.7 1 0.00211601 0.0041692 0.998644 0.0201628 -0.997884 -0.0041692 -0.997884 10.75 1 0.00207665 0.00357482 0.99871 0.0202002 -0.997923 -0.00357482 -0.997923 10.8 1 0.00203547 0.00299436 0.998788 0.0202242 -0.997965 -0.00299436 -0.997965 10.85 1 0.00199202 0.00242779 0.998877 0.0202351 -0.998008 -0.00242779 -0.998008 10.9 1 0.00194592 0.00187508 0.998976 0.0202333 -0.998054 -0.00187508 -0.998054 10.95 1 0.00189683 0.00133619 0.999085 0.0202193 -0.998103 -0.00133619 -0.998103 11 1 0.00184446 0.000811074 0.999203 0.0201935 -0.998156 -0.000811074 -0.998156 11.05 1 0.00178855 0.000299676 0.99933 0.0201563 -0.998211 -0.000299676 -0.998211 11.1 1 0.00172889 -0.000198074 0.999464 0.0201081 -0.998271 0.000198074 -0.998271 11.15 1 0.00166532 -0.000682253 0.999606 0.0200494 -0.998335 0.000682253 -0.998335 11.2 1 0.00159769 -0.00115294 0.999755 0.0199806 -0.998402 0.00115294 -0.998402 11.25 1 0.00152592 -0.00161024 0.99991 0.0199022 -0.998474 0.00161024 -0.998474 11.3 1 0.00144994 -0.00205425 1.00007 0.0198146 -0.99855 0.00205425 -0.99855 11.35 1 0.00136973 -0.00248508 1.00023 0.0197182 -0.99863 0.00248508 -0.99863 11.4 1 0.00128529 -0.00290285 1.0004 0.0196135 -0.998715 0.00290285 -0.998715 11.45 1 0.00119666 -0.00330768 1.00058 0.0195009 -0.998803 0.00330768 -0.998803 11.5 1 0.00110391 -0.00369971 1.00075 0.0193808 -0.998896 0.00369971 -0.998896 11.55 1 0.00100712 -0.00407907 1.00093 0.0192537 -0.998993 0.00407907 -0.998993 11.6 1 0.000906404 -0.00444592 1.00111 0.0191199 -0.999094 0.00444592 -0.999094 11.65 1 0.00080191 -0.00480041 1.00129 0.0189798 -0.999198 0.00480041 -0.999198 11.7 1 0.000693791 -0.00514269 1.00147 0.0188339 -0.999306 0.00514269 -0.999306 11.75 1 0.000582225 -0.00547293 1.00165 0.0186825 -0.999418 0.00547293 -0.999418 11.8 1 0.000467409 -0.0057913 1.00183 0.0185261 -0.999533 0.0057913 -0.999533 11.85 1 0.000349552 -0.00609797 1.00201 0.0183649 -0.99965 0.00609797 -0.99965 11.9 1 0.00022888 -0.00639313 1.00218 0.0181993 -0.999771 0.00639313 -0.999771 11.95 1 0.000105627 -0.00667695 1.00236 0.0180298 -0.999894 0.00667695 -0.999894 12 1 -1.99582e-05 -0.00694962 1.00253 0.0178565 -1.00002 0.00694962 -1.00002 12.05 1 -0.000147621 -0.00721133 1.0027 0.0176799 -1.00015 0.00721133 -1.00015 12.1 1 -0.000277099 -0.00746228 1.00287 0.0175003 -1.00028 0.00746228 -1.00028 12.15 1 -0.000408123 -0.00770266 1.00303 0.0173179 -1.00041 0.00770266 -1.00041 12.2 1 -0.000540422 -0.00793268 1.00319 0.0171331 -1.00054 0.00793268 -1.00054 12.25 1 -0.00067372 -0.00815252 1.00334 0.0169462 -1.00067 0.00815252 -1.00067 12.3 1 -0.00080774 -0.00836239 1.00349 0.0167573 -1.00081 0.00836239 -1.00081 12.35 1 -0.000942208 -0.0085625 1.00363 0.0165668 -1.00094 0.0085625 -1.00094 12.4 1 -0.00107685 -0.00875304 1.00377 0.0163749 -1.00108 0.00875304 -1.00108 12.45 1 -0.00121138 -0.00893423 1.0039 0.0161818 -1.00121 0.00893423 -1.00121 12.5 1 -0.00134555 -0.00910627 1.00403 0.0159878 -1.00135 0.00910627 -1.00135 12.55 1 -0.00147908 -0.00926936 1.00415 0.015793 -1.00148 0.00926936 -1.00148 12.6 1 -0.00161171 -0.00942371 1.00426 0.0155977 -1.00161 0.00942371 -1.00161 12.65 1 -0.0017432 -0.00956953 1.00437 0.0154021 -1.00174 0.00956953 -1.00174 12.7 1 -0.00187328 -0.00970701 1.00448 0.0152062 -1.00187 0.00970701 -1.00187 12.75 1 -0.00200174 -0.00983636 1.00457 0.0150104 -1.002 0.00983636 -1.002 12.8 1 -0.00212833 -0.00995778 1.00466 0.0148146 -1.00213 0.00995778 -1.00213 12.85 1 -0.00225284 -0.0100715 1.00474 0.0146192 -1.00225 0.0100715 -1.00225 12.9 1 -0.00237505 -0.0101776 1.00482 0.0144241 -1.00238 0.0101776 -1.00238 12.95 1 -0.00249477 -0.0102765 1.00489 0.0142296 -1.00249 0.0102765 -1.00249 13 1 -0.0026118 -0.0103681 1.00495 0.0140356 -1.00261 0.0103681 -1.00261 13.05 1 -0.00272596 -0.0104529 1.00501 0.0138425 -1.00273 0.0104529 -1.00273 13.1 1 -0.0028371 -0.0105309 1.00506 0.0136501 -1.00284 0.0105309 -1.00284 13.15 1 -0.00294504 -0.0106023 1.0051 0.0134587 -1.00295 0.0106023 -1.00295 13.2 1 -0.00304965 -0.0106673 1.00514 0.0132683 -1.00305 0.0106673 -1.00305 13.25 1 -0.0031508 -0.0107261 1.00517 0.0130789 -1.00315 0.0107261 -1.00315 13.3 1 -0.00324836 -0.0107789 1.0052 0.0128906 -1.00325 0.0107789 -1.00325 13.35

119

120

14. Cir uito on a oplamiento magnĂŠti o.

1 -0.00334223 -0.0108259 1.00522 0.0127035 -1.00334 0.0108259 -1.00334 13.4 1 -0.00343231 -0.0108671 1.00523 0.0125176 -1.00343 0.0108671 -1.00343 13.45 1 -0.00351851 -0.0109029 1.00524 0.012333 -1.00352 0.0109029 -1.00352 13.5 1 -0.00360076 -0.0109333 1.00525 0.0121497 -1.0036 0.0109333 -1.0036 13.55 1 -0.003679 -0.0109585 1.00524 0.0119677 -1.00368 0.0109585 -1.00368 13.6 1 -0.00375318 -0.0109787 1.00524 0.0117871 -1.00375 0.0109787 -1.00375 13.65 1 -0.00382327 -0.0109941 1.00522 0.0116078 -1.00382 0.0109941 -1.00382 13.7 1 -0.00388922 -0.0110047 1.00521 0.0114299 -1.00389 0.0110047 -1.00389 13.75 1 -0.00395103 -0.0110108 1.00519 0.0112535 -1.00395 0.0110108 -1.00395 13.8 1 -0.0040087 -0.0110124 1.00516 0.0110784 -1.00401 0.0110124 -1.00401 13.85 1 -0.00406221 -0.0110098 1.00513 0.0109047 -1.00406 0.0110098 -1.00406 13.9 1 -0.00411159 -0.011003 1.0051 0.0107324 -1.00411 0.011003 -1.00411 13.95 1 -0.00415686 -0.0109923 1.00506 0.0105615 -1.00416 0.0109923 -1.00416 14 1 -0.00419805 -0.0109776 1.00502 0.010392 -1.0042 0.0109776 -1.0042 14.05 1 -0.0042352 -0.0109592 1.00498 0.0102239 -1.00424 0.0109592 -1.00424 14.1 1 -0.00426836 -0.0109372 1.00493 0.0100572 -1.00427 0.0109372 -1.00427 14.15 1 -0.00429758 -0.0109117 1.00488 0.00989183 -1.0043 0.0109117 -1.0043 14.2 1 -0.00432293 -0.0108829 1.00483 0.00972783 -1.00432 0.0108829 -1.00432 14.25 1 -0.00434447 -0.0108507 1.00478 0.00956518 -1.00434 0.0108507 -1.00434 14.3 1 -0.00436228 -0.0108154 1.00472 0.00940385 -1.00436 0.0108154 -1.00436 14.35 1 -0.00437644 -0.0107771 1.00466 0.00924383 -1.00438 0.0107771 -1.00438 14.4 1 -0.00438704 -0.0107358 1.0046 0.00908511 -1.00439 0.0107358 -1.00439 14.45 1 -0.00439417 -0.0106917 1.00454 0.00892767 -1.00439 0.0106917 -1.00439 14.5 1 -0.00439792 -0.0106449 1.00447 0.0087715 -1.0044 0.0106449 -1.0044 14.55 1 -0.00439841 -0.0105954 1.00441 0.00861657 -1.0044 0.0105954 -1.0044 14.6 1 -0.00439572 -0.0105434 1.00434 0.00846288 -1.0044 0.0105434 -1.0044 14.65 1 -0.00438997 -0.0104889 1.00427 0.00831041 -1.00439 0.0104889 -1.00439 14.7 1 -0.00438126 -0.0104321 1.00421 0.00815914 -1.00438 0.0104321 -1.00438 14.75 1 -0.00436971 -0.010373 1.00414 0.00800905 -1.00437 0.010373 -1.00437 14.8 1 -0.00435543 -0.0103117 1.00407 0.00786015 -1.00436 0.0103117 -1.00436 14.85 1 -0.00433854 -0.0102483 1.004 0.0077124 -1.00434 0.0102483 -1.00434 14.9 1 -0.00431915 -0.0101829 1.00393 0.00756581 -1.00432 0.0101829 -1.00432 14.95 1 -0.00429738 -0.0101155 1.00386 0.00742035 -1.0043 0.0101155 -1.0043 15 1 -0.00427334 -0.0100463 1.00379 0.00727603 -1.00427 0.0100463 -1.00427 15.05 1 -0.00424715 -0.00997521 1.00372 0.00713283 -1.00425 0.00997521 -1.00425 15.1 1 -0.00421893 -0.00990242 1.00365 0.00699074 -1.00422 0.00990242 -1.00422 15.15 1 -0.0041888 -0.00982796 1.00359 0.00684976 -1.00419 0.00982796 -1.00419 15.2 1 -0.00415686 -0.00975191 1.00352 0.00670989 -1.00416 0.00975191 -1.00416 15.25 1 -0.00412324 -0.00967433 1.00345 0.00657111 -1.00412 0.00967433 -1.00412 15.3 1 -0.00408804 -0.00959529 1.00338 0.00643343 -1.00409 0.00959529 -1.00409 15.35 1 -0.00405137 -0.00951484 1.00332 0.00629684 -1.00405 0.00951484 -1.00405 15.4 1 -0.00401334 -0.00943304 1.00325 0.00616135 -1.00401 0.00943304 -1.00401 15.45 1 -0.00397407 -0.00934997 1.00319 0.00602695 -1.00397 0.00934997 -1.00397 15.5 1 -0.00393365 -0.00926567 1.00313 0.00589365 -1.00393 0.00926567 -1.00393 15.55 1 -0.00389218 -0.0091802 1.00306 0.00576145 -1.00389 0.0091802 -1.00389 15.6 1 -0.00384976 -0.00909362 1.003 0.00563035 -1.00385 0.00909362 -1.00385 15.65 1 -0.00380648 -0.00900598 1.00294 0.00550037 -1.00381 0.00900598 -1.00381 15.7 1 -0.00376245 -0.00891733 1.00288 0.00537149 -1.00376 0.00891733 -1.00376 15.75 1 -0.00371775 -0.00882773 1.00282 0.00524375 -1.00372 0.00882773 -1.00372 15.8 1 -0.00367246 -0.00873723 1.00277 0.00511713 -1.00367 0.00873723 -1.00367 15.85 1 -0.00362666 -0.00864587 1.00271 0.00499165 -1.00363 0.00864587 -1.00363 15.9 1 -0.00358045 -0.00855371 1.00266 0.00486731 -1.00358 0.00855371 -1.00358 15.95 1 -0.00353388 -0.0084608 1.0026 0.00474414 -1.00353 0.0084608 -1.00353 16 1 -0.00348704 -0.00836717 1.00255 0.00462214 -1.00349 0.00836717 -1.00349 16.05

14.2. Solu iones

1 -0.00343999 -0.00827288 1.0025 0.00450132 -1.00344 0.00827288 -1.00344 16.1 1 -0.00339281 -0.00817797 1.00245 0.00438169 -1.00339 0.00817797 -1.00339 16.15 1 -0.00334554 -0.00808249 1.0024 0.00426326 -1.00335 0.00808249 -1.00335 16.2 1 -0.00329825 -0.00798648 1.00235 0.00414606 -1.0033 0.00798648 -1.0033 16.25 1 -0.003251 -0.00788999 1.00231 0.00403008 -1.00325 0.00788999 -1.00325 16.3 1 -0.00320383 -0.00779304 1.00226 0.00391535 -1.0032 0.00779304 -1.0032 16.35 1 -0.00315679 -0.0076957 1.00222 0.00380188 -1.00316 0.0076957 -1.00316 16.4 1 -0.00310994 -0.00759799 1.00217 0.00368968 -1.00311 0.00759799 -1.00311 16.45 1 -0.0030633 -0.00749996 1.00213 0.00357876 -1.00306 0.00749996 -1.00306 16.5 1 -0.00301692 -0.00740165 1.00209 0.00346914 -1.00302 0.00740165 -1.00302 16.55 1 -0.00297083 -0.00730309 1.00205 0.00336084 -1.00297 0.00730309 -1.00297 16.6 1 -0.00292507 -0.00720433 1.00201 0.00325385 -1.00293 0.00720433 -1.00293 16.65 1 -0.00287966 -0.0071054 1.00197 0.00314821 -1.00288 0.0071054 -1.00288 16.7 1 -0.00283463 -0.00700634 1.00193 0.00304392 -1.00283 0.00700634 -1.00283 16.75 1 -0.00279 -0.00690718 1.0019 0.00294099 -1.00279 0.00690718 -1.00279 16.8 1 -0.0027458 -0.00680797 1.00186 0.00283943 -1.00275 0.00680797 -1.00275 16.85 1 -0.00270203 -0.00670873 1.00183 0.00273927 -1.0027 0.00670873 -1.0027 16.9 1 -0.00265873 -0.00660951 1.00179 0.0026405 -1.00266 0.00660951 -1.00266 16.95 1 -0.00261589 -0.00651033 1.00176 0.00254314 -1.00262 0.00651033 -1.00262 17 1 -0.00257354 -0.00641123 1.00173 0.00244719 -1.00257 0.00641123 -1.00257 17.05 1 -0.00253167 -0.00631224 1.00169 0.00235268 -1.00253 0.00631224 -1.00253 17.1 1 -0.00249031 -0.00621339 1.00166 0.0022596 -1.00249 0.00621339 -1.00249 17.15 1 -0.00244944 -0.00611473 1.00163 0.00216797 -1.00245 0.00611473 -1.00245 17.2 1 -0.00240908 -0.00601626 1.0016 0.00207779 -1.00241 0.00601626 -1.00241 17.25 1 -0.00236922 -0.00591804 1.00157 0.00198907 -1.00237 0.00591804 -1.00237 17.3 1 -0.00232987 -0.00582008 1.00154 0.00190182 -1.00233 0.00582008 -1.00233 17.35 1 -0.00229102 -0.00572242 1.00151 0.00181603 -1.00229 0.00572242 -1.00229 17.4 1 -0.00225268 -0.00562509 1.00149 0.00173172 -1.00225 0.00562509 -1.00225 17.45 1 -0.00221483 -0.00552811 1.00146 0.00164889 -1.00221 0.00552811 -1.00221 17.5 1 -0.00217747 -0.00543151 1.00143 0.00156754 -1.00218 0.00543151 -1.00218 17.55 1 -0.0021406 -0.00533532 1.0014 0.00148767 -1.00214 0.00533532 -1.00214 17.6 1 -0.00210421 -0.00523956 1.00138 0.00140929 -1.0021 0.00523956 -1.0021 17.65 1 -0.00206828 -0.00514426 1.00135 0.00133239 -1.00207 0.00514426 -1.00207 17.7 1 -0.00203282 -0.00504945 1.00132 0.00125697 -1.00203 0.00504945 -1.00203 17.75 1 -0.00199781 -0.00495515 1.0013 0.00118304 -1.002 0.00495515 -1.002 17.8 1 -0.00196325 -0.00486138 1.00127 0.00111058 -1.00196 0.00486138 -1.00196 17.85 1 -0.00192912 -0.00476817 1.00125 0.00103961 -1.00193 0.00476817 -1.00193 17.9 1 -0.0018954 -0.00467553 1.00122 0.000970104 -1.0019 0.00467553 -1.0019 17.95 1 -0.00186211 -0.00458349 1.0012 0.00090207 -1.00186 0.00458349 -1.00186 18 1 -0.00182921 -0.00449208 1.00117 0.000835498 -1.00183 0.00449208 -1.00183 18.05 1 -0.0017967 -0.00440131 1.00115 0.000770382 -1.0018 0.00440131 -1.0018 18.1 1 -0.00176457 -0.00431119 1.00112 0.000706717 -1.00176 0.00431119 -1.00176 18.15 1 -0.0017328 -0.00422176 1.0011 0.000644493 -1.00173 0.00422176 -1.00173 18.2 1 -0.0017014 -0.00413303 1.00107 0.000583702 -1.0017 0.00413303 -1.0017 18.25 1 -0.00167033 -0.00404501 1.00105 0.000524335 -1.00167 0.00404501 -1.00167 18.3 1 -0.00163961 -0.00395773 1.00103 0.000466382 -1.00164 0.00395773 -1.00164 18.35 1 -0.00160921 -0.00387119 1.001 0.000409832 -1.00161 0.00387119 -1.00161 18.4 1 -0.00157912 -0.00378543 1.00098 0.000354675 -1.00158 0.00378543 -1.00158 18.45 1 -0.00154933 -0.00370044 1.00095 0.000300897 -1.00155 0.00370044 -1.00155 18.5 1 -0.00151985 -0.00361624 1.00093 0.000248487 -1.00152 0.00361624 -1.00152 18.55 1 -0.00149065 -0.00353286 1.00091 0.000197432 -1.00149 0.00353286 -1.00149 18.6 1 -0.00146172 -0.00345029 1.00088 0.000147717 -1.00146 0.00345029 -1.00146 18.65 1 -0.00143307 -0.00336856 1.00086 9.93301e-05 -1.00143 0.00336856 -1.00143 18.7 1 -0.00140467 -0.00328768 1.00084 5.2255e-05 -1.0014 0.00328768 -1.0014 18.75

121

122

14. Cir uito on a oplamiento magnĂŠti o.

1 -0.00137654 -0.00320765 1.00081 6.47727e-06 -1.00138 0.00320765 -1.00138 18.8 1 -0.00134865 -0.00312849 1.00079 -3.80187e-05 -1.00135 0.00312849 -1.00135 18.85 1 -0.001321 -0.0030502 1.00077 -8.12488e-05 -1.00132 0.0030502 -1.00132 18.9 1 -0.00129358 -0.0029728 1.00075 -0.000123229 -1.00129 0.0029728 -1.00129 18.95 1 -0.0012664 -0.00289629 1.00072 -0.000163976 -1.00127 0.00289629 -1.00127 19 1 -0.00123944 -0.00282069 1.0007 -0.000203507 -1.00124 0.00282069 -1.00124 19.05 1 -0.00121271 -0.00274599 1.00068 -0.00024184 -1.00121 0.00274599 -1.00121 19.1 1 -0.00118619 -0.00267221 1.00066 -0.00027899 -1.00119 0.00267221 -1.00119 19.15 1 -0.00115989 -0.00259935 1.00063 -0.000314977 -1.00116 0.00259935 -1.00116 19.2 1 -0.0011338 -0.00252742 1.00061 -0.000349817 -1.00113 0.00252742 -1.00113 19.25 1 -0.00110792 -0.00245642 1.00059 -0.00038353 -1.00111 0.00245642 -1.00111 19.3 1 -0.00108224 -0.00238636 1.00057 -0.000416133 -1.00108 0.00238636 -1.00108 19.35 1 -0.00105678 -0.00231724 1.00055 -0.000447644 -1.00106 0.00231724 -1.00106 19.4 1 -0.00103152 -0.00224906 1.00053 -0.000478083 -1.00103 0.00224906 -1.00103 19.45 1 -0.00100646 -0.00218183 1.00051 -0.000507467 -1.00101 0.00218183 -1.00101 19.5 1 -0.000981617 -0.00211554 1.00048 -0.000535815 -1.00098 0.00211554 -1.00098 19.55 1 -0.000956975 -0.00205021 1.00046 -0.000563146 -1.00096 0.00205021 -1.00096 19.6 1 -0.00093254 -0.00198583 1.00044 -0.000589478 -1.00093 0.00198583 -1.00093 19.65 1 -0.000908313 -0.0019224 1.00042 -0.00061483 -1.00091 0.0019224 -1.00091 19.7 1 -0.000884296 -0.00185992 1.0004 -0.000639221 -1.00088 0.00185992 -1.00088 19.75 1 -0.00086049 -0.00179839 1.00038 -0.000662668 -1.00086 0.00179839 -1.00086 19.8 1 -0.000836898 -0.00173782 1.00037 -0.000685191 -1.00084 0.00173782 -1.00084 19.85 1 -0.000813522 -0.00167819 1.00035 -0.000706808 -1.00081 0.00167819 -1.00081 19.9 1 -0.000790364 -0.00161952 1.00033 -0.000727537 -1.00079 0.00161952 -1.00079 20 set terminal png set output ' /home/ ayose / Programa ion /AVALON/debug / s r / o l e i o n / G r a f i o s / o l e i o n p r o b l e m a s /14/ e j e m p l o 0 1 4 _ g r af i a . png ' set en oding iso_8859_1

set grid set autos ale set key bottom r i g h t t i t l e ' V a r i a b l e s ' box set t i t l e ' Grafi ado por d e f e t o de l a s s o l u i o n e s d e l i r u i t o ' plot ' /home/ ayose / Programa ion /AVALON/debug / s r / o l e i o n / G r a f i o s / o l e i o n p r o b l e m a s /14/ ejemplo014_x_trans . data ' using 9 : 1 t i t l e 'V en nodo 1 ' with l i n e s , ' /home/ ayose / Programa ion /AVALON/debug / s r / o l e i o n / G r a f i o s / o l e i o n p r o b l e m a s /14/ ejemplo014_x_trans . data '

using 9 : 2 t i t l e 'V en nodo 2 ' with l i n e s , ' /home/ ayose / Programa ion

/AVALON/debug / s r / o l e i o n / G r a f i o s / o l e i o n p r o b l e m a s /14/ ejemplo014_x_trans . data ' using 9 : 3 t i t l e 'V en nodo 3 ' with l i n e s , ' /home/ ayose / Programa ion /AVALON/debug / s r / o l e i o n / G r a f i o s / o l e i o n p r o b l e m a s /14/ ejemplo014_x_trans . data ' using 9 : 4 t i t l e ' I de Bobinas A opladas e n t r e nodos 2 , 0 ' with l i n e s , ' /home/ ayose / Programa ion /AVALON/debug / s r / o l e i o n / G r a f i o s / o l e i o n p r o b l e m a s /14/ ejemplo014_x_trans . data ' using 9 : 5 t i t l e ' I de Bobinas A opladas e n t r e nodos 3 , 0 ' with l i n e s , ' /home/ ayose / Programa ion / AVALON/debug / s r / o l e i o n / G r a f i o s / o l e i o n p r o b l e m a s /14/ ejemplo014_x_trans . data ' using 9 : 6 t i t l e ' I de Fuente t e n s i o n e n t r e nodos 1 , 0 ' with l i n e s , ' /home/ ayose / Programa ion /AVALON/debug / s r / o l e i o n / G r a f i o s / o l e i o n p r o b l e m a s /14/ ejemplo014_x_trans . data ' using 9 : 7 t i t l e ' I R e s i s t e n i a e n t r e nodos 0 , 3 ' with l i n e s , ' /home / ayose / Programa ion /AVALON/debug / s r / o l e i o n / G r a f i o s / o l e i o n p r o b l e m a s /14/ ejemplo014_x_trans . data ' using 9 : 8 t i t l e ' I R e s i s t e n i a e n t r e nodos 2 , 1 ' with l i n e s

14.2. Solu iones

123

Gr谩 o de salida.

Ve谩mos las variables al uladas on mayor detalle. Empezaremos por las tensiones en los nodos. Tensi贸n en nodo 1

Tensi贸n en nodo 2

124

Tensi贸n en nodo 3

Intensidades de las bobinas a opladas

14. Cir uito on a oplamiento magn茅ti o.

14.2. Solu iones

Intensidad de la malla 1 y de la malla2

125

126

14. Cir uito on a oplamiento magnĂŠti o.

Capítulo 15 Cir uito on fuente de tensión dependiente de tensión.

3 1 3

15.1.

Datos Generales.

Ar hivo *.sp ∗ SPICE i r u i t <ejemplo015> from XCir uit v3 . 6 rev 135

2 1 1 9 1 2 1 4

1 1 2 1 3 2 4 1

0 0 0 0 0 0 0 0

1 2 2 2 2 1 2 2

0 0 5 3 0 2 1 3

5 5 4 1 2 1 3 0

0 0 0 4 0 0 0 0

0 ,000005 20 50 0 0 3 100 0 ,000002 10 1 rho f a b A B C D

. end Tipo de análisis realizado Análisis esta ionario Análisis transitorio

Datos generales del ir uito Elementos del Cto: 8 EA: 0 Nodos: 5 A2: 6 No nulos: 27 Densidad: 0.22314 127

⊠ ⊠

128

15. Cir uito on fuente de tensión dependiente de tensión.

Dispersion: 0.7768595041

Los valores dados al ir uito son: Elemento Resisten ia entre nodos 1, 2 Condensador entre nodos 2, 3 Resisten ia entre nodos 3, 0 Fuente de V dependiente de V Resisten ia entre nodos 4, 5 Resisten ia entre nodos 5, 0 Condensador entre nodos 3, 0

Magnitud 10 Ω 2 · 10−6 F 100 Ω 100 50 Ω 20 Ω 5 · 10−6 F

Matriz T. row 0: (0, 0 + 2e-06 i) (1, -0 - 2e-06 i) (5, 1) row 1: (0, -0 - 2e-06 i) (1, 0 + 2e-06 i) (10, -1) row 2: (5, -1) (6, 1) row 3: (8, -1) (9, 1) row 4: (4, 0 + 5e-06 i) (7, -1) (8, 1) row 5: (0, 1) (2, -1) (5, -10) row 6: (2, 1) row 7: (4, -1) (7, -20) row 8: (3, -1) (4, 1) (8, -50) row 9: (0, 3) (2, -3) (3, 1) row 10: (1, -1) (10, -100)

15.2.

15.2.1.

Solu iones

Primer análisis Tiempo Ini ial Tiempo Final Paso de Tiempo Theta

0 0, 001 0, 00001

1 (Euler)

Esta ionario Resultados sistema esta ionario: Tensión en nodo 1: 1 - 2e-05 i Tensión en nodo 2: 4.4e-08 + 0.0002 i Tensión en nodo 3: 1 - 5.60615e-21 i Tensión en nodo 4: 1.32e-08 + 6e-05 i Tensión en nodo 5: 4.99592e-09 + 1.71429e-05 i I Resisten ia entre nodos 1, 3: -4.4e-10 - 2e-06 i I de Fuente tension entre nodos 3, 0: -4.4e-10 - 2e-06 i I Resisten ia entre nodos 0, 5: -2.49796e-10 - 8.57143e-07 i I Resisten ia entre nodos 5, 4: -1.64082e-10 - 8.57143e-07 i

15.2. Solu iones

129

I de Fuente de V dependiente de V entre nodos 3, 1: -1.64082e-10 - 8.57143e-07 i I Resisten ia entre nodos 0, 2: -4.4e-10 - 2e-06 i

Transitorio 0.913043 0.869565 1 0.26087 0.00915332 -0.00869565 -0.00869565 -0.000457666 -0.00503432 0.00503432 -0.00869565 0 0.916824 0.831758 1 0.249527 0.0167846 -0.00831758 -0.00831758 -0.000839229 -0.00465486 0.00465486 -0.00831758 1e-05 0.920441 0.795595 1 0.238678 0.023098 -0.00795595 -0.00795595 -0.0011549 -0.00431161 -0.00431161 -0.00795595 2e-05 0.9239 0.761004 1 0.228301 0.028272 -0.00761004 -0.00761004 -0.0014136 -0.00400058 -0.00400058 -0.00761004 3e-05 0.927208 0.727916 1 0.218375 0.0324622 -0.00727916 -0.00727916 -0.00162311 -0.00371825 0.00371825 -0.00727916 4e-05 0.930373 0.696268 1 0.20888 0.0358048 -0.00696268 -0.00696268 -0.00179024 -0.00346151 0.00346151 -0.00696268 5e-05 0.9334 0.665995 1 0.199799 0.0384182 -0.00665995 -0.00665995 -0.00192091 -0.00322761 -0.00322761 -0.00665995 6e-05 0.936296 0.637039 1 0.191112 0.0404058 -0.00637039 -0.00637039 -0.00202029 -0.00301412 0.00301412 -0.00637039 7e-05 0.939066 0.609342 1 0.182803 0.0418578 -0.00609342 -0.00609342 -0.00209289 -0.00281889 0.00281889 -0.00609342 8e-05 0.941715 0.582849 1 0.174855 0.0428527 -0.00582849 -0.00582849 -0.00214263 -0.00264004 0.00264004 -0.00582849 9e-05 0.944249 0.557507 1 0.167252 0.0434585 -0.00557507 -0.00557507 -0.00217293 -0.00247587 0.00247587 -0.00557507 0.0001 0.946673 0.533268 1 0.15998 0.0437349 -0.00533268 -0.00533268 -0.00218674 -0.00232491 0.00232491 -0.00533268 0.00011 0.948992 0.510082 1 0.153025 0.0437332 -0.00510082 -0.00510082 -0.00218666 -0.00218583 0.00218583 -0.00510082 0.00012 0.95121 0.487905 1 0.146371 0.0434983 -0.00487905 -0.00487905 -0.00217492 -0.00205746 0.00205746 -0.00487905 0.00013 0.953331 0.466692 1 0.140007 0.043069 -0.00466692 -0.00466692 -0.00215345 -0.00193877 0.00193877 -0.00466692 0.00014 0.95536 0.446401 1 0.13392 0.0424787 -0.00446401 -0.00446401 -0.00212394 -0.00182883 -0.00182883 -0.00446401 0.00015 0.957301 0.426992 1 0.128098 0.0417567 -0.00426992 -0.00426992 -0.00208784 -0.00172682 0.00172682 -0.00426992 0.00016 0.959157 0.408427 1 0.122528 0.0409279 -0.00408427 -0.00408427 -0.0020464 -0.001632 -0.001632 -0.00408427 0.00017 0.960933 0.390669 1 0.117201 0.040014 -0.00390669 -0.00390669 -0.0020007 -0.00154374 -0.00154374 -0.00390669 0.00018 0.962632 0.373684 1 0.112105 0.0390335 -0.00373684 -0.00373684 -0.00195168 -0.00146143 0.00146143 -0.00373684 0.00019 0.964256 0.357437 1 0.107231 0.0380024 -0.00357437 -0.00357437 -0.00190012 -0.00138457 0.00138457 -0.00357437 0.0002 0.96581 0.341896 1 0.102569 0.0369344 -0.00341896 -0.00341896 -0.00184672 -0.00131269 0.00131269 -0.00341896 0.00021 0.967297 0.327031 1 0.0981093 0.035841 -0.00327031 -0.00327031 -0.00179205 -0.00124537 0.00124537 -0.00327031 0.00022 0.968719 0.312812 1 0.0938436 0.0347322 -0.00312812 -0.00312812 -0.00173661 -0.00118223 0.00118223 -0.00312812 0.00023

130

15. Cir uito on fuente de tensi贸n dependiente de tensi贸n.

0.970079 0.299212 1 0.0897635 0.0336165 -0.00299212 -0.00299212 -0.00168082 -0.00112294 0.00112294 -0.00299212 0.00024 0.97138 0.286202 1 0.0858607 0.0325008 -0.00286202 -0.00286202 -0.00162504 -0.0010672 0.0010672 -0.00286202 0.00025 0.972624 0.273759 1 0.0821276 0.0313911 -0.00273759 -0.00273759 -0.00156956 -0.00101473 0.00101473 -0.00273759 0.00026 0.973814 0.261856 1 0.0785569 0.0302925 -0.00261856 -0.00261856 -0.00151462 -0.000965288 -0.000965288 -0.00261856 0.00027 0.974953 0.250471 1 0.0751414 0.0292089 -0.00250471 -0.00250471 -0.00146044 -0.00091865 0.00091865 -0.00250471 0.00028 0.976042 0.239581 1 0.0718743 0.0281437 -0.00239581 -0.00239581 -0.00140719 -0.000874613 -0.000874613 -0.00239581 0.00029 0.977084 0.229165 1 0.0687494 0.0270997 -0.00229165 -0.00229165 -0.00135499 -0.000832993 -0.000832993 -0.00229165 0.0003 0.97808 0.219201 1 0.0657603 0.0260791 -0.00219201 -0.00219201 -0.00130395 -0.000793624 0.000793624 -0.00219201 0.00031 0.979033 0.20967 1 0.0629011 0.0250834 -0.0020967 -0.0020967 -0.00125417 -0.000756354 0.000756354 -0.0020967 0.00032 0.979945 0.200554 1 0.0601663 0.0241141 -0.00200554 -0.00200554 -0.00120571 -0.000721044 -0.000721044 -0.00200554 0.00033 0.980817 0.191835 1 0.0575504 0.023172 -0.00191835 -0.00191835 -0.0011586 -0.000687567 0.000687567 -0.00191835 0.00034 0.981651 0.183494 1 0.0550482 0.0222579 -0.00183494 -0.00183494 -0.00111289 -0.000655806 -0.000655806 -0.00183494 0.00035 0.982448 0.175516 1 0.0526548 0.021372 -0.00175516 -0.00175516 -0.0010686 -0.000625656 0.000625656 -0.00175516 0.00036 0.983212 0.167885 1 0.0503654 0.0205146 -0.00167885 -0.00167885 -0.00102573 -0.000597018 -0.000597018 -0.00167885 0.00037 0.983941 0.160585 1 0.0481756 0.0196856 -0.00160585 -0.00160585 -0.00098428 -0.000569801 -0.000569801 -0.00160585 0.00038 0.98464 0.153603 1 0.046081 0.018885 -0.00153603 -0.00153603 -0.000944248 -0.000543922 0.000543922 -0.00153603 0.00039 0.985307 0.146925 1 0.0440775 0.0181123 -0.00146925 -0.00146925 -0.000905616 -0.000519304 -0.000519304 -0.00146925 0.0004 0.985946 0.140537 1 0.0421611 0.0173673 -0.00140537 -0.00140537 -0.000868367 -0.000495875 -0.000495875 -0.00140537 0.00041 0.986557 0.134427 1 0.040328 0.0166495 -0.00134427 -0.00134427 -0.000832476 -0.00047357 0.00047357 -0.00134427 0.00042 0.987142 0.128582 1 0.0385746 0.0159583 -0.00128582 -0.00128582 -0.000797917 -0.000452326 -0.000452326 -0.00128582 0.00043 0.987701 0.122992 1 0.0368975 0.0152932 -0.00122992 -0.00122992 -0.00076466 -0.000432085 -0.000432085 -0.00122992 0.00044 0.988236 0.117644 1 0.0352932 0.0146534 -0.00117644 -0.00117644 -0.000732672 -0.000412796 -0.000412796 -0.00117644 0.00045 0.988747 0.112529 1 0.0337587 0.0140384 -0.00112529 -0.00112529 -0.000701921 -0.000394407 -0.000394407 -0.00112529 0.00046 0.989236 0.107637 1 0.032291 0.0134474 -0.00107637 -0.00107637 -0.000672371 -0.000376871 -0.000376871 -0.00107637 0.00047 0.989704 0.102957 1 0.030887 0.0128797 -0.00102957 -0.00102957 -0.000643987 -0.000360146 -0.000360146 -0.00102957 0.00048 0.990152 0.0984803 1 0.0295441 0.0123346 -0.000984803 -0.000984803 -0.000616732 -0.000344189 -0.000344189 -0.000984803 0.00049 0.99058 0.0941986 1 0.0282596 0.0118114 -0.000941986 -0.000941986 -0.000590572 -0.000328963 -0.000328963 -0.000941986 0.0005

15.2. Solu iones

131

0.99099 0.090103 1 0.0270309 0.0113094 -0.00090103 -0.00090103 -0.000565468 -0.000314431 -0.000314431 -0.00090103 0.00051 0.991381 0.0861855 1 0.0258556 0.0108277 -0.000861855 -0.000861855 -0.000541385 -0.000300559 -0.000300559 -0.000861855 0.00052 0.991756 0.0824383 1 0.0247315 0.0103658 -0.000824383 -0.000824383 -0.000518288 -0.000287315 -0.000287315 -0.000824383 0.00053 0.992115 0.078854 1 0.0236562 0.00992281 -0.00078854 -0.00078854 -0.000496141 -0.000274668 -0.000274668 -0.00078854 0.00054 0.992457 0.0754256 1 0.0226277 0.00949817 -0.000754256 -0.000754256 -0.000474909 -0.00026259 -0.00026259 -0.000754256 0.00055 0.992785 0.0721462 1 0.0216439 0.00909117 -0.000721462 -0.000721462 -0.000454558 -0.000251054 -0.000251054 -0.000721462 0.00056 0.993099 0.0690094 1 0.0207028 0.00870112 -0.000690094 -0.000690094 -0.000435056 -0.000240034 -0.000240034 -0.000690094 0.00057 0.993399 0.066009 1 0.0198027 0.00832739 -0.00066009 -0.00066009 -0.00041637 -0.000229506 -0.000229506 -0.00066009 0.00058 0.993686 0.063139 1 0.0189417 0.00796935 -0.00063139 -0.00063139 -0.000398468 -0.000219447 -0.000219447 -0.00063139 0.00059 0.993961 0.0603939 1 0.0181182 0.00762639 -0.000603939 -0.000603939 -0.000381319 -0.000209835 -0.000209835 -0.000603939 0.0006 0.994223 0.057768 1 0.0173304 0.0072979 -0.00057768 -0.00057768 -0.000364895 -0.00020065 -0.00020065 -0.00057768 0.00061 0.994474 0.0552564 1 0.0165769 0.00698331 -0.000552564 -0.000552564 -0.000349166 -0.000191872 -0.000191872 -0.000552564 0.00062 0.994715 0.0528539 1 0.0158562 0.00668207 -0.000528539 -0.000528539 -0.000334103 -0.000183482 -0.000183482 -0.000528539 0.00063 0.994944 0.0505559 1 0.0151668 0.00639363 -0.000505559 -0.000505559 -0.000319682 -0.000175463 -0.000175463 -0.000505559 0.00064 0.995164 0.0483579 1 0.0145074 0.00611748 -0.000483579 -0.000483579 -0.000305874 -0.000167798 -0.000167798 -0.000483579 0.00065 0.995374 0.0462553 1 0.0138766 0.00585311 -0.000462553 -0.000462553 -0.000292655 -0.00016047 -0.00016047 -0.000462553 0.00066 0.995576 0.0442442 1 0.0132733 0.00560003 -0.000442442 -0.000442442 -0.000280002 -0.000153465 -0.000153465 -0.000442442 0.00067 0.995768 0.0423206 1 0.0126962 0.00535779 -0.000423206 -0.000423206 -0.000267889 -0.000146768 -0.000146768 -0.000423206 0.00068 0.995952 0.0404806 1 0.0121442 0.00512593 -0.000404806 -0.000404806 -0.000256296 -0.000140365 -0.000140365 -0.000404806 0.00069 0.996128 0.0387205 1 0.0116162 0.00490401 -0.000387205 -0.000387205 -0.000245201 -0.000134243 -0.000134243 -0.000387205 0.0007 0.996296 0.037037 1 0.0111111 0.00469163 -0.00037037 -0.00037037 -0.000234581 -0.00012839 -0.00012839 -0.00037037 0.00071 0.996457 0.0354267 1 0.010628 0.00448838 -0.000354267 -0.000354267 -0.000224419 -0.000122793 -0.000122793 -0.000354267 0.00072 0.996611 0.0338864 1 0.0101659 0.00429387 -0.000338864 -0.000338864 -0.000214694 -0.000117441 -0.000117441 -0.000338864 0.00073 0.996759 0.0324131 1 0.00972393 0.00410774 -0.000324131 -0.000324131 -0.000205387 -0.000112324 -0.000112324 -0.000324131 0.00074 0.9969 0.0310038 1 0.00930115 0.00392964 -0.000310038 -0.000310038 -0.000196482 -0.00010743 -0.00010743 -0.000310038 0.00075 0.997034 0.0296558 1 0.00889675 0.00375922 -0.000296558 -0.000296558 -0.000187961 -0.000102751 -0.000102751 -0.000296558 0.00076 0.997163 0.0283665 1 0.00850994 0.00359616 -0.000283665 -0.000283665 -0.000179808 -9.82757e05 -9.82757e-05 -0.000283665 0.00077

132

15. Cir uito on fuente de tensi贸n dependiente de tensi贸n.

0.997287 0.0271331 1 0.00813994 0.00344013 -0.000271331 -0.000271331 -0.000172007 -9.39961e05 -9.39961e-05 -0.000271331 0.00078 0.997405 0.0259534 1 0.00778603 0.00329086 -0.000259534 -0.000259534 -0.000164543 -8.99035e05 -8.99035e-05 -0.000259534 0.00079 0.997517 0.024825 1 0.00744751 0.00314803 -0.00024825 -0.00024825 -0.000157402 -8.59895e-05 -8.59895e-05 -0.00024825 0.0008 0.997625 0.0237457 1 0.0071237 0.00301139 -0.000237457 -0.000237457 -0.000150569 -8.22464e05 -8.22464e-05 -0.000237457 0.00081 0.997729 0.0227133 1 0.00681398 0.00288065 -0.000227133 -0.000227133 -0.000144033 -7.86665e05 -7.86665e-05 -0.000227133 0.00082 0.997827 0.0217257 1 0.00651772 0.00275558 -0.000217257 -0.000217257 -0.000137779 -7.52427e05 -7.52427e-05 -0.000217257 0.00083 0.997922 0.0207811 1 0.00623434 0.00263593 -0.000207811 -0.000207811 -0.000131796 -7.19683e05 -7.19683e-05 -0.000207811 0.00084 0.998012 0.0198776 1 0.00596328 0.00252145 -0.000198776 -0.000198776 -0.000126073 -6.88365e05 -6.88365e-05 -0.000198776 0.00085 0.998099 0.0190134 1 0.00570401 0.00241194 -0.000190134 -0.000190134 -0.000120597 -6.58413e05 -6.58413e-05 -0.000190134 0.00086 0.998181 0.0181867 1 0.00545601 0.00230718 -0.000181867 -0.000181867 -0.000115359 -6.29766e05 -6.29766e-05 -0.000181867 0.00087 0.99826 0.017396 1 0.00521879 0.00220695 -0.00017396 -0.00017396 -0.000110348 -6.02367e-05 -6.02367e-05 -0.00017396 0.00088 0.998336 0.0166396 1 0.00499189 0.00211108 -0.000166396 -0.000166396 -0.000105554 -5.76161e05 -5.76161e-05 -0.000166396 0.00089 0.998408 0.0159162 1 0.00477485 0.00201936 -0.000159162 -0.000159162 -0.000100968 -5.51097e05 -5.51097e-05 -0.000159162 0.000900001 0.998478 0.0152241 1 0.00456724 0.00193162 -0.000152241 -0.000152241 -9.65812e-05 -5.27124e05 -5.27124e-05 -0.000152241 0.000910001 0.998544 0.0145622 1 0.00436867 0.00184769 -0.000145622 -0.000145622 -9.23847e-05 -5.04195e05 -5.04195e-05 -0.000145622 0.000920001 0.998607 0.0139291 1 0.00417873 0.00176741 -0.000139291 -0.000139291 -8.83703e-05 -4.82264e05 -4.82264e-05 -0.000139291 0.000930001 0.998668 0.0133235 1 0.00399704 0.0016906 -0.000133235 -0.000133235 -8.45302e-05 -4.61288e05 -4.61288e-05 -0.000133235 0.000940001 0.998726 0.0127442 1 0.00382326 0.00161714 -0.000127442 -0.000127442 -8.08568e-05 -4.41225e05 -4.41225e-05 -0.000127442 0.000950001 0.998781 0.0121901 1 0.00365703 0.00154686 -0.000121901 -0.000121901 -7.73428e-05 -4.22035e05 -4.22035e-05 -0.000121901 0.000960001 0.998834 0.0116601 1 0.00349803 0.00147963 -0.000116601 -0.000116601 -7.39815e-05 -4.0368e05 -4.0368e-05 -0.000116601 0.000970001 0.998885 0.0111531 1 0.00334594 0.00141532 -0.000111531 -0.000111531 -7.07661e-05 -3.86124e05 -3.86124e-05 -0.000111531 0.000980001 0.998933 0.0106682 1 0.00320046 0.00135381 -0.000106682 -0.000106682 -6.76904e-05 -3.69331e05 -3.69331e-05 -0.000106682 0.000990001

set terminal png set output ' /home/ ayose / Programa ion /AVALON/debug / s r / o l e i o n / set set set set set

G r a f i o s / o l e i o n p r o b l e m a s /15/ e j e m p l o 0 1 5 _ g r af i a . png ' en oding iso_8859_1

grid autos ale key bottom r i g h t t i t l e ' V a r i a b l e s ' box t i t l e ' Grafi ado por d e f e t o de l a s s o l u i o n e s d e l i r u i t o '

15.2. Solu iones

133

plot ' /home/ ayose / Programa ion /AVALON/debug / s r / o l e i o n / G r a f i o s / o l e i o n p r o b l e m a s /15/ ejemplo015_x_trans . data ' using 1 2 : 1 t i t l e 'V en nodo 1 ' with l i n e s , ' /home/ ayose / Programa ion /AVALON/debug / s r / o l e i o n / G r a f i o s / o l e i o n p r o b l e m a s /15/ ejemplo015_x_trans . data '

using 1 2 : 2 t i t l e 'V en nodo 2 ' with l i n e s , ' /home/ ayose /

Programa ion /AVALON/debug / s r / o l e i o n / G r a f i o s / o l e i o n p r o b l e m a s /15/ ejemplo015_x_trans . data ' using 1 2 : 3 t i t l e 'V en nodo 3 ' with l i n e s , ' /home/ ayose / Programa ion /AVALON/debug / s r / o l e i o n / G r a f i o s / o l e i o n p r o b l e m a s /15/ ejemplo015_x_trans . data ' using 1 2 : 4 t i t l e 'V en nodo 4 ' with l i n e s , ' /home/ ayose / Programa ion /AVALON/ debug / s r / o l e i o n / G r a f i o s / o l e i o n p r o b l e m a s /15/ ejemplo015_x_trans . data ' using 1 2 : 5 t i t l e 'V en nodo 5 ' with l i n e s , ' /home/ ayose / Programa ion /AVALON/debug / s r / o l e i o n / G r a f i o s / o l e i o n p r o b l e m a s /15/ ejemplo015_x_trans . data ' using 1 2 : 6 t i t l e ' I R e s i s t e n i a e n t r e nodos 1 , 3 ' with l i n e s , ' /home/ ayose / Programa ion /AVALON/debug / s r / o l e i o n / G r a f i o s / o l e i o n p r o b l e m a s /15/ ejemplo015_x_trans . data ' using 1 2 : 7 t i t l e ' I de Fuente t e n s i o n e n t r e nodos 3 , 0 ' with l i n e s , ' /home/ ayose / Programa ion /AVALON/ debug / s r / o l e i o n / G r a f i o s / o l e i o n p r o b l e m a s /15/ ejemplo015_x_trans . data ' using 1 2 : 8 t i t l e ' I R e s i s t e n i a e n t r e nodos 0 , 5 ' with l i n e s , ' /home/ ayose / Programa ion /AVALON/debug / s r / o l e i o n / G r a f i o s / o l e i o n p r o b l e m a s /15/ ejemplo015_x_trans . data ' using 1 2 : 9 t i t l e ' I R e s i s t e n i a e n t r e nodos 5 , 0 ' with l i n e s , ' / home/ ayose / Programa ion /AVALON/debug / s r / o l e i o n / G r a f i o s / o l e i o n p r o b l e m a s /15/ ejemplo015_x_trans . data ' using 1 2 : 1 0 t i t l e ' I de Fuente de V d e p e n d i e n t e de V e n t r e nodos 3 , 1 ' with l i n e s , ' / home/ ayose / Programa ion /AVALON/debug / s r / o l e i o n / G r a f i o s / o l e i o n p r o b l e m a s /15/ ejemplo015_x_trans . data ' using 1 2 : 1 1 t i t l e ' I R e s i s t e n i a e n t r e nodos 0 , 2 ' with l i n e s

Grรก o de salida.

134

15. Cir uito on fuente de tensiรณn dependiente de tensiรณn.

Veรกmos las variables al uladas on mayor detalle. Empezaremos por las tensiones en los nodos. Tensiรณn en nodo 1

Tensiรณn en nodo 2

15.2. Solu iones

Tensi贸n en nodo 3

Tensi贸n en nodo 4

135

136

Tensi贸n en nodo 5

Intensidad en la malla 1

15. Cir uito on fuente de tensi贸n dependiente de tensi贸n.

15.2. Solu iones

Intensidad de la malla 2 y 3

137

Capítulo 16 Cir uito on fuente de intensidad dependiente de tensión.

La fuente de intensidad dependiente de tensión en el método nodal no se trabaja omo un elemento bipuerto en sí, pertene e a los elementos del grupo A1 por lo que puede expresarse en fun ión de admitan ia y si se desea añadir una e ua ión adi ional. 1

1 2 0

16.1.

Datos Generales.

Ar hivo *.sp ∗ SPICE i r u i t <ejemplo016> from XCir uit v3 . 6 rev 135

1 3 1 8 2 4

1 1 2 1 1 1

0 0 0 0 0 0

2 2 2 1 1 2

0 0 4 1 2 1

2 4 3 2 1 0

0 0 0 3 0 0

10 0 ,0001 50 0 0 2 0 ,0002 1 rho f a b A B C D

. end Tipo de análisis realizado Análisis esta ionario Análisis transitorio

Datos generales del ir uito Elementos del Cto: 6 EA: 0 Nodos: 4 A2: 4 139

⊠ ⊠

140

16. Cir uito on fuente de intensidad dependiente de tensión.

No nulos: 19 Densidad: 0.296875 Dispersion: 0.7031

Los valores dados al ir uito son: Elemento Resisten ia entre nodos 2, 0 Bobina entre nodos 0, 4 Resisten ia entre nodos 4, 3 Fuente de I dependiente de V Condensador entre nodos 2, 1 Fuente de tensión

Magnitud 10 Ω 0, 0001 H 50 Ω 2 0, 0002 F 1V

Matriz T. row 0: (0, row 1: (0, row 2: (0, row 3: (6, row 4: (0, row 5: (1, row 6: (3, row 7: (2,

16.2.

16.2.1.

0 + 0.0002 i) (1, -0 - 0.0002 i) (4, 1) -0 - 0.0002 i) (1, 0 + 0.0002 i) (5, -1) 2) (1, -2) (7, -1) -1) (7, 1) 1) -1) (5, -10) -1) (6, -0 - 0.0001 i) -1) (3, 1) (7, -50)

Solu iones

Primer análisis Tiempo Ini ial Tiempo Final Paso de Tiempo Theta

0 0, 01 0, 00005

1 (Euler)

Esta ionario Resultados sistema esta ionario: Tensión en nodo 1: 1 - 8.67776e-19 i Tensión en nodo 2: 3.99998e-06 + 0.00199999 i Tensión en nodo 3: -99.9996 + 0.199799 i Tensión en nodo 4: -3.99998e-07 - 0.000199999 i I de Fuente tension entre nodos 1, 0: -3.99998e-07 - 0.000199999 i I Resisten ia entre nodos 0, 2: -3.99998e-07 - 0.000199999 i I de Bobina entre nodos 0, 4: 1.99999 - 0.00399998 i I Resisten ia entre nodos 4, 3: 1.99999 - 0.00399998 i

16.2. Solu iones

Transitorio 1 0.952381 -104.857 -0.0952381 -0.0952381 -0.0952381 2.09524 2.09524 0 1 -0.0453515 -104.531 0.00453515 0.00453515 0.00453515 2.0907 2.0907 0.0001 1 -0.0431919 -104.315 0.00431919 0.00431919 0.00431919 2.08638 2.08638 0.0002 1 -0.0411351 -104.109 0.00411351 0.00411351 0.00411351 2.08227 2.08227 0.0003 1 -0.0391763 -103.914 0.00391763 0.00391763 0.00391763 2.07835 2.07835 0.0004 1 -0.0373108 -103.727 0.00373108 0.00373108 0.00373108 2.07462 2.07462 0.0005 1 -0.0355341 -103.55 0.00355341 0.00355341 0.00355341 2.07107 2.07107 0.0006 1 -0.033842 -103.381 0.0033842 0.0033842 0.0033842 2.06768 2.06768 0.0007 1 -0.0322304 -103.22 0.00322304 0.00322304 0.00322304 2.06446 2.06446 0.0008 1 -0.0306957 -103.066 0.00306957 0.00306957 0.00306957 2.06139 2.06139 0.0009 1 -0.029234 -102.92 0.0029234 0.0029234 0.0029234 2.05847 2.05847 0.001 1 -0.0278419 -102.781 0.00278419 0.00278419 0.00278419 2.05568 2.05568 0.0011 1 -0.0265161 -102.649 0.00265161 0.00265161 0.00265161 2.05303 2.05303 0.0012 1 -0.0252534 -102.523 0.00252534 0.00252534 0.00252534 2.05051 2.05051 0.0013 1 -0.0240509 -102.403 0.00240509 0.00240509 0.00240509 2.0481 2.0481 0.0014 1 -0.0229056 -102.288 0.00229056 0.00229056 0.00229056 2.04581 2.04581 0.0015 1 -0.0218148 -102.179 0.00218148 0.00218148 0.00218148 2.04363 2.04363 0.0016 1 -0.020776 -102.076 0.0020776 0.0020776 0.0020776 2.04155 2.04155 0.0017 1 -0.0197867 -101.977 0.00197867 0.00197867 0.00197867 2.03957 2.03957 0.0018 1 -0.0188445 -101.883 0.00188445 0.00188445 0.00188445 2.03769 2.03769 0.0019 1 -0.0179471 -101.793 0.00179471 0.00179471 0.00179471 2.03589 2.03589 0.002 1 -0.0170925 -101.708 0.00170925 0.00170925 0.00170925 2.03418 2.03418 0.0021 1 -0.0162786 -101.626 0.00162786 0.00162786 0.00162786 2.03256 2.03256 0.0022 1 -0.0155034 -101.549 0.00155034 0.00155034 0.00155034 2.03101 2.03101 0.0023 1 -0.0147651 -101.475 0.00147651 0.00147651 0.00147651 2.02953 2.02953 0.0024 1 -0.014062 -101.405 0.0014062 0.0014062 0.0014062 2.02812 2.02812 0.0025 1 -0.0133924 -101.338 0.00133924 0.00133924 0.00133924 2.02678 2.02678 0.0026 1 -0.0127547 -101.274 0.00127547 0.00127547 0.00127547 2.02551 2.02551 0.0027 1 -0.0121473 -101.214 0.00121473 0.00121473 0.00121473 2.02429 2.02429 0.0028 1 -0.0115689 -101.156 0.00115689 0.00115689 0.00115689 2.02314 2.02314 0.0029 1 -0.011018 -101.101 0.0011018 0.0011018 0.0011018 2.02204 2.02204 0.003 1 -0.0104933 -101.048 0.00104933 0.00104933 0.00104933 2.02099 2.02099 0.0031 1 -0.00999363 -100.998 0.000999363 0.000999363 0.000999363 2.01999 2.01999 0.0032 1 -0.00951774 -100.951 0.000951774 0.000951774 0.000951774 2.01904 2.01904 0.0033 1 -0.00906451 -100.906 0.000906451 0.000906451 0.000906451 2.01813 2.01813 0.0034 1 -0.00863287 -100.862 0.000863287 0.000863287 0.000863287 2.01727 2.01727 0.0035 1 -0.00822178 -100.821 0.000822178 0.000822178 0.000822178 2.01644 2.01644 0.0036 1 -0.00783027 -100.782 0.000783027 0.000783027 0.000783027 2.01566 2.01566 0.0037 1 -0.0074574 -100.745 0.00074574 0.00074574 0.00074574 2.01491 2.01491 0.0038 1 -0.00710228 -100.71 0.000710228 0.000710228 0.000710228 2.0142 2.0142 0.0039 1 -0.00676408 -100.676 0.000676408 0.000676408 0.000676408 2.01353 2.01353 0.004 1 -0.00644198 -100.644 0.000644198 0.000644198 0.000644198 2.01288 2.01288 0.0041 1 -0.00613522 -100.613 0.000613522 0.000613522 0.000613522 2.01227 2.01227 0.0042 1 -0.00584307 -100.584 0.000584307 0.000584307 0.000584307 2.01169 2.01169 0.0043 1 -0.00556483 -100.556 0.000556483 0.000556483 0.000556483 2.01113 2.01113 0.0044 1 -0.00529983 -100.529 0.000529983 0.000529983 0.000529983 2.0106 2.0106 0.0045 1 -0.00504746 -100.504 0.000504746 0.000504746 0.000504746 2.01009 2.01009 0.0046 1 -0.00480711 -100.48 0.000480711 0.000480711 0.000480711 2.00961 2.00961 0.0047 1 -0.0045782 -100.457 0.00045782 0.00045782 0.00045782 2.00916 2.00916 0.0048 1 -0.00436019 -100.436 0.000436019 0.000436019 0.000436019 2.00872 2.00872 0.0049 1 -0.00415256 -100.415 0.000415256 0.000415256 0.000415256 2.00831 2.00831 0.005 1 -0.00395482 -100.395 0.000395482 0.000395482 0.000395482 2.00791 2.00791 0.0051

141

142

16. Cir uito on fuente de intensidad dependiente de tensi贸n.

1 -0.00376649 -100.376 0.000376649 0.000376649 0.000376649 2.00753 2.00753 0.0052 1 -0.00358714 -100.358 0.000358714 0.000358714 0.000358714 2.00717 2.00717 0.0053 1 -0.00341632 -100.341 0.000341632 0.000341632 0.000341632 2.00683 2.00683 0.0054 1 -0.00325364 -100.325 0.000325364 0.000325364 0.000325364 2.00651 2.00651 0.0055 1 -0.0030987 -100.31 0.00030987 0.00030987 0.00030987 2.0062 2.0062 0.0056 1 -0.00295115 -100.295 0.000295115 0.000295115 0.000295115 2.0059 2.0059 0.0057 1 -0.00281061 -100.281 0.000281061 0.000281061 0.000281061 2.00562 2.00562 0.0058 1 -0.00267678 -100.267 0.000267678 0.000267678 0.000267678 2.00535 2.00535 0.0059 1 -0.00254931 -100.255 0.000254931 0.000254931 0.000254931 2.0051 2.0051 0.006 1 -0.00242791 -100.243 0.000242791 0.000242791 0.000242791 2.00486 2.00486 0.0061 1 -0.0023123 -100.231 0.00023123 0.00023123 0.00023123 2.00462 2.00462 0.0062 1 -0.00220219 -100.22 0.000220219 0.000220219 0.000220219 2.0044 2.0044 0.0063 1 -0.00209732 -100.21 0.000209732 0.000209732 0.000209732 2.00419 2.00419 0.0064 1 -0.00199745 -100.2 0.000199745 0.000199745 0.000199745 2.00399 2.00399 0.0065 1 -0.00190233 -100.19 0.000190233 0.000190233 0.000190233 2.0038 2.0038 0.0066 1 -0.00181175 -100.181 0.000181175 0.000181175 0.000181175 2.00362 2.00362 0.0067 1 -0.00172547 -100.172 0.000172547 0.000172547 0.000172547 2.00345 2.00345 0.0068 1 -0.00164331 -100.164 0.000164331 0.000164331 0.000164331 2.00329 2.00329 0.0069 1 -0.00156506 -100.156 0.000156506 0.000156506 0.000156506 2.00313 2.00313 0.007 1 -0.00149053 -100.149 0.000149053 0.000149053 0.000149053 2.00298 2.00298 0.0071 1 -0.00141955 -100.142 0.000141955 0.000141955 0.000141955 2.00284 2.00284 0.0072 1 -0.00135195 -100.135 0.000135195 0.000135195 0.000135195 2.0027 2.0027 0.0073 1 -0.00128758 -100.129 0.000128758 0.000128758 0.000128758 2.00258 2.00258 0.00739999 1 -0.00122626 -100.123 0.000122626 0.000122626 0.000122626 2.00245 2.00245 0.00749999 1 -0.00116787 -100.117 0.000116787 0.000116787 0.000116787 2.00234 2.00234 0.00759999 1 -0.00111226 -100.111 0.000111226 0.000111226 0.000111226 2.00222 2.00222 0.00769999 1 -0.00105929 -100.106 0.000105929 0.000105929 0.000105929 2.00212 2.00212 0.00779999 1 -0.00100885 -100.101 0.000100885 0.000100885 0.000100885 2.00202 2.00202 0.00789999 1 -0.000960808 -100.096 9.60808e-05 9.60808e-05 9.60808e-05 2.00192 2.00192 0.00799999 1 -0.000915056 -100.091 9.15056e-05 9.15056e-05 9.15056e-05 2.00183 2.00183 0.00809999 1 -0.000871482 -100.087 8.71482e-05 8.71482e-05 8.71482e-05 2.00174 2.00174 0.00819999 1 -0.000829982 -100.083 8.29982e-05 8.29982e-05 8.29982e-05 2.00166 2.00166 0.00829999 1 -0.000790459 -100.079 7.90459e-05 7.90459e-05 7.90459e-05 2.00158 2.00158 0.00839999 1 -0.000752819 -100.075 7.52819e-05 7.52819e-05 7.52819e-05 2.00151 2.00151 0.00849999 1 -0.00071697 -100.072 7.1697e-05 7.1697e-05 7.1697e-05 2.00143 2.00143 0.00859999 1 -0.000682829 -100.068 6.82829e-05 6.82829e-05 6.82829e-05 2.00137 2.00137 0.00869999 1 -0.000650313 -100.065 6.50313e-05 6.50313e-05 6.50313e-05 2.0013 2.0013 0.00879999 1 -0.000619346 -100.062 6.19346e-05 6.19346e-05 6.19346e-05 2.00124 2.00124 0.00889999 1 -0.000589853 -100.059 5.89853e-05 5.89853e-05 5.89853e-05 2.00118 2.00118 0.00899999 1 -0.000561765 -100.056 5.61765e-05 5.61765e-05 5.61765e-05 2.00112 2.00112 0.00909999 1 -0.000535014 -100.053 5.35014e-05 5.35014e-05 5.35014e-05 2.00107 2.00107 0.00919999 1 -0.000509537 -100.051 5.09537e-05 5.09537e-05 5.09537e-05 2.00102 2.00102 0.00929999 1 -0.000485274 -100.048 4.85274e-05 4.85274e-05 4.85274e-05 2.00097 2.00097 0.00939999 1 -0.000462165 -100.046 4.62165e-05 4.62165e-05 4.62165e-05 2.00092 2.00092 0.00949999 1 -0.000440157 -100.044 4.40157e-05 4.40157e-05 4.40157e-05 2.00088 2.00088 0.00959999 1 -0.000419198 -100.042 4.19198e-05 4.19198e-05 4.19198e-05 2.00084 2.00084 0.00969999 1 -0.000399236 -100.04 3.99236e-05 3.99236e-05 3.99236e-05 2.0008 2.0008 0.00979999 1 -0.000380224 -100.038 3.80224e-05 3.80224e-05 3.80224e-05 2.00076 2.00076 0.0098999

set terminal png set output ' /home/ ayose / Programa ion /AVALON/debug / s r / o l e i o n / G r a f i o s / o l e i o n p r o b l e m a s /16/ e j e m p l o 0 1 6 _ g r af i a . png '

set en oding iso_8859_1 set grid

16.2. Solu iones

143

set autos ale set key bottom r i g h t t i t l e ' V a r i a b l e s ' box set t i t l e ' Grafi ado por d e f e t o de l a s s o l u i o n e s d e l i r u i t o ' plot ' /home/ ayose / Programa ion /AVALON/debug / s r / o l e i o n / G r a f i o s / o l e i o n p r o b l e m a s /16/ ejemplo016_x_trans . data ' using 9 : 1 t i t l e 'V en nodo 1 ' with l i n e s , ' /home/ ayose / Programa ion /AVALON/debug / s r / o l e i o n / G r a f i o s / o l e i o n p r o b l e m a s /16/ ejemplo016_x_trans . data '

using 9 : 2 t i t l e 'V en nodo 2 ' with l i n e s , ' /home/ ayose / Programa ion

/AVALON/debug / s r / o l e i o n / G r a f i o s / o l e i o n p r o b l e m a s /16/ ejemplo016_x_trans . data ' using 9 : 3 t i t l e 'V en nodo 3 ' with l i n e s , ' /home/ ayose / Programa ion /AVALON/debug / s r / o l e i o n / G r a f i o s / o l e i o n p r o b l e m a s /16/ ejemplo016_x_trans . data ' using 9 : 4 t i t l e 'V en nodo 4 ' with l i n e s , ' /home/ ayose / Programa ion /AVALON/debug / s r / o l e i o n / G r a f i o s / o l e i o n p r o b l e m a s /16/ ejemplo016_x_trans . data ' using 9 : 5 t i t l e ' I de Fuente t e n s i o n e n t r e nodos 1 , 0 ' with l i n e s , ' /home/ ayose / Programa ion /AVALON/debug / s r / o l e i o n / G r a f i o s / o l e i o n p r o b l e m a s /16/ ejemplo016_x_trans . data ' using 9 : 6 t i t l e ' I R e s i s t e n i a e n t r e nodos 0 , 2 ' with l i n e s , ' /home/ ayose / Programa ion /AVALON/debug / s r / o l e i o n / G r a f i o s / o l e i o n p r o b l e m a s /16/ ejemplo016_x_trans . data ' using 9 : 7 t i t l e ' I de Bobina e n t r e nodos 0 , 4 ' with l i n e s , ' /home/ ayose / Programa ion /AVALON/debug / s r / o l e i o n / G r a f i o s / o l e i o n p r o b l e m a s /16/ ejemplo016_x_trans . data ' using 9 : 8 t i t l e ' I R e s i s t e n i a e n t r e nodos 4 , 3 ' with l i n e s

Gr谩 o de salida.

Ve谩mos las variables por separado para apre iar mejor su evolu i贸n temporal Tensi贸n en nodo 1 y 2

144

16. Cir uito on fuente de intensidad dependiente de tensi贸n.

Tensi贸n en nodo 3 y4

Intensidad de la malla 1

16.2. Solu iones

Intensidad de la malla 2

145

Capítulo 17 Cir uito on transformador.

El transformador es también un elemento biterminal implementado en el programa de resolu ión. Se pro ederá a analizar un ir uitos on este elemento tan ara terísti o en los ál ulos de espe ialidad. A su vez aprove haremos este ir uito para usar un elemento que aún no se había utilizado en ejemplos anteriores la ondu tan ia. 1

17.1.

Datos Generales.

Ar hivo *.sp ∗ SPICE i r u i t <ejemplo017> from XCir uit v3 . 6 rev 135

4 1 0 2 0 1 1 Cte 0 50 a b 1 B C D 0 1 0 1 0 2 0 10 7 1 0 2 1 0 2 0 0 0 ,5 . end Tipo de análisis realizado Análisis esta ionario Análisis transitorio

Datos generales del ir uito Elementos del Cto: 3 EA: 0 Nodos: 2 A2: 3 No nulos: 9 Densidad: 0.36 Dispersion: 0.64 147

⊠ ⊠

148

17. Cir uito on transformador.

Los valores dados al ir uito son: Elemento Condu tan ia entre nodos 2, 0 Transformador Fuente de tensión alterna

Magnitud 10 Ω−1 a = 0, 5 sin(2π · 50) V

Matriz T. row 0: (2, row 1: (1, row 2: (0, row 3: (2, row 4: (0,

17.2.

17.2.1.

1) (4, -1) 10) (3, 1) 1) (1, -0.5) 1) (3, -2) -1)

Solu iones

Primer análisis Tiempo Ini ial Tiempo Final Paso de Tiempo Theta

0 0, 04 0, 0004

1 (Euler)

Esta ionario Resultados sistema esta ionario: Tensión en nodo 1: -1 Tensión en nodo 2: -2 I de Trafo entre nodos 1, 0: 40 I de Trafo entre nodos 2, 0: 20 I de Fuente tension entre nodos 0, 1: 40

Transitorio -0.125333 -0.250666 5.01333 2.50666 5.01333 0 -0.24869 -0.49738 9.9476 4.9738 9.9476 0.0004 -0.368125 -0.736249 14.725 7.36249 14.725 0.0008 -0.481754 -0.963507 19.2701 9.63507 19.2701 0.0012 -0.587785 -1.17557 23.5114 11.7557 23.5114 0.0016 -0.684547 -1.36909 27.3819 13.6909 27.3819 0.002 -0.770513 -1.54103 30.8205 15.4103 30.8205 0.0024 -0.844328 -1.68866 33.7731 16.8866 33.7731 0.0028 -0.904827 -1.80965 36.1931 18.0965 36.1931 0.0032 -0.951056 -1.90211 38.0423 19.0211 38.0423 0.0036 -0.982287 -1.96457 39.2915 19.6457 39.2915 0.004 -0.998027 -1.99605 39.9211 19.9605 39.9211 0.0044 -0.998027 -1.99605 39.9211 19.9605 39.9211 0.0048

17.2. Solu iones

-0.982287 -1.96457 39.2915 19.6457 39.2915 0.0052 -0.951057 -1.90211 38.0423 19.0211 38.0423 0.0056 -0.904827 -1.80965 36.1931 18.0965 36.1931 0.006 -0.844328 -1.68866 33.7731 16.8866 33.7731 0.0064 -0.770513 -1.54103 30.8205 15.4103 30.8205 0.0068 -0.684547 -1.36909 27.3819 13.6909 27.3819 0.0072 -0.587785 -1.17557 23.5114 11.7557 23.5114 0.0076 -0.481754 -0.963507 19.2701 9.63507 19.2701 0.008 -0.368125 -0.736249 14.725 7.36249 14.725 0.0084 -0.24869 -0.49738 9.9476 4.9738 9.9476 0.0088 -0.125333 -0.250667 5.01333 2.50667 5.01333 0.0092 -7.93633e-08 -1.58727e-07 3.17453e-06 1.58727e-06 3.17453e-06 0.0096 0.125333 0.250666 -5.01333 -2.50666 -5.01333 0.01 0.24869 0.49738 -9.94759 -4.9738 -9.94759 0.0104 0.368124 0.736249 -14.725 -7.36249 -14.725 0.0108 0.481754 0.963507 -19.2701 -9.63507 -19.2701 0.0112 0.587785 1.17557 -23.5114 -11.7557 -23.5114 0.0116 0.684547 1.36909 -27.3819 -13.6909 -27.3819 0.012 0.770513 1.54103 -30.8205 -15.4103 -30.8205 0.0124 0.844328 1.68866 -33.7731 -16.8866 -33.7731 0.0128 0.904827 1.80965 -36.1931 -18.0965 -36.1931 0.0132 0.951056 1.90211 -38.0423 -19.0211 -38.0423 0.0136 0.982287 1.96457 -39.2915 -19.6457 -39.2915 0.014 0.998027 1.99605 -39.9211 -19.9605 -39.9211 0.0144 0.998027 1.99605 -39.9211 -19.9605 -39.9211 0.0148 0.982287 1.96457 -39.2915 -19.6457 -39.2915 0.0152 0.951057 1.90211 -38.0423 -19.0211 -38.0423 0.0156 0.904827 1.80965 -36.1931 -18.0965 -36.1931 0.016 0.844328 1.68866 -33.7731 -16.8866 -33.7731 0.0164 0.770513 1.54103 -30.8205 -15.4103 -30.8205 0.0168 0.684547 1.36909 -27.3819 -13.6909 -27.3819 0.0172 0.587785 1.17557 -23.5114 -11.7557 -23.5114 0.0176 0.481754 0.963508 -19.2702 -9.63508 -19.2702 0.018 0.368125 0.736249 -14.725 -7.36249 -14.725 0.0184 0.24869 0.49738 -9.9476 -4.9738 -9.9476 0.0188 0.125333 0.250667 -5.01334 -2.50667 -5.01334 0.0192 1.58727e-07 3.17453e-07 -6.34906e-06 -3.17453e-06 -6.34906e-06 0.0196 -0.125333 -0.250666 5.01332 2.50666 5.01332 0.02 -0.24869 -0.497379 9.94759 4.97379 9.94759 0.0204 -0.368124 -0.736249 14.725 7.36249 14.725 0.0208 -0.481754 -0.963507 19.2701 9.63507 19.2701 0.0212 -0.587785 -1.17557 23.5114 11.7557 23.5114 0.0216 -0.684547 -1.36909 27.3819 13.6909 27.3819 0.022 -0.770513 -1.54103 30.8205 15.4103 30.8205 0.0224 -0.844328 -1.68866 33.7731 16.8866 33.7731 0.0228 -0.904827 -1.80965 36.1931 18.0965 36.1931 0.0232 -0.951056 -1.90211 38.0423 19.0211 38.0423 0.0236 -0.982287 -1.96457 39.2915 19.6457 39.2915 0.024 -0.998027 -1.99605 39.9211 19.9605 39.9211 0.0244 -0.998027 -1.99605 39.9211 19.9605 39.9211 0.0248 -0.982287 -1.96457 39.2915 19.6457 39.2915 0.0252 -0.951057 -1.90211 38.0423 19.0211 38.0423 0.0256 -0.904827 -1.80965 36.1931 18.0965 36.1931 0.026 -0.844328 -1.68866 33.7731 16.8866 33.7731 0.0264

149

150

17. Cir uito on transformador.

-0.770513 -1.54103 30.8205 15.4103 30.8205 0.0268 -0.684547 -1.36909 27.3819 13.6909 27.3819 0.0272 -0.587785 -1.17557 23.5114 11.7557 23.5114 0.0276 -0.481754 -0.963508 19.2702 9.63508 19.2702 0.028 -0.368125 -0.73625 14.725 7.3625 14.725 0.0284 -0.24869 -0.49738 9.9476 4.9738 9.9476 0.0288 -0.125333 -0.250667 5.01334 2.50667 5.01334 0.0292 -2.3809e-07 -4.7618e-07 9.5236e-06 4.7618e-06 9.5236e-06 0.0296 0.125333 0.250666 -5.01332 -2.50666 -5.01332 0.03 0.24869 0.497379 -9.94759 -4.97379 -9.94759 0.0304 0.368124 0.736249 -14.725 -7.36249 -14.725 0.0308 0.481753 0.963507 -19.2701 -9.63507 -19.2701 0.0312 0.587785 1.17557 -23.5114 -11.7557 -23.5114 0.0316 0.684547 1.36909 -27.3819 -13.6909 -27.3819 0.032 0.770513 1.54103 -30.8205 -15.4103 -30.8205 0.0324 0.844328 1.68866 -33.7731 -16.8866 -33.7731 0.0328 0.904827 1.80965 -36.1931 -18.0965 -36.1931 0.0332 0.951056 1.90211 -38.0423 -19.0211 -38.0423 0.0336 0.982287 1.96457 -39.2915 -19.6457 -39.2915 0.034 0.998027 1.99605 -39.9211 -19.9605 -39.9211 0.0344 0.998027 1.99605 -39.9211 -19.9605 -39.9211 0.0348 0.982287 1.96457 -39.2915 -19.6457 -39.2915 0.0352 0.951057 1.90211 -38.0423 -19.0211 -38.0423 0.0356 0.904827 1.80965 -36.1931 -18.0965 -36.1931 0.036 0.844328 1.68866 -33.7731 -16.8866 -33.7731 0.0364 0.770513 1.54103 -30.8205 -15.4103 -30.8205 0.0368 0.684547 1.36909 -27.3819 -13.6909 -27.3819 0.0372 0.587785 1.17557 -23.5114 -11.7557 -23.5114 0.0376 0.481754 0.963508 -19.2702 -9.63508 -19.2702 0.038 0.368125 0.73625 -14.725 -7.3625 -14.725 0.0384 0.24869 0.49738 -9.94761 -4.9738 -9.94761 0.0388 0.125334 0.250667 -5.01334 -2.50667 -5.01334 0.0392 3.17453e-07 6.34906e-07 -1.26981e-05 -6.34906e-06 -1.26981e-05

set terminal png set output ' /home/ ayose / Programa ion /AVALON/debug / s r / o l e i o n / G r a f i o s / o l e i o n p r o b l e m a s /17/ e j e m p l o 0 1 7 _ g r af i a . png '

set en oding iso_8859_1 set grid set autos ale set yrange [ â&#x2C6;&#x2019; 5 5 : 4 5 â&#x201E;&#x201E; set key bottom r i g h t t i t l e ' V a r i a b l e s ' box set t i t l e ' Grafi ado por d e f e t o de l a s s o l u i o n e s d e l i r u i t o ' plot ' /home/ ayose / Programa ion /AVALON/debug / s r / o l e i o n / G r a f i o s / o l e i o n p r o b l e m a s /17/ ejemplo017_x_trans . data ' using 6 : 1 t i t l e 'V en nodo 1 ' with l i n e s , ' /home/ ayose / Programa ion /AVALON/debug / s r / o l e i o n / G r a f i o s / o l e i o n p r o b l e m a s /17/ ejemplo017_x_trans . data '

using 6 : 2 t i t l e 'V en nodo 2 ' with l i n e s , ' /home/ ayose / Programa ion

/AVALON/debug / s r / o l e i o n / G r a f i o s / o l e i o n p r o b l e m a s /17/ ejemplo017_x_trans . data ' using 6 : 3 t i t l e ' I de Trafo e n t r e nodos 1 , 0 ' with l i n e s , ' /home/ ayose / Programa ion /AVALON/debug / s r / o l e i o n / G r a f i o s / o l e i o n p r o b l e m a s /17/ ejemplo017_x_trans . data ' using 6 : 4 t i t l e ' I de Trafo e n t r e nodos 2 , 0 ' with l i n e s , ' /home/ ayose / Programa ion /AVALON/debug / s r / o l e i o n / G r a f i o s /

17.2. Solu iones

o l e i o n p r o b l e m a s /17/ ejemplo017_x_trans . data ' using 6 : 5 t i t l e ' I de Fuente t e n s i o n e n t r e nodos 0 , 1 ' with l i n e s

Gr谩 o de salida.

Ve谩mos las variables por separado para apre iar mejor su evolu i贸n temporal Tensi贸n en nodo 1 y 2

151

152 Intensidades en las mallas del ir uito

17. Cir uito on transformador.

CapĂtulo 18 Cir uito on bipuerto on parĂĄmetros hĂbridos.

Para ir nalizando on este manual de ejer i ios resueltos on Ă valon realizaremos un estudio de un ir uito on un uadripolo de nido por parĂĄmetros hĂbridos. 1

2 h

En este uadripolo simularemos al al ular sus parĂĄmetros un ir uito en Ď&#x20AC; de resisten ias muy utilizado en ele tri idad en la simula iĂłn de lĂneas de distribu iĂłn. El poten ial de este tipo de elementos es muy amplio debido a que sabiendo alular los parĂĄmetros hĂbridos de un ir uito determinado podremos realizar anĂĄlisis aĂşn mĂĄs omplejos. AdemĂĄs por otro lado de la simpli a iĂłn visual que esto supone ya que al onvertir una parte de un ir uito en uno de estos elementos el alumno puede entrarse y fo alizar el anĂĄlisis en la parte del ir uito que mĂĄs le onvenga.

El ĂĄ ulo de los parĂĄmetros hĂbridos serĂa el siguiente: Para V2 = 0 V1 20 V1 5

= =

I1 + I2 I1 + I2

25Âˇ15 25â&#x2C6;&#x2014;15 I2 20 25 V2

â&#x2021;&#x2019;

I1 I2

= =

5 40 V1 3 40 V1

â&#x2021;&#x2019;

V2 V1

= =

375 40 I2 20 25 V2

Para I1 = 0 V2 V1

= =

153

154

18. Cir uito on bipuerto on parámetros híbridos.

Con estas expresiones, se está en disposi ión de sustituir en las fórmulas de los parámetros y al ularlos

I1o V =0 2

h11 =

h21 = h22 = 18.1.

= 80

20 25 V2 V2

0,8

3 40 V1 5 40 V1

0,6

I1 V =0 2

V1 5 40 V1

V2 I =0 1

h12 =

V2 I =0 1

I2 375 40 I2 V1

= 0,11

Datos Generales.

Ar hivo *.sp ∗ SPICE i r u i t <ejemplo018> from XCir uit v3 . 6 rev 135

3 1 0 2 0 2 0 0 ,0001 4 1 0 2 1 0 0 2 rho f a b A B C D 16 1 0 2 1 0 2 0 0 0 0 0 0 0 80 0 ,8 0 ,6 0 ,11 . end Tipo de análisis realizado Análisis esta ionario Análisis transitorio

⊠ ⊠

Datos generales del ir uito Elementos del Cto: 3 EA: 0 Nodos: 2 A2: 3 No nulos: 11 Densidad: 0.44 Dispersion: 0.56

Los valores dados al ir uito son: Elemento Bobina entre nodo 2, 0 uadripolo a través de h Fuente de tensión ontínua

Matriz T. row 0: (2, row 1: (1, row 2: (0, row 3: (0, row 4: (1,

1) (3, 1) 0.11) (3, 0.6) (4, -1) 1) 1) (1, -0.8) (3, -80) -1) (4, -0 - 0.0001 i)

Magnitud 0, 0001 H h11 = 80 h12 = 0, 8 h21 = 0, 6 h22 = 0, 11 2V

155

18.2. Solu iones

18.2.

18.2.1.

Solu iones

Primer an谩lisis Tiempo Ini ial Tiempo Final Paso de Tiempo Theta

0 0, 0001 0, 000001

1 (Euler)

Esta ionario Resultados sistema esta ionario: Tensi贸n en nodo 1: 2 - 7.75482e-26 i Tensi贸n en nodo 2: -1.56e-11 - 1.5e-06 i I de Fuente tension entre nodos 1, 0: -0.025 - 1.5e-08 i I de uadripolo en h entre nodos 1, 0: 0.025 + 1.5e-08 i I de Bobina entre nodos 0, 2: 0.015 - 1.56e-07 i

Transitorio 4 -0.263158 -0.0526316 0.0526316 0.00263158 0 2 -0.108495 -0.0260849 0.0260849 0.00371653 1e-06 2 -0.0989778 -0.0259898 0.0259898 0.00470631 2e-06 2 -0.0902956 -0.025903 0.025903 0.00560926 3e-06 2 -0.0823749 -0.0258237 0.0258237 0.00643301 4e-06 2 -0.075149 -0.0257515 0.0257515 0.0071845 5e-06 2 -0.068557 -0.0256856 0.0256856 0.00787007 6e-06 2 -0.0625432 -0.0256254 0.0256254 0.0084955 7e-06 2 -0.057057 -0.0255706 0.0255706 0.00906607 8e-06 2 -0.052052 -0.0255205 0.0255205 0.00958659 9e-06 2 -0.047486 -0.0254749 0.0254749 0.0100615 1e-05 2 -0.0433206 -0.0254332 0.0254332 0.0104947 1.1e-05 2 -0.0395205 -0.0253952 0.0253952 0.0108899 1.2e-05 2 -0.0360538 -0.0253605 0.0253605 0.0112504 1.3e-05 2 -0.0328912 -0.0253289 0.0253289 0.0115793 1.4e-05 2 -0.030006 -0.0253001 0.0253001 0.0118794 1.5e-05 2 -0.0273739 -0.0252737 0.0252737 0.0121531 1.6e-05 2 -0.0249727 -0.0252497 0.0252497 0.0124028 1.7e-05 2 -0.0227821 -0.0252278 0.0252278 0.0126307 1.8e-05 2 -0.0207837 -0.0252078 0.0252078 0.0128385 1.9e-05 2 -0.0189605 -0.0251896 0.0251896 0.0130281 2e-05 2 -0.0172973 -0.025173 0.025173 0.0132011 2.1e-05 2 -0.01578 -0.0251578 0.0251578 0.0133589 2.2e-05 2 -0.0143958 -0.025144 0.025144 0.0135028 2.3e-05 2 -0.013133 -0.0251313 0.0251313 0.0136342 2.4e-05 2 -0.011981 -0.0251198 0.0251198 0.013754 2.5e-05 2 -0.01093 -0.0251093 0.0251093 0.0138633 2.6e-05 2 -0.00997126 -0.0250997 0.0250997 0.013963 2.7e-05

156

18. Cir uito on bipuerto on parĂĄmetros hĂbridos.

2 -0.00909659 -0.025091 0.025091 0.014054 2.8e-05 2 -0.00829864 -0.025083 0.025083 0.0141369 2.9e-05 2 -0.00757069 -0.0250757 0.0250757 0.0142126 3e-05 2 -0.0069066 -0.0250691 0.0250691 0.0142817 3.1e-05 2 -0.00630075 -0.025063 0.025063 0.0143447 3.2e-05 2 -0.00574806 -0.0250575 0.0250575 0.0144022 3.3e-05 2 -0.00524384 -0.0250524 0.0250524 0.0144546 3.4e-05 2 -0.00478385 -0.0250478 0.0250478 0.0145025 3.5e-05 2 -0.00436422 -0.0250436 0.0250436 0.0145461 3.6e-05 2 -0.00398139 -0.0250398 0.0250398 0.0145859 3.7e-05 2 -0.00363215 -0.0250363 0.0250363 0.0146223 3.8e-05 2 -0.00331354 -0.0250331 0.0250331 0.0146554 3.9e-05 2 -0.00302288 -0.0250302 0.0250302 0.0146856 4e-05 2 -0.00275771 -0.0250276 0.0250276 0.0147132 4.1e-05 2 -0.00251581 -0.0250252 0.0250252 0.0147384 4.2e-05 2 -0.00229512 -0.025023 0.025023 0.0147613 4.3e-05 2 -0.0020938 -0.0250209 0.0250209 0.0147822 4.4e-05 2 -0.00191013 -0.0250191 0.0250191 0.0148013 4.5e-05 2 -0.00174257 -0.0250174 0.0250174 0.0148188 4.6e-05 2 -0.00158972 -0.0250159 0.0250159 0.0148347 4.7e-05 2 -0.00145027 -0.0250145 0.0250145 0.0148492 4.8e-05 2 -0.00132305 -0.0250132 0.0250132 0.0148624 4.9e-05 2 -0.00120699 -0.0250121 0.0250121 0.0148745 5e-05 2 -0.00110112 -0.025011 0.025011 0.0148855 5.1e-05 2 -0.00100453 -0.02501 0.02501 0.0148955 5.2e-05 2 -0.000916412 -0.0250092 0.0250092 0.0149047 5.3e-05 2 -0.000836025 -0.0250084 0.0250084 0.0149131 5.4e-05 2 -0.000762689 -0.0250076 0.0250076 0.0149207 5.5e-05 2 -0.000695787 -0.025007 0.025007 0.0149276 5.6e-05 2 -0.000634753 -0.0250063 0.0250063 0.014934 5.7e-05 2 -0.000579073 -0.0250058 0.0250058 0.0149398 5.8e-05 2 -0.000528277 -0.0250053 0.0250053 0.0149451 5.9e-05 2 -0.000481937 -0.0250048 0.0250048 0.0149499 6e-05 2 -0.000439662 -0.0250044 0.0250044 0.0149543 6.1e-05 2 -0.000401095 -0.025004 0.025004 0.0149583 6.2e-05 2 -0.000365911 -0.0250037 0.0250037 0.0149619 6.3e-05 2 -0.000333814 -0.0250033 0.0250033 0.0149653 6.4e-05 2 -0.000304532 -0.025003 0.025003 0.0149683 6.5e-05 2 -0.000277818 -0.0250028 0.0250028 0.0149711 6.6e-05 2 -0.000253448 -0.0250025 0.0250025 0.0149736 6.7e-05 2 -0.000231216 -0.0250023 0.0250023 0.014976 6.8e-05 2 -0.000210934 -0.0250021 0.0250021 0.0149781 6.9e-05 2 -0.000192431 -0.0250019 0.0250019 0.01498 7e-05 2 -0.000175551 -0.0250018 0.0250018 0.0149817 7.1e-05 2 -0.000160152 -0.0250016 0.0250016 0.0149833 7.2e-05 2 -0.000146103 -0.0250015 0.0250015 0.0149848 7.3e-05 2 -0.000133287 -0.0250013 0.0250013 0.0149861 7.4e-05 2 -0.000121596 -0.0250012 0.0250012 0.0149874 7.5e-05 2 -0.000110929 -0.0250011 0.0250011 0.0149885 7.6e-05 2 -0.000101199 -0.025001 0.025001 0.0149895 7.7e-05 2 -9.23215e-05 -0.0250009 0.0250009 0.0149904 7.8e-05 2 -8.42231e-05 -0.0250008 0.0250008 0.0149912 7.9e-05 2 -7.68352e-05 -0.0250008 0.0250008 0.014992 8e-05 2 -7.00952e-05 -0.0250007 0.0250007 0.0149927 8.1e-05

18.2. Solu iones

157

2 -6.39465e-05 -0.0250006 0.0250006 0.0149933 8.2e-05 2 -5.83372e-05 -0.0250006 0.0250006 0.0149939 8.3e-05 2 -5.32199e-05 -0.0250005 0.0250005 0.0149945 8.4e-05 2 -4.85515e-05 -0.0250005 0.0250005 0.014995 8.5e-05 2 -4.42926e-05 -0.0250004 0.0250004 0.0149954 8.6e-05 2 -4.04073e-05 -0.0250004 0.0250004 0.0149958 8.7e-05 2 -3.68628e-05 -0.0250004 0.0250004 0.0149962 8.8e-05 2 -3.36292e-05 -0.0250003 0.0250003 0.0149965 8.9e-05 2 -3.06793e-05 -0.0250003 0.0250003 0.0149968 9e-05 2 -2.79881e-05 -0.0250003 0.0250003 0.0149971 9.1e-05 2 -2.5533e-05 -0.0250003 0.0250003 0.0149973 9.2e-05 2 -2.32933e-05 -0.0250002 0.0250002 0.0149976 9.3e-05 2 -2.125e-05 -0.0250002 0.0250002 0.0149978 9.4e-05 2 -1.9386e-05 -0.0250002 0.0250002 0.014998 9.5e-05 2 -1.76854e-05 -0.0250002 0.0250002 0.0149982 9.6e-05 2 -1.61341e-05 -0.0250002 0.0250002 0.0149983 9.7e-05 2 -1.47188e-05 -0.0250001 0.0250001 0.0149985 9.8e-05 2 -1.34277e-05 -0.0250001 0.0250001 0.0149986 9.9e-05

set terminal png set output ' /home/ ayose / Programa ion /AVALON/debug / s r / o l e i o n / G r a f i o s / o l e i o n p r o b l e m a s /18/ e j e m p l o 0 1 8 _ g r af i a . png '

using 6 : 2 t i t l e 'V en nodo 2 ' with l i n e s , ' /home/ ayose / Programa ion

/AVALON/debug / s r / o l e i o n / G r a f i o s / o l e i o n p r o b l e m a s /18/ ejemplo018_x_trans . data ' using 6 : 3 t i t l e ' I de Fuente t e n s i o n e n t r e nodos 1 , 0 ' with l i n e s , ' /home/ ayose / Programa ion /AVALON/debug / s r / o l e i o n / G r a f i o s / o l e i o n p r o b l e m a s /18/ ejemplo018_x_trans . data ' using 6 : 4 t i t l e ' I de C u a t r i p o l o en h e n t r e nodos 1 , 0 ' with l i n e s , ' /home/ ayose / Programa ion /AVALON/debug / s r / o l e i o n / G r a f i o s / o l e i o n p r o b l e m a s /18/ ejemplo018_x_trans . data ' using 6 : 5 t i t l e ' I de Bobina e n t r e nodos 0 , 2 ' with l i n e s

Grรก o de salida.

158

Veamos la tensión en el nodo 2

18. Cir uito on bipuerto on parámetros híbridos.