قياسات وأجهزة نظري

  ‫א‬٢٦٧



  ٢٦٧

‫א‬

 



   W،،‫א‬‫א‬،‫א‬

  

  ‫א‬ ‫א‬ ‫א‬ ‫א‬‫א‬  ‫א‬ ‫א‬  ‫א‬ ‫א‬ 



 

‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  K ‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬



  ‫א‬        ،‫א‬ ‫א‬‫א‬  

‫א‬  ‫א‬ ‫א‬ ‫א‬ ‫א‬ ‫א‬   ‫א‬    ،  

‫א‬،‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬،‫א‬

 K‫א‬‫א‬،‫א‬

  ?   ?   ? ‫א‬ ‫א‬  



‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬



 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬? ،‫א‬،‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬

   W    ‫א‬ ‫א‬  ‫א‬    ‫א‬



 K‫א‬

‫א‬‫א‬‫א‬‫א‬

 



  ٢٦٧

‫א‬

 



 

 ،KKK،‫א‬‫א‬‫א‬‫א‬

 ‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬



‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬



 K‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬‫א‬

،‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬

K ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  K‫א‬

‫א‬‫א‬  ‫א‬‫א‬،‫א‬‫א‬ ‫א‬‫א‬



،‫א‬‫א‬‫א‬‫א‬،



 K‫א‬‫א‬،‫א‬،‫א‬‫א‬

‫א‬،‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬

 KKKKKK،‫א‬  



 ‫א‬‫א‬‫א‬‫א‬‫א‬



١

‫א‬‫א‬‫ א‬‫א‬‫א‬

‫א‬‫א‬

 ‫ א‬٢٦٧

‫א‬

‫א‬‫א‬‫א‬‫א‬

 



 K‫א‬‫א‬‫א‬W‫א‬‫א‬    W‫א‬‫א‬W‫א‬‫א‬‫א‬‫א‬ K‫א‬‫א‬‫א‬‫א‬‫א‬ • K‫א‬‫א‬‫א‬‫א‬‫א‬ •

K‫א‬‫א‬‫א‬‫א‬ •

K‫א‬‫א‬‫א‬ • K‫א‬‫א‬ •

K‫א‬‫א‬‫א‬‫א‬‫א‬ •  

 K٪١٠٠‫א‬‫א‬‫א‬ W‫א‬‫א‬‫א‬

   

 KW‫א‬‫א‬

 

 W‫א‬‫א‬

K‫א‬‫א‬ •

K‫א‬K‫א‬ •  K‫א‬‫א‬‫א‬W‫א‬‫א‬

-١-

 

‫א‬‫א‬

 ‫ א‬٢٦٧

‫א‬

‫א‬‫א‬‫א‬‫א‬

 



 ‫א‬‫א‬‫א‬‫א‬  

 W‫א‬‫א‬

K‫א‬‫א‬‫א‬‫א‬‫א‬ • K‫א‬‫א‬‫א‬‫א‬‫א‬ •

K‫א‬‫א‬‫א‬‫א‬ •

K‫א‬‫א‬‫א‬ • K‫א‬‫א‬ •

K‫א‬‫א‬‫א‬‫א‬‫א‬ •

-٢-

‫א‬‫א‬

 ‫ א‬٢٦٧

‫א‬

‫א‬‫א‬‫א‬‫א‬

 



Introduction  ١ J١

 ‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬  ‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬

 

 General Concepts ٢ J١

 K‫א‬‫א‬W‫א‬  W‫א‬‫א‬‫א‬  measured quantity E١F Standard system E٢F

measuring instruments E٣F measuring technology E٤F

 W‫א‬‫א‬  

 ‫א‬‫א‬‫א‬‫א‬W E١F  KKKKKKKKKKKKK‫א‬

 K‫א‬‫א‬‫א‬‫א‬‫א‬W E٢F  W

The international standards system‫א‬‫א‬‫א‬‫ א‬EF

K  ‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬

The primary standards system ‫א‬‫א‬‫א‬‫א‬‫ א‬EF

‫א‬،‫א‬‫א‬ ‫א‬‫א‬

K  ‫א‬‫א‬‫א‬‫א‬‫א‬

K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

The secondary standards system‫א‬‫א‬‫א‬‫ א‬EF -٣-

‫א‬‫א‬

 ‫ א‬٢٦٧

‫א‬

‫א‬‫א‬‫א‬‫א‬

 



K ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬K  ‫א‬‫א‬

  ‫א‬E  ‫א‬‫א‬F  ‫א‬‫א‬‫א‬‫א‬‫א‬

K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

The working standard‫א‬‫א‬‫ א‬EF

‫א‬‫א‬K‫א‬‫א‬

K‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬W E٣F K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬W E٤F

 Electrical And Electronic Instruments‫א‬‫א‬‫א‬ ٣ J١ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

K ‫א‬‫א‬‫א‬

،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

EF‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬KEF

‫א‬‫א‬‫א‬‫א‬  ،‫א‬،‫א‬‫א‬

 K‫א‬‫א‬‫א‬،‫א‬‫א‬  

 ‫א‬‫א‬‫א‬ ١ J٣ J١

Functions and Characteristics of Electrical and Electronic Instruments

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬K‫א‬

‫א‬‫א‬،K‫א‬‫א‬‫א‬،‫א‬ -٤-

‫א‬‫א‬

 ‫ א‬٢٦٧

‫א‬

‫א‬‫א‬‫א‬‫א‬

 



،‫א‬‫א‬KK‫א‬‫א‬‫א‬٪١٠٠

‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬

‫א‬‫א‬  (amplifier)‫א‬‫א‬

 K‫א‬

 Electrical Units‫א‬‫א‬‫א‬

 

١ J١ J٣ J١

،‫א‬‫א‬‫ א‬‫א‬

،‫א‬K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬     K ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬

 W‫א‬‫א‬‫א‬‫א‬‫א‬  

 (Q)‫א‬‫ א‬E١F

(I)‫א‬‫ א‬E٢F

(V)‫א‬‫א‬‫א‬‫א‬‫ א‬E٣F

(R)‫ א‬E٤F

(L)‫א‬‫א‬‫א‬ E٥F

(C)‫ א‬E٦F

-٥-

‫א‬‫א‬

 ‫ א‬٢٦٧

‫א‬

‫א‬‫א‬‫א‬‫א‬

 



‫א‬‫א‬‫א‬،‫א‬‫א‬ ‫א‬‫א‬E١ J١F  K‫א‬‫א‬‫א‬‫א‬



 ‫א‬



 ‫א‬

  m

 (meter) 

l

(Length)‫א‬

kg

(kilogram)‫א‬

m

(Mass)‫א‬

t

°K

 (second)

 (Time)‫א‬

(degree Kelvin)

T

 (Temperature)‫א‬‫א‬

cd

(candela)

A

(Ampere)

  V

  (Volt)

V

(Electromotive force)‫א‬‫א‬‫א‬‫א‬

C

(Coulomb)

Q

(Quantity of charge)‫א‬

R

 F

(Ohm)

(Electrical resistance)‫א‬‫א‬

(Farad)‫א‬

C

(Capacitance)‫א‬

H

(Henry)

L

(Inductance)‫א‬‫א‬‫א‬

 s

Ω

 

 W‫א‬‫א‬‫א‬

(Luminous intensity)‫א‬ i

(Electric current)‫א‬‫א‬  W‫א‬‫א‬‫א‬

 ‫א‬‫א‬E١ J١F  

 Error Sources in Measurements‫א‬‫א‬ ٤ J١

‫א‬‫א‬‫א‬

 W‫א‬‫א‬،  W(Instrumental Error)‫א‬‫א‬

 E J JFW‫א‬

E‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ FW‫א‬ E–FW‫א‬ E–FW‫א‬

EF

E F

E F E F

 W(Gross Error)‫א‬‫א‬  ‫א‬

-٦-

E١F

EF

E٢F

‫א‬‫א‬

 ‫ א‬٢٦٧

‫א‬

‫א‬‫א‬‫א‬‫א‬

 



‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬

E F

E F

(Environmental Error)‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬W‫א‬‫א‬‫א‬‫א‬

EF

‫א‬‫א‬‫א‬‫א‬W‫א‬‫א‬

E F



‫א‬‫א‬‫א‬‫א‬‫א‬

E٣F

  ‫א‬‫א‬

K

‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬

 ‫א‬‫א‬‫א‬ K ‫א‬‫א‬ (Expected Value) 

 K‫א‬(Error)‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬

W‫א‬‫א‬‫א‬‫א‬

 K(Percentage Error)‫א‬(Absolute Error)‫א‬

-٧-

‫א‬‫א‬

 ‫ א‬٢٦٧

‫א‬

‫א‬‫א‬‫א‬‫א‬

 



 Absolute Error (eab)‫א‬‫א‬

 K ‫א‬‫א‬‫א‬‫א‬‫א‬

 W‫א‬ E١ J١F

e ab = Yn − X n

 W

 ‫א‬‫א‬: eab

‫א‬‫ א‬: Yn  ‫א‬‫ א‬: Xn

 Relative ErrorEerF‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬‫א‬

 W‫א‬

(e r ) =

e ab Yn − X n = Yn Yn

E٢ J١F  Percentage Error (e%) ‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬‫א‬  W‫א‬

(e % ) =

e ab Y − Xn × 100 % = n × 100 % Yn Yn

E٣ J١F  

 

 W‫א‬

Accuracy‫א‬

 K‫א‬‫א‬‫א‬

-٨-

‫א‬‫א‬

 ‫ א‬٢٦٧

‫א‬

‫א‬‫א‬‫א‬‫א‬

 



Relative Accuracy (Ar) ‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬‫א‬ (Ar)‫א‬‫א‬  W(Ar)‫א‬‫א‬

Ar =

Xn Y − Xn =1 − n = 1 − er Yn Yn

E٤ J١F  W

 K‫א‬‫א‬WAr

Percentage Accuracy (a%)‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬‫א‬ (a%)‫א‬‫א‬ a% =

Xn Y − Xn % = 100 % − n × 100 % Yn Yn

E٥ J١F

a % = 100% − Percentage Error = 100% − e %

 

E٦ J١F  W

 ‫א‬‫א‬‫א‬: a%

 E١ J١F

‫א‬، 49 V ‫א‬‫א‬  W‫א‬، 50 V ‫א‬‫א‬‫א‬‫א‬  ‫א‬‫ א‬EF

‫א‬‫ א‬EF

‫א‬‫ א‬EF

‫א‬‫ א‬EF  Weab‫א‬‫א‬  e ab = Yn − X n = 50 − 49 = 1 volt 

-٩-

We%‫א‬‫א‬

 W‫א‬

EF

EF

‫א‬‫א‬

 ‫ א‬٢٦٧

‫א‬

‫א‬‫א‬‫א‬‫א‬

 



e% =

e ab 50 V − 49 V × 100 % = × 100 % = 2 % Yn 50 V

WAr‫א‬‫א‬

EF

Wa%‫א‬‫א‬

EF

50 V − 49 V 1 =1− = 0.98 50 v 50

Ar =1 −

a % = 100% − e % = 100% − 2 % = 98 %

 

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬(Precision)‫א‬‫א‬K‫א‬

 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

K  ‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬ 

 W‫א‬K

E٧ J١F













 (Pr ecision ) i = 1 −

Xi − Xn Xn

 W (i)‫א‬‫א‬W(Precision)i

 (i)‫א‬‫א‬W X i

  (n)‫א‬‫א‬‫א‬‫א‬‫ א‬W X n

-١٠-

‫א‬‫א‬

 ‫ א‬٢٦٧

‫א‬

‫א‬‫א‬‫א‬‫א‬

 



 E٢ J١F

 W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬ Vi (volts)‫א‬‫א‬  1 98  2 102  3 101  4 97  5 100  6 103  7 98  8 106  9 107  10 99  E٢ J١FE٢ J١F

 

 K(P4%FWE٤F‫א‬(Precision)‫א‬‫א‬‫א‬‫א‬  W‫א‬

 WE٧ J١F‫א‬ Pi % = 100 % −

Vi − V Vn

×100 % 

 ‫א‬‫א‬١٠‫א‬‫א‬‫א‬n

 i = 4W،E٤F‫א‬‫א‬‫א‬‫א‬‫א‬

 

 W،‫א‬‫א‬‫א‬‫א‬‫א‬ X10 X=

98 + 102 + 101 + 97 + 100 + 103 + 98 + 106 + 107 + 99 = 101.1 10

P4% = 100 % −

97 − 101.1 ×100 % = 95.94 % 101.1

 ‫א‬‫א‬‫ א‬٥ J١

Statistical Analysis of Errors in Measurements -١١-

‫א‬‫א‬

 ‫ א‬٢٦٧

‫א‬

‫א‬‫א‬‫א‬‫א‬

 



K ‫א‬‫א‬‫א‬‫א‬،‫א‬

‫א‬،E‫א‬F‫א‬‫א‬،

‫א‬‫א‬‫א‬‫א‬‫א‬FK‫א‬‫א‬‫א‬‫א‬

،‫א‬ ‫א‬‫א‬W‫א‬W‫א‬‫א‬‫א‬‫א‬KE‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬ ‫א‬W  ‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬،‫א‬

،‫א‬‫א‬‫א‬،‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬

K ‫א‬‫א‬‫א‬‫א‬

‫א‬K‫א‬‫א‬‫א‬‫א‬

،‫א‬‫א‬‫א‬

 W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬(Average deviationF‫א‬‫א‬‫א‬،(arithmetic mean)‫א‬‫א‬

 K(Standard deviation)

 Average value (arithmetic mean)‫א‬‫א‬‫א‬‫א‬

١ J٥ J١

 (X1 , X 2 , X 3 .....X n ) ‫א‬‫א‬‫א‬n X ‫א‬‫א‬‫א‬‫א‬

 WKn‫א‬‫א‬‫א‬

X=

 

X 1 + X 2 + X 3 + ........ + X n n

E٨ J١F  deviation‫א‬‫א‬

 

٢ J٥ J١

 X i ‫א‬‫א‬‫א‬ ،‫א‬‫א‬‫א‬( d i )i‫א‬‫א‬‫א‬‫א‬

 WK X ‫א‬‫א‬‫א‬‫א‬‫א‬ E٩ J١F

di = Xi − X -١٢-

‫א‬‫א‬

 ‫ א‬٢٦٧

‫א‬

‫א‬‫א‬‫א‬‫א‬

 



 WK‫א‬‫א‬‫א‬‫א‬‫א‬ E١٠ J١F

d 1 + d 2 + d 3 + . . .. + d n = 0

 W

n

∑ d i = X1 − X + X 2 − X ...... + X n − X

i =1 n

n

i =1

i =1

∑ d i = .∑ X i

= X 1 + X 2 + .... − X n − X − X − ........ − X

− nX = 0

 W‫א‬‫א‬‫א‬‫א‬ E١١ J١F

















n

 ∑ di = 0 i =1

 K  ‫א‬‫א‬  Average deviation‫א‬‫א‬‫א‬

 

١ J٢ J٥ J١

 WK‫א‬‫א‬‫א‬‫א‬(D)‫א‬‫א‬‫א‬ D =

d 1 + d 2 + d 3 + . ... + d n

E١٢ J١F

n Standard deviation‫א‬‫א‬‫א‬

٢ J٢ J٥ J١

K‫א‬‫א‬‫א‬‫א‬(S)‫א‬‫א‬‫א‬

 W

 E١٣ J١F

S =

d 12 + d 22 + d 32 + ... + d 2n n or (n − 1)

‫א‬(n-1)‫א‬‫א‬( n < 30 )‫א‬‫א‬‫א‬‫א‬،‫א‬

n ‫א‬‫א‬،n‫א‬‫א‬( n ≥ 30 )‫א‬‫א‬‫א‬

 Kn-1  

 E٣ J١F -١٣-

‫א‬‫א‬

 ‫ א‬٢٦٧

‫א‬

‫א‬‫א‬‫א‬‫א‬

 



 W‫א‬،‫א‬‫א‬

 K X ‫א‬‫א‬‫א‬‫ א‬EF

K d i ‫א‬‫ א‬EF

n

K ∑ d i ‫א‬‫א‬‫ א‬EF i =1

KD‫א‬‫א‬‫ א‬EF

KS‫א‬‫א‬‫ א‬EF

 ‫א‬

 ‫א‬ X1

50.1 49.7 49.6 50.2

X2 X3 X4

 E٣ J١FE٣ J١F

 

 W‫א‬

X =

 W X ‫א‬‫א‬

EF

 W d i ‫א‬‫א‬

EF

 W ∑ d i ‫א‬‫א‬‫א‬

EF

50.1 + 49.7 + 49.6 + 50.2 = 49.9 4

d1 = 50.1 − 49.9 = 0.2 d 2 = 49.7 − 49.9 = - 0.2 d 3 = 49.6 − 49.9 = - 0.3

d 4 = 50.2 − 49.9 = 0.3 n

i =1

4

∑ di i =1

D =

= d 1 + d 2 + d 3 + d 4 = 0.2 − 0.2 − 0.3 + 0.3 = 0

0.2 + − 0.2 + − 0.3 + 0.3 4

WD‫א‬‫א‬‫א‬ =

-١٤-

1 = 0.25 4

EF

‫א‬‫א‬

 ‫ א‬٢٦٧

‫א‬

‫א‬‫א‬‫א‬‫א‬

 



 WS‫א‬‫א‬‫א‬  S =

d 12 + d 22 + d 32 + d 24 = 4 −1

EF

0.2 2 + 0.2 2 + 0.3 2 + 0.3 2 = 0.294 3  

 Limiting Errors‫א‬‫ א‬٦ J١

‫א‬‫א‬‫א‬‫א‬

‫א‬KFull scale reading‫א‬‫א‬

‫א‬‫א‬K ± 2% ‫א‬‫א‬voltmeter‫א‬

K2%‫א‬‫א‬‫א‬‫א‬

‫א‬K2%‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬‫א‬  E٤ J١F

 ‫א‬‫א‬‫א‬‫א‬ 2 % 300 v 

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K

 K120 v  ‫א‬

 W‫א‬‫א‬

 Limiting Error at full scale = 0.02 × 300 v = 6 v  W120 v‫א‬‫א‬‫א‬ Limiting Error at 120 v =

6 × 100 % = 5 % 120

-١٥-

‫א‬‫א‬

 ‫ א‬٢٦٧

‫א‬

‫א‬‫א‬‫א‬‫א‬

 



  Elements of Electronic Instruments‫א‬‫א‬ ٧ J١

 W‫א‬KE١ J١F‫א‬‫א‬‫א‬‫א‬  

Transducer

Signal modifier





Indicating device     

 ‫א‬‫א‬E١ J١F

 

 ‫א‬‫א‬‫א‬WTransducer E١F

‫א‬‫א‬‫א‬‫א‬WSignal Modifier E٢F ‫א‬‫א‬K ‫א‬

‫؛‬‫א‬‫א‬

‫א‬‫א‬،‫א‬ K‫א‬‫א‬‫א‬‫א‬

WIndicating Device E٣F K(Ammeter)‫א‬(Voltmeter)‫א‬‫א‬

W ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

، ‫א‬‫א‬، ‫א‬‫א‬، ‫א‬‫א‬W  ‫א‬

‫א‬‫א‬K  ‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬

       

-١٦-

‫א‬‫א‬

 ‫ א‬٢٦٧

‫א‬

‫א‬‫א‬‫א‬‫א‬

 



 

 ‫א‬‫א‬‫א‬‫א‬‫ א‬٨ J١

Selection, Usage and Care of Measuring Instruments

‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬K  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬،

K ‫א‬‫א‬‫א‬ ‫א‬‫א‬ ‫א‬

‫א‬F‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬،(The operating and instructions manual)E ‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ،‫א‬KE‫א‬‫א‬F‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬K ‫א‬‫א‬‫א‬‫א‬،‫א‬

،‫א‬،W

‫א‬K ‫א‬‫א‬‫א‬K،

 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

،‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 K ‫א‬

               

-١٧-

‫א‬‫א‬

 ‫ א‬٢٦٧

‫א‬

‫א‬‫א‬‫א‬‫א‬

 



 ‫א‬‫א‬ ‫א‬،1.5 A‫א‬‫א‬ ١ J١ K(e%)‫א‬‫א‬(eab)‫א‬‫א‬‫א‬K 1.46 A

 

‫א‬،2 kΩ‫א‬‫א‬ ‫א‬ ٢ J١ W‫א‬،1.93 kΩ

 K‫א‬‫א‬

K‫א‬‫א‬‫א‬

EF

E F

‫א‬ ‫א‬،30.15 V‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ٣ J١ K29.9 V

W‫א‬‫א‬‫א‬،‫א‬‫א‬ ٤ J١ ‫א‬

(volts)‫א‬‫א‬

(1) (2) (3) (4) (5) (6)

20.20 19.90 20.05 20.10 19.85 20.00

    

 K‫א‬‫א‬‫א‬‫א‬ 

-١٨-

‫א‬‫א‬

 ‫ א‬٢٦٧

‫א‬

‫א‬‫א‬‫א‬‫א‬

 



W‫א‬‫א‬‫א‬‫א‬‫א‬ ٥ J١ ‫א‬‫א‬  1

(mm)‫א‬ 2.21 2.18 2.20 2.21 2.17 2.19

2 3  4  5  6

-١٩-

‫א‬‫א‬

 ‫ א‬٢٦٧

‫א‬

‫א‬‫א‬‫א‬‫א‬

 



 K‫א‬‫ א‬EF

K‫א‬‫א‬‫א‬‫א‬‫א‬E F W‫א‬‫א‬‫א‬‫א‬98%‫א‬‫א‬ ٦ J١

 300 V175 V‫א‬‫א‬‫א‬‫א‬ EF‫א‬‫א‬‫א‬‫א‬‫א‬

EF

E F

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ٧ J١ ‫؟‬‫א‬‫א‬K٣٠٠

،‫א‬‫א‬‫א‬ ٨ J١ W‫א‬‫א‬‫א‬‫א‬،5.6 kΩ ‫א‬  1  2  3  4  5  6  7  8

(kΩ)‫א‬ 5.75 5.60 5.65 5.50 5.70 5.55 5.80 5.55

 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

-٢٠-

‫א‬‫א‬

 ‫ א‬٢٦٧

‫א‬

‫א‬‫א‬‫א‬‫א‬

 



 

W‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬ ٩ J١ ‫א‬‫א‬       

1 2 3 4 5 6 7 8

(kHz)‫א‬ 532 548 543 535 546 531 543 536

-٢١-

‫א‬‫א‬

 ‫ א‬٢٦٧

‫א‬

‫א‬‫א‬‫א‬‫א‬

 



 W‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬

K‫א‬‫א‬‫א‬ K‫א‬‫א‬‫א‬

‫א‬2%300V‫א‬‫א‬‫א‬‫א‬

EF

E F

E F ١٠ J١

K120 V‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬

-٢٢-

 

  ‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬

٢

‫א‬‫א‬

 

‫א‬‫א‬‫א‬‫א‬

٢٦٧

 

‫א‬ ‫א‬

 K‫א‬‫א‬‫א‬‫א‬‫א‬W‫א‬‫א‬    W‫א‬‫א‬W‫א‬‫א‬‫א‬‫א‬ K‫א‬‫א‬‫א‬ • K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ •

K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  • K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ •  

 

 K٪١٠٠‫א‬‫א‬‫א‬W‫א‬‫א‬‫א‬

   

 KW‫א‬‫א‬

 

 W‫א‬‫א‬

K‫א‬‫א‬ •

K‫א‬K‫א‬ •

K‫א‬‫א‬‫א‬‫א‬W‫א‬‫א‬

-٢١-

 

‫א‬‫א‬

 

‫א‬‫א‬‫א‬‫א‬

٢٦٧

 

‫א‬ ‫א‬

Introduction  ١ J٢

E ‫א‬F‫א‬‫א‬ ‫א‬ ‫א‬ 

‫א‬‫א‬،‫א‬‫א‬‫א‬W‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬  

D'Arsonval Meter Movement ‫א‬‫א‬‫א‬ ٢ J٢

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 KW،‫א‬‫א‬

 Construction of D'Arsonval Meter‫א‬‫א‬‫א‬ ١ J٢ J٢

،E١ J٢F،‫א‬‫א‬‫א‬

،(soft iron)‫א‬‫א‬،(horseshoe)‫א‬‫א‬

،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ،‫א‬

‫א‬K ‫א‬‫א‬‫א‬

‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬‫א‬،

-٢٢-

‫א‬‫א‬

 

‫א‬‫א‬‫א‬‫א‬

٢٦٧

‫א‬

 

‫א‬

   

   

Scale

 

 

Pointer

 

 ‫א‬

 

Permenant Magnet

 

 

Spring

 



 

Core

N   North Pole

S

 

 

 

Moving Coil

South Pole

 K‫א‬‫א‬‫א‬E١ J٢F

     

Operation of D'Arsonval Meter‫א‬‫א‬‫א‬ ٢ J٢ J٢

،‫א‬،‫א‬ ‫א‬‫א‬‫א‬‫א‬

 ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬

،  ‫א‬‫א‬‫א‬K‫א‬

‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬K‫א‬‫א‬،‫א‬‫א‬

‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬

‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬

-٢٣-

‫א‬‫א‬

 

‫א‬‫א‬‫א‬‫א‬

٢٦٧

‫א‬

 

‫א‬

 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫ א‬٣ J٢ J٢

D'Arsonval Meter in Direct Current Circuits

 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

١ J٣ J٢ J٢

D'Arsonval Meter as D.C Ammeter ،‫א‬‫א‬   ‫א‬‫א‬‫א‬‫א‬



،‫א‬K‫א‬‫א‬‫א‬‫א‬

‫א‬  ‫א‬K50µA‫א‬‫א‬‫א‬ ،‫א‬‫א‬‫א‬،‫א‬‫א‬K‫א‬

‫א‬‫א‬‫א‬،‫א‬(Rsh)‫א‬‫א‬‫א‬ ‫א‬ ‫א‬‫א‬‫א‬E٢ J٢FK  ‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ Im

Rm

+

 

_

   

Rsh

Ish

   

I

 

 

Vm

 K‫א‬‫א‬‫א‬‫א‬E٢ J٢F

‫א‬‫א‬‫א‬Im‫א‬‫א‬Ish‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬K  W،E٢ J٢F‫א‬‫א‬  ‫א‬‫א‬ WRsh

 E‫א‬F‫א‬‫א‬‫א‬ WRm  ‫א‬‫א‬ ‫א‬‫א‬ WIsh

 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ WIm  ‫א‬‫א‬‫א‬‫א‬

-٢٤-

WI

‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬

 E١ J٢F

 

٢٦٧

‫א‬

 

‫א‬

 W‫א‬‫א‬‫א‬E٢ J٢F Vm = I m ⋅ R m

‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬Rsh‫א‬  W،‫א‬‫א‬

E٢ J٢F

Vm = Vsh

،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  W

E٣ J٢F

I = I m + I sh W،‫א‬‫א‬‫א‬‫א‬‫א‬Rsh‫א‬‫א‬‫א‬

 E٤ J٢F

I sh = I − I m

 WRsh‫א‬،Vm‫א‬Ish‫א‬‫א‬‫א‬‫א‬

E٥ J٢F

R sh =

Vsh I ⋅Rm = m (I − I m ) I sh

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  Wn‫א‬‫א‬،‫א‬n‫א‬،‫א‬

 E٦ J٢F

n =

I Im

 WE٥ J٢F‫א‬‫א‬  E٧ J٢F

R sh =

-٢٥-

(I m ⋅ R m ) / I m (I − I m ) / I m

=

Rm (n - 1)

‫א‬‫א‬

 

‫א‬‫א‬‫א‬‫א‬

٢٦٧

 

‫א‬ ‫א‬

 E١ J٢F

 W‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬K I m = 1 mA    ‫א‬100 Ω Rm‫א‬

 K I = 10 mA ‫א‬‫א‬(Rsh)‫א‬  W‫א‬

R sh

Im ⋅ R m 1 × 10 −3 × 100 = 11.11 Ω  = = (I − I m ) 9 × 10 −3

 WE٥ J٢F‫א‬

 

n =

10 × 10 −3 1 × 10 −3

 WE٦ J٢F‫א‬n‫א‬  = 10

 WE٧ J٢F‫א‬

R sh =

Rm 100Ω 100 = = = 11.11 Ω (n − 1) 10 − 1 9

 The Ayrton shunt‫א‬‫א‬ ١ J١ J٣ J٢ J٢

‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬Rsh‫א‬

‫א‬  ‫א‬‫א‬ ‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬Rsh‫א‬

 K ‫א‬‫א‬‫א‬ ‫א‬‫א‬(range selector switch)‫א‬‫א‬

 KRc، Rb, Ra Rsh‫א‬‫א‬‫א‬‫א‬E٣ J٢F   WRsh‫א‬‫א‬

 

E٨ J٢F

R sh = R a + R b + R c

 WE٧ J٢F‫א‬ Rsh

E٩ J٢F

R sh = R m / (n − 1)

 W (١٠-٢)

n = I1 I m -٢٦-

‫א‬‫א‬

٢٦٧

 

‫א‬‫א‬‫א‬‫א‬

‫א‬

 

‫א‬

 

Rm

Im

 

R sh Rc

   

Ra

Rb

 

I1-Im

 

I2

I3

 

I1

I

 

-

+

K[I1]‫א‬‫א‬‫א‬‫א‬E٣ J٢F

 

 ‫א‬‫א‬ R a , R b , R c ‫א‬‫א‬‫א‬ Im

Rc

Rm

 KE٤ J٢F

R sh

 

   

Ra

Rb

 

I2-Im I3 I

 

I2

 

I1

 

+ K[I2]‫א‬‫א‬‫א‬‫א‬E٤ J٢F

 

‫א‬Rb+Rc‫א‬‫א‬Ra‫א‬‫א‬‫א‬[I2]‫א‬‫א‬

 ‫א‬Rm+ Ra‫א‬‫א‬‫א‬Rb + Rc‫א‬Rm  W‫א‬‫א‬

E١١ J٢F

 VR b + R c = VR a + R m  W‫א‬‫א‬‫א‬‫א‬ -٢٧-

‫א‬‫א‬

 

‫א‬‫א‬‫א‬‫א‬

٢٦٧

‫א‬

 

‫א‬

E١٢ J٢F

(R b + R c )(I 2 − I m ) = I m (R a + R m )

E١٣ J٢F

I 2 (R b + R c ) − I m (R b + R c ) = I m (R a + R m )

E١٤ J٢F

 W،‫א‬  W‫א‬‫א‬‫א‬Im (Rb + Rc)

I 2 (R b + R c ) = I m (R a + R b + R c + R m ) = I m (R sh + R m )

 ‫א‬(Rb + Rc)‫א‬ E١٥ J٢F

Rb + Rc =

I m (R sh + R m ) I2

  Ra ‫א‬(Rb + Rc)‫א‬Rsh‫א‬‫א‬‫א‬  W‫א‬

E١٦ J٢F

R a = R sh − (R b + R c )

 WE٥ J٢F[I3]‫א‬ Rm

Im

   

R sh Rc

   

Ra

Rb

 

I3-Im I3

 

I1

I

-

 

I2

 

+

K[I3]‫א‬‫א‬‫א‬‫א‬E٥ J٢F

   

Rc‫א‬RaHRm‫א‬‫א‬ Rc‫א‬‫א‬Rb‫א‬  W‫א‬‫א‬ ‫א‬Rm+ Ra+ Rb‫א‬‫א‬‫א‬

E١٧ J٢F

VR C = VR m + R a + R b -٢٨-

‫א‬‫א‬

 

‫א‬‫א‬‫א‬‫א‬

E١٨ J٢F

٢٦٧

‫א‬

 

‫א‬

 W‫א‬‫א‬‫א‬‫א‬ R c (I 3 − I m ) = I m (R a + R b + R m )

 W‫א‬

E١٩ J٢F

I 3 R c − I m R c = I m (R a + R b + R m )

E٢٠ J٢F

I 3 R c = I m (R a + R b + R c + R m ) = I m (R sh + R m )

 W‫א‬‫א‬‫א‬RcIm  ‫א‬(Rc)‫א‬

E٢١ J٢F

Rc =

I m (R sh + R m ) I3

 W‫א‬‫א‬Rb‫א‬‫א‬

E٢٢ J٢F

R b = R sh − (R a + R c )  E٢ J٢F

‫א‬،‫א‬‫א‬‫א‬،E٦ J٢F‫א‬‫א‬  K(Ra, Rb & Rc)‫א‬‫א‬

 

Im = 100 µA

 

Rm = 1 kΩ

    Rb

Rc

 

Ra

   

I3 = 1 A

I 2 = 100 mA

I1 = 10 mA

 KE٢ J٢F‫א‬‫א‬E٦ J٢F

 

 

 W‫א‬

 W‫א‬‫א‬ n = 10 mA 100 µA = 100  -٢٩-

‫א‬‫א‬

 

‫א‬‫א‬‫א‬‫א‬

٢٦٧

‫א‬

 

‫א‬

 W‫א‬‫א‬

R sh = R a + R b + R c = R m (n − 1) R sh = 1 kΩ (100 − 1) = 10.1 Ω

 W R b + R c  Rb + Rc =

I m (R sh + R m ) I2

Rb + Rc =

100 µA (10.1 + 1000) = 1.01 Ω 100 mA

 W

R a = R sh − (R b + R c ) = 10.1 − 1.01 = 9.09

 W R c  Rc =

I m (R sh + R m ) I3

Rc =

100 µA (1010.1 Ω ) = 0.101 Ω 1A

 W R b 

R b = R sh − (R a + R c ) = 10.1 − (9.09 + 0.101) = 0.909 Ω

 ‫א‬‫א‬‫א‬‫א‬‫א‬ ٢ J١ J٣ J٢ J٢

Ammeter Loading Effect

 ‫א‬‫א‬‫א‬  ‫א‬ ‫א‬



 ‫א‬  ‫א‬،‫א‬‫א‬‫א‬

  ‫א‬‫א‬K ‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬

‫א‬ E٧ J٢F   ‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬

Ie = E / R1WEIeF‫א‬‫א‬‫א‬‫א‬

-٣٠-

‫א‬‫א‬

 

‫א‬‫א‬‫א‬‫א‬

٢٦٧

‫א‬

 

‫א‬  

R1

Ie

X

 

E

 

Y

 K‫א‬‫א‬E٧ J٢F

 

 

 

،ERmF‫א‬  ‫א‬‫א‬‫א‬‫א‬

 W،‫א‬،E٨ J٢F

E٢٣ J٢F

Im = E R1

Im

(R 1 + R m )  

X Rm

E Y

     

 K‫א‬‫א‬‫א‬E٨ J٢F

 

  ‫א‬‫א‬،R1 = 10 kΩ‫א‬،E = 10V‫א‬‫א‬

 WE٧ J٢F

I e = E R 1 = 10V 10 kΩ = 1 mA 

 ‫א‬‫א‬،2 kΩE٨ J٢F‫א‬‫א‬‫א‬‫א‬‫א‬ Im = E

(R 1 + R m ) = 10 V

(10 kΩ + 2 kΩ )



 W‫א‬

= 0.833 mA

‫א‬ ‫א‬‫א‬ ‫א‬، ‫א‬‫א‬Rm

 K‫א‬‫א‬16.7%

  ،‫א‬‫א‬‫א‬‫א‬



‫א‬ ‫א‬،‫א‬‫א‬K ‫א‬‫א‬‫א‬‫א‬

 K10 Ω‫א‬‫א‬،‫א‬

 J Voltmeter) ‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫ א‬٢ J٣ J٢ J٢  EDC

-٣١-

‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬

 

٢٦٧

 

‫א‬ ‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬ ‫א‬ 

‫א‬‫א‬‫א‬‫א‬K ‫א‬‫א‬ ‫א‬ ‫א‬‫א‬‫א‬‫א‬،‫א‬

‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬،E10 mvF‫א‬‫א‬K ‫א‬‫א‬‫א‬

‫א‬،‫א‬‫א‬‫א‬

،(RS) ‫א‬‫א‬‫א‬،10 mv‫א‬

 J٢F،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  KE٩

-٣٢-

‫א‬‫א‬

 

‫א‬‫א‬‫א‬‫א‬

٢٦٧

 

Rm

Im

‫א‬ ‫א‬

 

RS

   

VRs

Vm

   

V

 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E٩ J٢F E٢٤ J٢F

 

 WV‫א‬‫א‬،RS‫א‬ I m = V (R m + R S )

R S = (V I m ) − R m

E٢٥ J٢F

 W‫א‬(Sensitivity (S))‫א‬

E٢٦ J٢F

S = 1 I FS

 W

 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬W I FS

 WS‫א‬

E٢٧ J٢F E٢٨ J٢F

S ≡

1 1 = = ohm / volt = Ω V Ampere volt ohms

 WRS‫א‬ RS = S ⋅ V − R m

 

‫א‬،V  ‫א‬‫א‬RS‫א‬‫א‬‫א‬ 

 K‫א‬‫א‬RS‫א‬V‫א‬

 E٣ J٢F

‫א‬‫א‬،100 µA‫א‬‫א‬‫א‬IFS‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬.1 kΩ . 50 V ‫א‬ E٢٨ J٢F‫א‬

-٣٣-

‫א‬‫א‬

 

‫א‬‫א‬‫א‬‫א‬

٢٦٧

‫א‬

 

 R S = SV − R m S = 1 I F.S = 1 100 µA = 10 kΩ / V

‫א‬

 WS‫א‬  WRSS

R S = ( 10 kΩ / V × 50 V) − 1 kΩ = 499 kΩ

 

‫א‬‫א‬

 W‫א‬‫א‬

 

 E٤ J٢F

 KE١٠ J٢F‫א‬‫א‬RS1, RS2, RS3‫א‬‫א‬‫א‬ I m = 50 µA

 

R m = 1 kΩ

  RS1

 

RS2 10 V

3V

−

RS3

30 V

+

 KE٤ J٢F‫א‬‫א‬‫א‬E١٠ J٢F

-٣٤-

         

‫א‬‫א‬

 

‫א‬‫א‬‫א‬‫א‬

٢٦٧

‫א‬

 

‫א‬

 W‫א‬

 WS‫א‬

 S = 1 / I FS = 1 / 50 µA = 20 kΩ / V

 W3 V‫א‬‫א‬RS1

R S1 = S ⋅ V1 − R m = 20 kΩ / V × 3V − 1 kΩ = 59 kΩ

 W10 V‫א‬‫א‬RS2

R S2 = S ⋅ V2 − R m = 20 kΩ / V × 10V − 1 kΩ = 199 kΩ

 W30 V‫א‬‫א‬RS3   R S3 = S ⋅ V3 − R m = 20 kΩ / V × 30V − 1 kΩ = 599 kΩ  E٥ J٢F  KE١١ J٢F‫א‬‫א‬Ra, Rb, Rc‫א‬‫א‬‫א‬  



R m = 1 kΩ

I m = 50 µA

  Ra

 

Rc

Rb

  3V

−  

10 V

30 V

   

+

 KE٥ J٢F‫א‬‫א‬‫א‬E١١ J٢F

 S = 1 / I FS = 1 / 50 µA = 20 kΩ / V

 

 W‫א‬

 WS‫א‬

 W3 V‫א‬‫א‬Ra

R a = S ⋅ V1 − R m = 20 kΩ / V × 3V − 1 kΩ = 59 kΩ

 W10 V‫א‬‫א‬Rb

R a + R b = S ⋅ V2 − R m = 20 kΩ / V × 10V − 1 kΩ = 199 kΩ R b = 199 kΩ − R b = 199 kΩ − 59 kΩ = 140 kΩ -٣٥-

‫א‬‫א‬

 

‫א‬‫א‬‫א‬‫א‬

٢٦٧

‫א‬

 

‫א‬

 W30 V‫א‬‫א‬Rc

R a + R b + R c = S ⋅ V3 − R m = 20 kΩ / V × 30V − 1 kΩ = 599 kΩ

R c = 599 kΩ − (R a + R b ) = 599 kΩ − 199 kΩ = 400 kΩ

 ‫א‬‫א‬‫א‬‫א‬‫א‬ ١ J٢ J٣ J٢ J٢

Voltmeter Loading Effect

‫א‬‫א‬‫א‬‫א‬ ‫א‬

‫א‬،‫א‬‫א‬‫א‬‫א‬،

 K‫א‬،‫א‬‫א‬‫א‬ ‫א‬

‫א‬،‫א‬  ‫א‬‫א‬E١٢ J٢F

 ‫א‬   ‫א‬،‫א‬  ،RB‫א‬ VR B = E ×

 W‫א‬RB‫א‬

RB RA + RB

E٢٩ J٢F     VR B = 30V ×

5 kΩ = 5V 25 kΩ + 5 kΩ

 

RA = 25KΩ E = 30V RB = 5KΩ

  VR B

 K‫א‬‫א‬‫א‬E١٢ J٢F

    

  ‫א‬‫א‬،10kΩ‫א‬‫א‬‫א‬‫א‬‫א‬  ،RB‫א‬ ‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬

 WReq‫א‬‫א‬‫א‬

R eq = R B // R V = -٣٦-

RB × RV RB + RV

‫א‬‫א‬

 

‫א‬‫א‬‫א‬‫א‬

٢٦٧

‫א‬

 

‫א‬  ‫א‬‫א‬، =

‫א‬

5 kΩ × 10 kΩ = 3.33 kΩ 5 kΩ + 10 kΩ

 W‫א‬،‫א‬ VR B = E ×

R eq R eq + R A

= 30 V ×

3.33 kΩ = 3.53 V 3.33 kΩ + 25 kΩ

‫א‬‫א‬‫א‬،29.4 % ‫א‬‫א‬‫א‬  K‫א‬‫א‬

‫א‬‫א‬‫א‬،‫א‬‫א‬

E١٢ J٢F‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬،‫א‬،‫א‬‫א‬‫א‬ K500kΩ

‫א‬‫א‬‫א‬‫א‬‫ א‬٣ J٣ J٢ J٢

 D'Arsonval Meter as Ohmmeter ‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬،  K‫א‬‫א‬

‫א‬‫א‬ ‫א‬‫א‬‫א‬

 K‫א‬‫א‬،E١٣ J٢F‫א‬  

Rz

Rm

Ifs

         

E

 

X

 ‫א‬‫א‬‫א‬‫א‬E١٣ J٢F -٣٧-

   

‫א‬‫א‬

 

‫א‬‫א‬‫א‬‫א‬

٢٦٧

 

‫א‬ ‫א‬

،E١٣ J٢F‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬ERxF‫א‬‫א‬،EEFERmFERzF

  [E١٣ J٢FX, Y‫]א‬‫א‬

 K‫א‬‫א‬‫א‬

 

I =

 WERxF‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

E Rz + Rm + Rx

E٣٠ J٢F

 R x = ∞ W   ‫א‬،ERxF‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬

 : R x = 0 ‫א‬، I = 0 W‫א‬‫א‬

I=

E Rz + Rm

E٣١ J٢F

 KEIFSF‫א‬‫א‬‫א‬‫א‬‫א‬،EE, Rz, RmF I f .s =

E Rz + Rm

E٣٢ J٢F  W، R x = R z + R m ‫א‬

I =

E 1 = I FS 2 ( Rz + Rm ) 2

E٣٣ J٢F

 ‫א‬K‫א‬‫א‬،Ifs‫א‬‫א‬  W، R x = 2 ( R z + R m )

I =

E 3 ( Rz + Rm

)

=

1 I FS 3

E٣٤ J٢F  W، R x = 3 ( R z + R m ) ‫א‬

I =

E 4 ( Rz + Rm

)

=

1 I FS 4

E٣٥ J٢F

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬

(∞)،‫א‬‫א‬‫א‬،‫א‬‫א‬ -٣٨-

‫א‬‫א‬

 

‫א‬‫א‬‫א‬‫א‬

٢٦٧

‫א‬

 

‫א‬

   ‫א‬ ‫א‬ERxF‫א‬‫א‬،‫א‬‫א‬

‫א‬[]‫א‬،‫א‬‫א‬  ،(Rz + Rm) X, Y‫א‬‫א‬K(Rz + Rm)‫א‬‫א‬

‫א‬K ‫א‬‫א‬EshortF‫א‬،E١٣ J٢F  .(Rz)‫א‬‫א‬‫א‬

 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫ א‬٤ J٢ J٢

D'Arsonval Meter in Alternating Current Circuits

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬K ‫א‬  K‫א‬‫א‬‫א‬‫א‬

، ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬،،،‫א‬

،‫א‬‫א‬‫א‬‫א‬،‫א‬K‫א‬‫א‬ ‫א‬‫א‬  ،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

،‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬F‫א‬‫א‬‫א‬‫א‬K‫א‬ ‫א‬‫א‬(rectification) ‫א‬‫א‬  KE ‫א‬

 K‫א‬،(diode rectifier)‫א‬

 ‫א‬‫א‬‫א‬‫א‬‫א‬

D'Arsonval Meter with Half Wave Rectification

١ J٤ J٢ J٢

،‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬



،‫א‬‫א‬‫א‬E١٠ J٢F   ‫א‬‫א‬‫א‬         -٣٩-

 K‫א‬

‫א‬‫א‬

 

‫א‬‫א‬‫א‬‫א‬

٢٦٧

‫א‬

 

‫א‬

R  S

 

If.s

  E r.m.s

 

E av

 

Rm

   

 ‫א‬‫א‬E١٤ J٢F

 

،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬

، ،E  ‫א‬‫א‬F‫א‬‫א‬‫א‬‫א‬

‫א‬K‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬(Eav)‫א‬‫א‬‫א‬

 W(Erms)‫א‬

Q E av =

E max = 0.318 E max π

Q E r.m.s =

E max 2

E٣٦ J٢F

, ∴ E max = 1.414 E r.m.s

∴ E av = 0.318 × 1.414 E r.m.s = 0.45 E r.m.s

E٣٧ J٢F E٣٨ J٢F

E av = 2.22 E av E٣٩ J٢F 0.45 ‫א‬‫א‬Eform factor)‫א‬،[2.22] ‫א‬ ∴ E r.m.s =

،‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬

 W(Rs)‫א‬‫א‬ -٤٠-

‫א‬‫א‬

 

‫א‬‫א‬‫א‬‫א‬

٢٦٧

 

RT = RS + R m =

E d.c 0.45 E r.m.s = I d.c I d.c

‫א‬ ‫א‬

E٤٠ J٢F  W

 K‫א‬‫א‬‫א‬W R T E d.c 0.45 E r.m.s − Rm = − Rm I d.c I d.c

RS =

E٤١ J٢F

‫א‬ E٢٨ J٢F ،E٤١ J٢F‫א‬‫א‬

‫א‬‫א‬  ،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬10 V ‫א‬،10 V

‫א‬‫א‬‫א‬‫א‬،4.5 V  W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 Sa.c = 0.45 Sd.c E٤٢ J٢F

 W R T ‫א‬‫א‬

RT =

E d.c = S d.c E d.c I d.c

E٤٣ J٢F  W

S d.c =

1 I f .s

RT =

0.45 E r.m.s = 0.45 S d.c E r.m.s = S a.c E r.m.s I d.c

∴ R T = R S + R m = S d.c E d.c = S a.c E r.m.s

E٤٤ J٢F E٤٥ J٢F  

 E٦ J٢F

‫א‬EE١٥ J٢F‫א‬F‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬

 K E r.m.s = 10 V ‫א‬،‫א‬‫א‬‫א‬  

-٤١-

 

‫א‬‫א‬

 

‫א‬‫א‬‫א‬‫א‬

٢٦٧

‫א‬

 

‫א‬

RS  

 

E r.m.s = 10 V

If .s = 1 mA

   

E av

R m = 300 Ω

    

 KE٦ J٢F‫א‬‫א‬‫א‬‫א‬E١٥ J٢F

 

 W‫א‬

 WE٣٨ J٢F‫א‬‫א‬‫א‬ E av = E d.c = 0.45 E r.m.s = 0.45 × 10 = 4.5 V

 WE٢٦ J٢F‫א‬‫א‬‫א‬‫א‬‫א‬ S d.c =

1 = 1000 Ω / V = 1 kΩ / V I fs

 WE٤٢ J٢F‫א‬‫א‬‫א‬‫א‬‫א‬ S a.c = 0.45 S d.c = 0.45 × 1 kΩ / V = 0.45 kΩ / V

 WE٤٥ J٢F‫א‬‫א‬‫א‬

R T = R S + R m = S d.c × E d.c = 1 kΩ / V × 4.5 V = 4.5 kΩ

 W

R T = R S + R m = S a.c × E r.m.s = 0.45 kΩ / V × 10 V = 4.5 kΩ

 W‫א‬‫א‬‫א‬ R S = 4.5 kΩ − 300 Ω = 4.5 kΩ − 0.3 kΩ = 4.2 kΩ

 W‫א‬

RS =

0.45 E r.m.s 0.45 × 10 − Rm = − 300 = 4200 Ω = 4.2 kΩ I d.c 1 × 10 −3

 

-٤٢-

‫א‬‫א‬

 

‫א‬‫א‬‫א‬‫א‬

٢٦٧

 

‫א‬ ‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 J٢F  (Rsh) ‫א‬  ،‫א‬

 KE١٦

RS  

 

I f .s

  E in

 

Rm

   

   

 K‫א‬‫א‬‫א‬‫א‬E١٦ J٢F

 

‫א‬(reverse-biased)(D2)‫א‬‫א‬‫א‬

،‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬،‫א‬‫א‬

‫א‬‫א‬‫א‬ ،(forward-biased)    (D2)‫א‬

‫א‬K(D1)‫א‬‫א‬‫א‬‫א‬،(reverse-biased leakage current)

،‫א‬‫א‬‫א‬(D1)‫א‬‫א‬‫א‬(Rsh)‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬(D1)‫א‬    E٧ J٢F

‫א‬‫א‬EE١٧ J٢F‫א‬F‫א‬‫א‬‫א‬

50Ω‫א‬‫א‬‫א‬،‫א‬‫א‬

 K‫א‬

 W‫א‬

 KRS‫א‬‫א‬‫א‬

K‫א‬‫א‬‫א‬‫א‬ -٤٣-

E١F

E٢F

‫א‬‫א‬

 

‫א‬‫א‬‫א‬‫א‬

٢٦٧

‫א‬

 

‫א‬

K‫א‬‫א‬‫א‬‫א‬

 W‫א‬

E٣F

 WRS‫א‬‫א‬‫א‬E١F

 W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ I f .s × R m = I sh × R sh

D1

RS

IT I sh

E in = 10 Vr.m.s

D2

Rsh = 200 Ω

I f .s = 100 µA

 

R m = 200 Ω

     

 KE٧ J٢F‫א‬‫א‬‫א‬‫א‬E١٧ J٢F

I sh =

If s × R m R sh

 

WIsh‫א‬‫א‬‫א‬‫א‬، =

100 µA × 200 Ω = 100 µA 200 Ω

 WIT‫א‬‫א‬ I T = I f s + I sh = 100 µA + 100 µA = 200 µA

 W‫א‬‫א‬ E d.c = E av = 0.45 × E r.m.s = 0.45 × 10 V = 4.5 V

 WRT‫א‬‫א‬ RT =

E d.c 4.5 V = = 22.5 kΩ I T 200 µA

 ‫א‬ ‫א‬‫א‬ ‫א‬‫א‬ RS, Rd

 WRsh‫א‬‫א‬‫א‬Rm‫א‬‫א‬‫א‬‫א‬ -٤٤-

‫א‬‫א‬

 

‫א‬‫א‬‫א‬‫א‬

RT = RS + Rd +

RS = RT − Rd −

٢٦٧

 

‫א‬ ‫א‬

R m × R sh R m + R sh

 WRS‫א‬‫א‬‫א‬

R m × R sh R m + R sh

R S = 22.5 × 10 3 Ω − 50 Ω −

200 Ω × 200 Ω = 22.35 × 10 3 Ω = 22.35 kΩ 200 Ω + 200 Ω

 W‫א‬‫א‬‫א‬‫א‬E٢F

S d.c =

  S a.c =

R T 22.5 kΩ = = 5 kΩ / V E d.c 4.5 V

R T 22.5 kΩ = = 2.25 kΩ / V E a.c 10 V

 W‫א‬‫א‬‫א‬‫א‬E٣F

   

 ‫א‬‫א‬‫א‬‫א‬‫ א‬٢ J٤ J٢ J٢  D'Arsonval Meter with Full Wave Rectification ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  ،‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬

K ‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E١٨ J٢F  K(bridge rectifier)    

 

  -٤٥-

‫א‬‫א‬

 

‫א‬‫א‬‫א‬‫א‬

٢٦٧

‫א‬

 

‫א‬

   

   

RS

 

If.s Rm

     

 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E١٨ J٢F  

‫א‬‫א‬،‫א‬‫א‬

‫א‬F‫א‬‫א‬‫א‬‫א‬K  ‫א‬‫א‬

‫א‬‫א‬،،E‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  W‫א‬‫א‬‫א‬‫א‬

E٤٦ J٢F

Q E av =

2 E max = 0.636 E max π

 E٤٧ J٢F

Q E max = 1.414 E r.m.s

 E٤٨ J٢F

∴ E av = 0.636 × 1.414 E r.m.s = 0.9 E r.m.s

 E٤٩ J٢F

∴ E r.m.s =

E av = 1.11 E av 0.9

‫א‬‫א‬‫א‬‫א‬‫א‬[1.11]‫א‬

‫א‬، ‫א‬‫א‬‫א‬،‫א‬

K ‫א‬‫א‬‫א‬     ‫א‬

‫א‬‫א‬ ‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬

-٤٦-

‫א‬‫א‬

 

‫א‬‫א‬‫א‬‫א‬

٢٦٧

‫א‬

 

‫א‬

‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬

 K‫א‬

 E٨ J٢F ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 KEr.m.s=10 V‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬،E١٩ J٢F  

 

RS

E r.m.s = 10 V

 

I f .s = 1 mA  

 

 

R m = 500 Ω

   

 KE٨ J٢F‫א‬‫א‬‫א‬‫א‬E١٩ J٢F

S d.c =

1 I FS

=

1 = 1 kΩ / V 1 mA

 W‫א‬

 W‫א‬‫א‬‫א‬‫א‬

 W‫א‬‫א‬

E d.c = 0.9 × E r.m.s = 0.9 × 10 Vr.m.s = 9 V

R T = S d.c × E d.c = 1kΩ / V × 9 V = 9 kΩ = R S + R m

 W‫א‬‫א‬

∴ R S = 9 kΩ − 500 Ω = 8.5 kΩ

 

-٤٧-

‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬

 

٢٦٧

‫א‬

 

‫א‬

 E٩ J٢F

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

،‫א‬50 Ω‫א‬‫א‬‫א‬‫א‬،E٢٠ J٢F  KRS‫א‬‫א‬‫א‬

 W‫א‬

K‫א‬‫א‬‫א‬‫א‬

K‫א‬‫א‬‫א‬‫א‬

EF

EF

EF

 ‫א‬

 W‫א‬‫א‬RS‫א‬‫א‬‫א‬ EF E d.c = 0.9 × E r.m.s = 0.9 × 10 Vr.m.s = 9 V

  E in = 10 Vr.m.s

 

  RS

  IT

I sh

 

R sh = 500 Ω

 

I f .s = 1 mA

R m = 500 Ω

 

 KE٩ J٢F‫א‬‫א‬‫א‬‫א‬E٢٠ J٢F

 

 W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ I sh × R sh = I m × R m = 1 mA × 500 Ω = 0.5 V I sh =

0.5 V = 1 mA 500Ω

I T = I m + I sh = 1 mA + 1 mA = 2 mA

 WIT‫א‬‫א‬‫א‬  WRT‫א‬‫א‬

-٤٨-

‫א‬‫א‬

 

‫א‬‫א‬‫א‬‫א‬

RT =

٢٦٧

 

‫א‬ ‫א‬

E d.c 9V = = 4.5 kΩ IT 2 mA

 WRS‫א‬‫א‬‫א‬ R T = R S + 2R d +

R m R sh R m + R sh

4.5 kΩ = R S + 2 × 50 +

500 Ω × 500 Ω 500 Ω + 500 Ω

R S = 4.5 kΩ − 350 Ω = 4.15 kΩ

 W‫א‬‫א‬‫א‬‫א‬ EF R T = S d.c × E d.c S d.c =

R T 4.5 kΩ = = 500 Ω / V E d.c 9V

 W‫א‬‫א‬‫א‬‫א‬ EF S a.c =

RT 4.5 kΩ = = 450 Ω / V E r.m.s 10 Vr.m.s

                  -٤٩-

‫א‬‫א‬

 

‫א‬‫א‬‫א‬‫א‬

٢٦٧

 

‫א‬ ‫א‬

 ‫א‬‫א‬   ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫ א‬E١F K100 µA‫א‬‫א‬850 Ω

‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬‫ א‬E٢F

 100 µA‫א‬‫א‬‫א‬100 mA 

K(Rm = 570 Ω)‫א‬‫א‬

‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬‫ א‬E٣F 200 µA‫א‬‫א‬‫א‬150 V

K(Rm = 570 Ω)‫א‬‫א‬

 

 ‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬  ‫א‬ ‫ א‬E٤F K100 µA(Im)‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫ א‬E٥F K20 kΩ/V‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫ א‬E٦F K50 kΩ/V‫א‬

‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬‫ א‬E٧F ‫א‬‫א‬1 mA‫א‬‫א‬‫א‬150 mA

K105 Ω

W (2 kΩ‫א‬‫א‬‫א‬F‫א‬‫א‬ E٨F K18 kΩ‫א‬‫א‬0-10 V‫א‬A EF

F . 298 kΩ‫א‬‫א‬0-300 V‫א‬B E -٥٠-

‫א‬‫א‬

 

‫א‬‫א‬‫א‬‫א‬

٢٦٧

‫א‬

 

‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬R1, R2& R3‫א‬‫ א‬E٩F W‫א‬

Im = 50 µA

Rm = 1 kΩ

R3

R2

R1

I 3 = 100 mA

I 2 = 10 mA

     

I1 = 1 mA

  ‫א‬‫א‬‫א‬‫א‬‫א‬R1, R2, R3& R4‫א‬‫ א‬E١٠F W‫א‬

Im = 50 µA

Rm = 1 kΩ

         

R1

R3

R2

R4

     

-

I 4 = 100 mA

I 3 = 10 mA

I 2 = 1 mA I1 = 100 µA

     

-٥١-

‫א‬‫א‬

 

‫א‬‫א‬‫א‬‫א‬

٢٦٧

‫א‬

 

‫א‬

‫א‬‫א‬‫א‬‫א‬ R1 JR3‫א‬‫ א‬E١١F W‫א‬

R1

R2

R3

     

Im = 50 µA

 

Rm = 2 kΩ

  1V

5V

10 V

   

‫א‬‫א‬‫א‬  ‫א‬ R1 JR5‫א‬‫ א‬E١٢F W‫א‬

-٥٢-

‫א‬‫א‬

 

‫א‬‫א‬‫א‬‫א‬

٢٦٧

‫א‬

 

R1

R2

R3

‫א‬

R5

R4

 

Im = 50 µA

   

Rm = 2 kΩ 1V

10 V

5V

50 V

100 V

   

Rx‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬ E١٣F K‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬

R2= 4.6 kΩ

Im = 50 µA

Rm = 2 kΩ

     

Rsh=500 Ω

R= 1 kΩ   =

 

Rx

 

E = 1.5 V ‫א‬‫א‬ ،‫א‬‫א‬6 kΩ‫א‬‫א‬ E١٤F 1 V, 5 V, 10 V, W  ‫א‬‫א‬‫؛‬10 kΩ/V

 ‫א‬‫א‬‫א‬‫א‬،100 V K‫א‬3%

   

10 kΩ

 

E=8V

  6 kΩ

-٥٣-

V0

   

‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬

 

٢٦٧

‫א‬

 

‫א‬

‫א‬X, Y‫א‬5 kΩ/V‫א‬‫א‬A‫ א‬E١٥F ‫א‬‫א‬B‫א‬،30V‫א‬‫א‬15V‫א‬‫א‬‫א‬

.B‫א‬‫א‬50V‫א‬‫א‬16.13V‫א‬‫א‬X, Y‫א‬

   

100 kΩ

 

E = 100 V

X R

   

V0

Y

   

‫א‬‫א‬‫א‬‫א‬50 kΩ‫א‬‫א‬ E١٦F 10 V‫א‬‫א‬±2%20 kΩ/V ‫؟‬‫א‬‫א‬

     

30 kΩ E = 12 V

  50 kΩ

V0

   

E ‫א‬F‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬ E١٧F ‫؟‬‫א‬‫א‬‫א‬‫א‬‫א‬،150 µApeak

‫א‬‫א‬،1mA‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬ E١٨F

‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬ K‫א‬‫א‬‫א‬

-٥٤-

 

‫א‬‫א‬

 

‫א‬‫א‬‫א‬‫א‬

٢٦٧

 

‫א‬ ‫א‬

‫א‬‫א‬،1mA‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬ E١٩F

‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬ K‫א‬‫א‬‫א‬

0.8 mA‫א‬E‫א‬F‫א‬‫א‬‫א‬‫ א‬E٢٠F ‫؟‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 

0.8 mA‫א‬E‫א‬F‫א‬‫א‬‫א‬‫ א‬E٢١F ‫؟‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

1mA‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬ E٢٢F

،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬،500 Ω‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ K30 Vrms‫א‬‫א‬‫א‬‫א‬‫א‬

200µA‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬ E٢٣F

،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬،500 Ω‫א‬‫א‬

 .50Vp-p‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬E ‫א‬F‫א‬‫א‬‫א‬ E٢٤F ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ W‫א‬

RS

RD = 300 Ω

I f .s = 1 mA

E in = 20 Vr.m.s

R m = 250 Ω

           

-٥٥-

‫א‬‫א‬

 

‫א‬‫א‬‫א‬‫א‬

٢٦٧

‫א‬

 

‫א‬

‫א‬‫א‬E ‫א‬F‫א‬‫א‬‫א‬ E٢٥F ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ W‫א‬

RS

E in = 20 Vr.m.s

IT

RD2 = 300 Ω

 

I sh RD1= 300 Ω

 

R sh = 250Ω

  I f .s = 1 mA  

R m = 250 Ω 

   

‫א‬‫א‬E  ‫א‬F‫א‬‫א‬‫א‬ E٢٦F ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ K‫א‬

 

RS

E in = 20 Vr.m.s

   

I f .s = 1 mA 

 

R m = 250 Ω

   

‫א‬‫א‬E ‫א‬F‫א‬‫א‬‫א‬ E٢٧F

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ KE300 Ω‫א‬‫א‬‫א‬F‫א‬

-٥٦-

‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬

 

٢٦٧

‫א‬

 

‫א‬

  RS

E in = 20 Vr.m.s

   

I f .s = 2 mA  

 

R m = 500 Ω

-٥٧-



 ‫א‬‫א‬

‫א‬‫א‬

٣

‫א‬‫א‬ ‫א‬‫א‬

 

٢٦٧

 

‫א‬ 

 

 K‫א‬‫א‬‫א‬‫א‬‫א‬W‫א‬‫א‬    W‫א‬‫א‬W‫א‬‫א‬‫א‬‫א‬ K‫א‬‫א‬‫א‬‫א‬ •

K‫א‬‫א‬‫א‬‫א‬‫א‬ •

K‫א‬‫א‬‫א‬‫א‬ • K‫א‬‫א‬‫א‬ •    K٪١٠٠‫א‬‫א‬‫א‬‫א‬ W‫א‬‫א‬‫א‬

 

 KW‫א‬‫א‬

 

 W‫א‬‫א‬

K‫א‬‫א‬ •

K‫א‬K‫א‬ •   K‫א‬‫א‬‫א‬‫א‬W‫א‬‫א‬

- ٥٧ -

‫א‬‫א‬

 

‫א‬‫א‬

٢٦٧

‫א‬ 

   

 (Introduction) ١ J٣ F‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬،E‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬

  ،‫א‬(parameters)‫א‬

 K‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬

، ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬



KEEF١ J٣F‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬ ‫א‬ KEEF١ J٣F

‫א‬‫א‬  ‫א‬‫א‬  ‫א‬‫א‬‫א‬  K‫א‬





 



 ‫א‬



 





   

  ‫א‬

 

 ‫א‬





 

‫א‬

 

 

 ‫א‬‫א‬‫א‬‫א‬‫א‬EF

 ‫א‬‫א‬EF



 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E١ J٣F  

- ٥٨ -

             

‫א‬‫א‬ ‫א‬‫א‬

 

٢٦٧

 

‫א‬ 

 

 (Digital Voltmeters [DVM])‫א‬‫א‬ ٢ J٣ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬   ‫א‬‫א‬W‫א‬ ‫א‬‫א‬K‫א‬‫א‬

‫א‬(Decade Counting Units)‫א‬‫א‬‫א‬(A/D Converters)‫א‬

‫א‬  ‫א‬(Display Unit)‫א‬‫א‬

 W‫א‬‫א‬‫א‬‫א‬

 (Single-slope DVM's)‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ K١  (Dual-slope DVM's)‫א‬‫א‬‫א‬‫א‬‫א‬ K٢

(Voltage-to-Frequency Converters)‫א‬ K٣

(Successive-Approximation DVM's)‫א‬‫א‬‫א‬‫א‬‫א‬ K٤  K‫א‬‫א‬‫א‬

(Single-Slope DVM's)‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬



١ J٢ J٣

 ‫א‬ ‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬  ‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬

‫א‬‫א‬  ،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E٢ J٣F



‫א‬‫א‬‫א‬،(-Vref)‫א‬‫א‬،

(Integrator)‫א‬‫א‬‫א‬‫א‬K ‫א‬(Vx)‫א‬‫א‬‫א‬

‫א‬ (Counter)‫א‬‫א‬(AND)‫א‬،(Comparator)  W‫א‬‫א‬K(digital readout)

 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ K١

 (1)  ‫א‬F(main gate control)‫א‬‫א‬‫א‬ K٢ ،(leading edge)‫א‬‫א‬S‫א‬،EE٣ J٣F  K[High]‫א‬‫א‬AND‫א‬‫א‬‫א‬

K  ‫א‬‫א‬ ‫א‬‫א‬C‫א‬،S‫א‬ K٣ ‫]א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 K[E٣ J٣F(2)

- ٥٩ -

‫א‬‫א‬

 

‫א‬‫א‬

٢٦٧

‫א‬ 

   

‫א‬‫א‬(Vx)‫א‬‫א‬[High]‫א‬ K٤

AND‫א‬‫א‬‫א‬،K[E٣ J٣F(3) ‫]א‬

K[High]

 



‫א‬

S‫א‬

R Vref (−)

-

 

1

‫א‬ C

‫א‬

S

+

 Vx

 

‫א‬

3 2

5



 



-

‫א‬

+



4

         

 ‫א‬

 K‫א‬E٢ J٣F

   

 J٣F (4)  ‫]א‬Clock ‫א‬‫א‬‫א‬

،[High]‫א‬‫א‬‫א‬‫א‬،AND‫א‬‫א‬‫א‬[E٣



K٥

[E٣ J٣F(5) ‫]א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 K(Binary Counter)‫א‬‫א‬‫א‬‫א‬

   ‫א‬‫א‬  ‫א‬،Vx

 ‫א‬،‫א‬‫א‬AND‫א‬‫א‬‫א‬،‫א‬

 K‫א‬‫א‬‫א‬‫א‬(Clock)

K٦

‫א‬،Vx‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

K٧

،(main gate control)‫א‬‫א‬‫א‬‫א‬،

K٨

 K‫א‬‫א‬(digital readout)‫א‬

‫א‬(falling edge)‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬‫א‬ - ٦٠ -

‫א‬‫א‬

 

‫א‬‫א‬

٢٦٧

 

‫א‬ 

 

‫א‬‫א‬،C‫א‬‫א‬،S‫א‬  K‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬E٣ J٣F

 K(Timing Diagram)E٢ J٣F    

S‫א‬  S‫א‬

 

1

 

Vx t1

T

 

2

t2

 

 

3

 

4

 

5

 

   

 K‫א‬‫א‬‫א‬E٣ J٣F  ‫א‬ ‫א‬‫א‬  ‫א‬‫א‬( T )‫א‬‫א‬

  

K‫א‬‫א‬‫א‬،‫א‬

 W[Vio(t)]‫א‬‫א‬ 1 t Vio ( t ) = − ∫ − Vref dt RC t



E١ J٣F

1

∴ Vio ( t ) =

1 Vref ( t − t 1 ) RC

E٢ J٣F

‫א‬ ‫א‬  t2‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬t1

 W‫א‬‫א‬‫א‬‫א‬‫א‬ - ٦١ -

‫א‬‫א‬

 

‫א‬‫א‬

٢٦٧

 

‫א‬ 

 

at

t = t2

⇒

E٣ J٣F

Vio ( t 2 ) = Vx

1 Vref ( t 2 − t 1 )  E٤ J٣F RC  W،‫א‬‫א‬T‫א‬t2t1‫א‬‫א‬ T = t2 – t 1 ∴ Vio ( t 2 ) = Vx =

∴ Vx = or

1 Vref T RC

E٥ J٣F

Vx Vref

E٦ J٣F

T = RC

 KVx‫א‬‫א‬‫א‬T‫א‬‫א‬‫א‬‫א‬

  ، ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ،E‫א‬R, C‫א‬‫א‬F‫א‬‫א‬‫א‬ 

‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬

 K‫א‬‫א‬

 E١ J٣F

‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬t2t1T‫א‬‫א‬‫א‬

‫א‬‫א‬، Vx = 5 V ‫א‬، C = 0.1 µf ‫א‬ R = 100 kΩ

 K Vref = − 10 V

 ‫א‬

 W،E٦ J٣F‫א‬‫א‬

 

T = RC

Vx 5 = 100 × 10 3 × 0.1 × 10 −6 × = 5 × 10 −3 sec = 5 m sec 10 Vref

(Dual-Slope DVM's)‫א‬‫א‬‫א‬‫א‬‫א‬

٢ J٢ J٣

، ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 K  E٤ J٣F

- ٦٢ -

‫א‬‫א‬

٢٦٧

 

‫א‬‫א‬

‫א‬ 

   

R‫א‬‫א‬A1‫א‬‫א‬‫א‬

  ‫א‬‫א‬،A2‫א‬‫א‬‫א‬،C‫א‬

[High]    ،  ‫א‬[Low]  W‫א‬‫א‬K ‫א‬

 W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ K١

 KCS2‫א‬  J١

 KA‫א‬S1‫א‬  J٢

K(0000…...0)‫א‬‫א‬  J٣ ‫داﺋﺮة‬ ‫ﺗﺤﻜﻢ‬ ‫ﻣﻨﻄﻘﻴﺔ‬

S2

 

Vref (-) B

Vi

A

R

 

C

 

S1

+

A1

+

   

A2

 

‫ﻋﺪاد‬

 

‫ﻧﺒﻀﺎت‬ ‫اﻟﺴﺎﻋﺔ‬

 

 KE٤ J٣F

 

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ K٢  K‫א‬،E٥ J٣F

 ‫א‬‫א‬ K٣ ،[High]‫א‬  K‫א‬‫א‬(Clock)‫א‬AND‫א‬‫א‬

 

 

- ٦٣ -

‫א‬‫א‬

 

‫א‬‫א‬

٢٦٧

‫א‬ 

   

 

‫ﺧﺮج اﻟﻤﻜﺎﻣﻞ‬

  t1

‫ﺧﺮج اﻟﻤﻘﺎرن‬

t2

 

t3

     

 KE٤ J٣F‫א‬‫א‬‫א‬E٥ J٣F

 t2‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬ K٤

‫א‬‫א‬‫א‬‫א‬ [Overflow Pulse]،E٥ J٣F

‫א‬،‫א‬Vref‫א‬‫א‬،B‫א‬S1‫א‬

 K(0000 ……0)‫א‬‫א‬(at time t2)

‫א‬‫א‬‫א‬t3t2‫א‬C‫א‬ K٥ ،t3‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬  ‫א‬(Clock) ‫א‬AND‫א‬‫א‬  ،[Low]‫א‬‫א‬

 ‫א‬‫א‬‫א‬، ‫א‬‫א‬‫א‬ t3t2  K‫א‬

‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬ t3‫א‬ K٦  K‫א‬

 WA‫א‬S1‫א‬‫א‬ 1 t V1 ( t ) = − ∫ Vin dt RC t

t1 ≤ t ≤ t 2

E٧ J٣F

1

∴ V1 ( t ) = − at

Vin (t − t1 ) RC

t = t2

∴ V1 ( t 2 ) = − If

⇒

E٨ J٣F E٩ J٣F

V1 ( t ) = V1 ( t 2 )

Vin (t 2 − t1 ) RC

E١٠ J٣F E١١ J٣F

T1 = t 2 − t 1

- ٦٤ -

‫א‬‫א‬

 

‫א‬‫א‬

٢٦٧

‫א‬ 

   

 E١٢ J٣F

∴ V1 ( t 2 ) = −

Vin T1 RC

‫א‬V2(t)‫א‬،t3t2، ‫א‬‫א‬‫א‬

 W

1 t V2 ( t ) = V1 ( t 2 ) + ∫ Vref dt RC t

E١٣ J٣F

2

∴ V2 ( t ) = V1 ( t 2 ) +

at

t = t3

⇒

1 Vref ( t − t 2 ) RC

E١٤ J٣F E١٥ J٣F

V2 ( t 3 ) = 0

∴

1 1 Vref ( t 3 − t 2 ) = Vin T1 RC RC

E١٦ J٣F

If

T2 = t 3 − t 2 therefore,

E١٧ J٣F E١٨ J٣F

Vref T2 = Vin T1 which equal, T2 Vin = T1 Vref

⇒

Vin = Vref

T2 T1

E١٩ J٣F

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 KT2‫א‬‫א‬

 

 E٢ J٣F

،-5 V  ‫א‬‫א‬‫א‬t2‫א‬Vref‫א‬‫א‬‫א‬  KT1=1 secVi =1 V‫א‬‫؟‬t3t2‫א‬‫א‬‫א‬

 ‫א‬

 W،E١٩ J٣F‫א‬‫א‬ T2 = T1 ×

Vin 1 = 1 × = 0.2 sec Vref 5 - ٦٥ -

‫א‬‫א‬

 

‫א‬‫א‬

٢٦٧

 

‫א‬ 

 

 (Digital Multimeter [DMM])‫א‬‫א‬‫א‬ ٣ J٣ ‫א‬L  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬   K(Decade Counter)‫א‬‫א‬

 ‫א‬ E٦ J٣F



(Compensated Attenuator)،‫א‬‫א‬(Attenuator)

‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬‫א‬ 

K‫א‬‫א‬‫א‬،‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬



‫א‬‫א‬‫א‬L‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬

،(Rectifier)‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬



 K‫א‬‫א‬‫א‬

E٦ J٣F ‫א‬(Current-to-Voltage Converter) ‫א‬

‫א‬‫א‬‫א‬‫א‬KE٧ J٣F‫א‬‫א‬

  ‫א‬‫א‬ ‫א‬K  ‫א‬‫א‬،Σi،(Summing Junction)

 ، ‫א‬‫א‬،‫א‬ KIi‫א‬ IR‫א‬

 ‫א‬‫א‬‫א‬(Voltage drop)IR‫א‬ ‫א‬L  ‫א‬‫א‬‫א‬ ‫א‬‫א‬K‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬

- ٦٦ -

‫א‬‫א‬

 

‫א‬‫א‬

٢٦٧

‫א‬ 

   

  DCV

 

ACV DCMA



OHMS

 DCV

DCMA

‫א‬

   

DCMA OHMS

  

  

     

 

 K‫א‬E٦ J٣F

   

10 Ω

 

100 Ω

‫ﺗﻴﺎر ﻣﺠﻬﻮل‬

 

‫א‬



Ii

 

 





IR



  ‫א‬



OHMS

‫א‬

ACV





ACV

DCV

 

‫א‬

1 kΩ

     

J

 

+

 

‫א‬

 KE٧ J٣F

- ٦٧ -

   

 

‫א‬‫א‬ ‫א‬‫א‬

 

٢٦٧

 

‫א‬ 

 

‫א‬‫א‬‫א‬



‫א‬L‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬K‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬                              

- ٦٨ -

‫א‬‫א‬

 

‫א‬‫א‬

٢٦٧

‫א‬ 

   

 ‫א‬‫א‬

 

 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ K١

K‫א‬‫א‬‫א‬‫א‬‫א‬‫ א‬K٢ K‫א‬‫א‬‫א‬‫א‬‫א‬‫ א‬K٣

K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫ א‬K٤

،‫א‬‫א‬‫א‬‫א‬‫א‬( T )‫א‬‫א‬‫א‬ K٥ K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫ א‬K٦

K‫א‬‫א‬‫א‬‫א‬‫א‬‫ א‬K٧

K‫א‬‫א‬‫א‬‫א‬‫א‬‫ א‬K٨ K‫א‬‫א‬‫ א‬K٩

‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬t2t1T‫א‬‫א‬‫א‬ K١٠ ، Vx = 5 V ‫א‬، C = 50 nf ‫א‬ R = 200 kΩ ‫א‬ K Vref = − 10 V ‫א‬‫א‬

K C = 75 nf ‫א‬ R = 250 kΩ ‫א‬‫א‬،‫א‬‫א‬ K١١ -5 V‫א‬‫א‬‫א‬t2‫א‬Vref‫א‬‫א‬‫א‬ K١٢ KT1=3 secVi =1.1 V‫א‬‫؟‬t3t2‫א‬‫א‬‫א‬،

 KT1=2 secVi =1.5 V‫א‬‫א‬،‫א‬‫א‬ K١٣

- ٦٩ -

 



 ‫א‬‫א‬

‫א‬‫א‬

٤

‫א‬‫א‬‫א‬

 ٢٦٧

‫א‬

‫א‬‫א‬

 



 

 K‫א‬‫א‬‫א‬‫א‬‫א‬W‫א‬‫א‬    W‫א‬‫א‬W‫א‬‫א‬‫א‬‫א‬‫א‬ K‫א‬‫א‬‫א‬‫א‬ •

K‫א‬‫א‬‫א‬‫א‬‫א‬ • K‫א‬‫א‬‫א‬‫א‬‫א‬ •

K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ •    K٪١٠٠‫א‬‫א‬‫א‬‫א‬ W‫א‬‫א‬‫א‬  

 KW‫א‬‫א‬

 

 W‫א‬‫א‬

K‫א‬‫א‬ •

K‫א‬K‫א‬ •   K‫א‬‫א‬‫א‬‫א‬W‫א‬‫א‬

-٧١-

‫א‬‫א‬‫א‬

 ٢٦٧

‫א‬

‫א‬‫א‬

 



 

 Introduction ١ J٤ ،‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬



،،‫א‬‫א‬

  ،‫א‬‫א‬K‫א‬،‫א‬‫א‬

  ‫א‬‫א‬، ‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬



K ‫א‬‫א‬،‫א‬

‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬،

،‫א‬‫א‬‫א‬‫א‬‫א‬



 K‫א‬‫א‬‫א‬

 Oscilloscope Block Diagram ‫א‬‫א‬‫א‬‫ א‬٢ J٤ ‫א‬‫א‬(Cathode-Ray Tube or CRT)‫א‬

KEE١ J٤F ‫א‬F ‫א‬‫א‬‫א‬

،‫א‬‫א‬Y, X ‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬

 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬  ‫א‬ Y 



، ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬ C1   ‫א‬‫א‬،‫א‬‫א‬E١ J٤F S1 ‫א‬

‫א‬‫א‬ ‫א‬  ،‫א‬‫א‬‫א‬

d.cS1،‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬  K‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬  ،Y‫א‬‫א‬Y‫א‬‫א‬



‫א‬K‫א‬‫א‬‫א‬‫א‬Y‫א‬

 (preamplifier).‫א‬‫א‬‫א‬‫א‬ -٧٢-

‫א‬‫א‬‫א‬

 ٢٦٧

‫א‬

‫א‬‫א‬

 



 

     

 

 

           

   

 K‫א‬‫א‬‫א‬E١ J٤F ‫א‬‫א‬‫א‬  (time base)  ‫א‬

 



 ‫א‬ ‫א‬‫א‬‫א‬،(saw tooth waveform)‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬

‫א‬‫א‬KEX ‫א‬F‫א‬‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬‫א‬

، ‫א‬‫א‬‫א‬



‫א‬، ‫א‬‫א‬‫א‬، ‫א‬‫א‬  C2‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

K ‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬X

 ‫א‬ ‫א‬xz،[]E٢ J٤F‫א‬

 K‫א‬‫א‬  

-٧٣-

‫א‬‫א‬‫א‬

 ٢٦٧

‫א‬

‫א‬‫א‬

 



 

   [][]

 

 Kxz،[]‫א‬‫א‬E٢ J٤F ‫א‬‫א‬‫א‬، ‫א‬‫א‬



‫א‬ [E١ J٤F  S3]  K ‫א‬‫א‬

، ‫א‬‫א‬‫א‬‫א‬ ،‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬، ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬



K ‫א‬‫א‬E١ J٤FS2‫א‬،‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

  (graticule)  ‫א‬‫א‬



 ‫א‬‫א‬‫א‬‫א‬KE ‫א‬F‫א‬ ‫א‬،Y‫א‬‫א‬‫א‬‫א‬K

[VOLTS/DIV]Y، [(١ J٤FS1] ‫א‬

 ‫א‬Y‫א‬‫א‬‫א‬.Y‫א‬‫א‬ Y‫א‬VOLTS/DIV‫א‬K‫א‬Y‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬[TRIGGER LEVEL]‫א‬‫א‬‫א‬



،AUTOTrigger level‫א‬،‫א‬‫א‬‫א‬K‫א‬‫א‬

 K[? J?،?H?]‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬ VARIABLE  ‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬

TIME/DIV‫א‬KTIME/DIVCONTROL

K‫א‬CalibrateVARIABLE CONTROL‫א‬

 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ shift JX

-٧٤-

‫א‬‫א‬‫א‬

 ٢٦٧

‫א‬

‫א‬‫א‬

 



 

FOCUS  INTENSITY،‫א‬



‫א‬،‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬  K‫א‬E‫א‬F‫א‬‫א‬‫א‬‫א‬‫א‬

 Oscilloscope as a measuring instrument‫א‬‫א‬‫א‬‫א‬٣ J٤ ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬

‫א‬،2 - 10MHz‫א‬‫א‬‫א‬K‫א‬‫א‬  K‫א‬‫א‬

 ‫א‬، ‫א‬‫א‬‫א‬‫א‬



‫א‬‫א‬K‫א‬‫א‬(Calibration)‫א‬ ‫א‬‫א‬،‫א‬‫א‬‫א‬K ،50Hz‫א‬‫א‬K‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬10ms/divTIME/DIV  K‫א‬‫א‬10 div

 Voltage Measurements‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

١ J٣ J٤

‫א‬ E‫א‬‫א‬F‫א‬‫א‬



‫א‬FA‫א‬K(sine waves)E٣ J٤FK‫א‬

2 div‫א‬E‫א‬‫א‬F B ‫א‬،‫א‬‫א‬4.5div‫א‬E‫א‬

،100mv[VOLTS/DIV]‫א‬‫א‬‫א‬K‫א‬‫א‬

 W‫א‬E‫א‬‫א‬F          

 KE JFE٣ J٤F -٧٥-

 

‫א‬‫א‬‫א‬

 ٢٦٧

‫א‬

‫א‬‫א‬

 



 

Wave A: VA = (4.5 DIV) × 100 mv/DIV = 450 mv Wave B: VB = (2.0 DIV) × 100 mv/DIV = 200 mv

 Frequency Measurements‫א‬‫א‬

٢ J٣ J٤

‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬



‫א‬(CAL)‫א‬‫א‬،Y

، ‫א‬ ‫א‬، ‫א‬  ‫א‬  W(T)‫א‬‫א‬،‫א‬‫א‬

T = (Horizontal divisions/cycle) × (TIME/DIV)

 W،(T)‫א‬‫א‬،(F)‫א‬  F = 1/T. ‫א‬،0.5 ms [TIME/DIV]‫א‬‫א‬

 WE٣ J٤F‫א‬(F)‫א‬(T)‫א‬

Wave A : TA = [(8.8 DIV) × 0.5 ms/DIV]/2 cycles = 2.2 ms FA = 1/ (2.2ms) ≅ 455 Hz Wave B : TB = [(8.8 DIV) × 0.5 ms/DIV]/6 cycles = 0.73 ms FB = 1/(0.73ms) ≅ 1.36 kHz

 Lissajous Figures‫א‬

٣ J٣ J٤

،‫א‬‫א‬‫א‬‫א‬



‫א‬  [Lissajous figures]

 K‫א‬‫א‬‫א‬‫א‬K‫א‬

‫א‬‫א‬Y(F2)‫א‬‫א‬‫א‬

‫א‬‫א‬،‫א‬X(F1)‫א‬‫א‬

KE٤ J٤F ‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  

-٧٦-

‫א‬‫א‬‫א‬

 ٢٦٧

‫א‬

‫א‬‫א‬

 



 

 F1/F2 = 3/2 F1/F2 = 5/3  [][]

 K‫א‬E٤ J٤F ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 



 W‫א‬‫א‬‫א‬،‫א‬‫א‬  

 F1LF2=E‫א‬‫א‬‫א‬FLE‫א‬‫א‬‫א‬F  Phase Angle Computation‫א‬

 

٤ J٣ J٤

‫א‬(Phase difference)‫א‬



 W‫א‬‫א‬‫א‬

‫א‬  ‫א‬‫א‬‫א‬  ‫א‬W‫א‬‫א‬

،(CAL)  ‫א‬‫א‬‫א‬ ‫א‬(Channel-1 and 2)

،‫א‬‫א‬‫א‬‫א‬

 K‫א‬

،‫א‬E٥ J٤F 1.4 divisions‫א‬‫א‬، ‫א‬‫א‬8 divisions

 ‫א‬‫א‬ ،8 div = 360°،  ،360°   (One cycle)‫א‬‫א‬‫א‬K  W

1 div = 360°/8 = 45°

        -٧٧-

‫א‬‫א‬‫א‬

 ٢٦٧

‫א‬

‫א‬‫א‬

 



 

         

       

 K‫א‬E٥ J٤F  

θ = 1.4 div × (45°/div) = 63°

 W‫א‬‫א‬‫א‬    

‫א‬‫א‬  ‫א‬،‫א‬W‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬،(Channel-1 and 2)‫א‬‫א‬  K‫א‬‫א‬‫א‬،E٦ J٤F

 ‫א‬‫א‬‫א‬،‫א‬ ‫א‬،0°



 ‫א‬‫א‬   F‫א‬‫א‬45°

 ‫א‬‫א‬‫א‬ ،E ‫א‬‫א‬

[ellipse]‫א‬‫א‬‫א‬،[0° < θ < 90°]90°0°  K‫א‬‫א‬‫א‬‫א‬

   

  -٧٨-



 



‫א‬‫א‬‫א‬

 ٢٦٧

‫א‬

‫א‬‫א‬

 



 

                             

 

 K‫א‬(1/1)E٦ J٤F ‫א‬ ‫א‬‫א‬90°‫א‬‫א‬‫א‬

 

‫א‬‫א‬KE‫א‬‫א‬F‫א‬

‫א‬ ‫א‬‫א‬[90° < θ < 180°]180°90°

‫א‬‫א‬‫א‬[ellipse]

 K‫א‬

‫א‬‫א‬‫א‬180°‫א‬‫א‬‫א‬،‫א‬

‫א‬F‫א‬‫א‬135°  KE‫א‬

-٧٩-

‫א‬‫א‬‫א‬

 ٢٦٧

‫א‬

‫א‬‫א‬

 



 

 ‫א‬[θ] ‫א‬‫א‬E٧ J٤F 

 K[ellipse]‫א‬‫א‬‫א‬‫א‬

                 

 K‫א‬‫א‬E٧ J٤F

   

 W‫א‬‫א‬‫א‬E٧ J٤F[θ] ‫א‬ Sin(θ) = Y1/Y2

 

 W

 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬W(Y1)  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬W(Y2)

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬ 

-٨٠-

‫א‬‫א‬‫א‬

 ٢٦٧

‫א‬

‫א‬‫א‬

 



 

 ‫א‬‫א‬‫א‬

 

K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 J١

K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 J٣

K‫א‬‫א‬

K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

-٨١-

 J٢

 J٤

 J٥

 J٦  



 ‫א‬‫א‬

‫א‬‫א‬

٥

‫א‬‫א‬

 ‫א‬٢٦٧

‫א‬

‫א‬‫א‬

 



 

 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬W‫א‬‫א‬    W‫א‬‫א‬W‫א‬‫א‬‫א‬‫א‬ K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ •

K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ •

K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ •

K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ •    K٪١٠٠‫א‬‫א‬‫א‬‫א‬ W‫א‬‫א‬‫א‬

 

 KW‫א‬‫א‬

 

 W‫א‬‫א‬

K‫א‬‫א‬ •

K‫א‬K‫א‬ •   K‫א‬‫א‬‫א‬‫א‬W‫א‬‫א‬

-٨٣-

‫א‬‫א‬

 ‫א‬٢٦٧

‫א‬

‫א‬‫א‬

 



 

Introduction  ١ J٥

‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

K ‫א‬‫א‬  ‫א‬‫א‬‫א‬K‫א‬ K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

  ‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ،، ‫א‬F‫א‬  ‫א‬‫א‬‫א‬‫א‬

 KE

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  

 Direct Current Bridges‫א‬‫א‬‫א‬‫א‬‫א‬‫ א‬٢ J٥  Wheatstone Bridge١ J٢ J٥

EE١ J٥FF

‫א‬K‫א‬‫א‬‫א‬

E  F‫א‬K ‫א‬‫א‬‫א‬(E)  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

I1    E

 

A I3

   

I2 R2

R1

B

G R3

R4

I4

 

 K‫א‬‫א‬‫א‬E١ J٥F

-٨٤-

 

‫א‬‫א‬

 ‫א‬٢٦٧

‫א‬

‫א‬‫א‬

 



 

‫א‬‫א‬،‫א‬‫א‬

‫א‬،‫א‬‫א‬ER2F‫א‬‫א‬ER4F‫א‬  K‫א‬‫א‬‫א‬

 Condition of Balance of Wheatstone Bridge‫א‬‫א‬

١ J١ J٢ J٥

‫א‬،‫א‬BA‫א‬‫א‬‫א‬‫א‬‫א‬

 W،R2‫א‬‫א‬R1‫א‬ E١ J٥F

I1 R 1 = I 2 R 2

 W،R4‫א‬‫א‬R3‫א‬‫א‬ E٢ J٥F

I3 R 3 = I 4 R 4

 W،‫א‬‫א‬

 I1 = I 3 , I 2 = I 4

E٣ J٥F

 WE٢ J٥F‫א‬E١ J٥F‫א‬ I1 R 1 I 2 R 2 = I3 R 3 I4 R 4

E٤ J٥F  WE٤ J٥F‫א‬E٣ J٥F‫א‬

R1 R = 2 R3 R4

E٦ J٥F

 W‫א‬،‫א‬‫א‬‫א‬E٦ J٥F‫א‬ E٧ J٥F

R1 R 4 = R 2 R 3

 E١ J٥F

‫א‬‫א‬E٢ J٥F‫א‬‫א‬‫א‬Rx‫א‬‫א‬‫א‬         -٨٥-

 K‫א‬‫א‬

‫א‬‫א‬

 ‫א‬٢٦٧

‫א‬

‫א‬‫א‬

 



 

  R1 = 12 kΩ E

A

   

  G

R2 = 15 kΩ B

 

R3 = 32 kΩ  

 

Rx

 KE١ J٥F‫א‬E٢ J٥F

 ‫א‬

 WEE٧ J٥FF‫א‬‫א‬،‫א‬‫א‬‫א‬ R1 R x = R 2 R 3

 WRx‫א‬‫א‬ Rx =

R 2 R 3 15 kΩ ⋅ 32 kΩ = 40 kΩ = R1 12 kΩ

 General solution of Wheatstone Bridge‫א‬‫א‬٢ J١ J٢ J٥ ‫א‬K ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬KK‫א‬‫א‬‫א‬‫א‬

Vth‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬

‫א‬RG‫א‬‫א‬‫א‬،rth‫א‬  W‫א‬‫א‬

 I G =

Vth  rth + R G

E٨ J٥F  WrthVth  VthW 

-٨٦-

‫א‬‫א‬

 ‫א‬٢٦٧

‫א‬

‫א‬‫א‬

 



 

RG‫א‬F Vth BA‫א‬‫א‬  KE‫א‬‫א‬

‫א‬‫א‬‫א‬Vth  WVthE٣ J٥FK‫א‬

E٩ J٥F  E١٠ J٥F

 Vth =









 Vth = V1 − V2 = I1 R 1 − I 2 R 2

R1 R2 E E − R1 − R2 = E ( ) R1 + R 3 R2 + R4 R1 + R 3 R 2 + R 4

-٨٧-

‫א‬‫א‬

 ‫א‬٢٦٧

‫א‬

‫א‬‫א‬

 



 

 rthW 

‫א‬‫א‬‫א‬‫א‬‫א‬rth  KE٤ J٥FrthBA‫א‬‫א‬ V1 E

A

I1

   

C

I2

Vth

B

R3 

   

 

V2

R2

R1

 

 

R4 D

 KVth‫א‬E٣ J٥F    

C R1

   

≡

R2

B  

A R3

R4 D

C

   

R2

R1

A

B

R3

 

R4 D

 

 Krth‫א‬‫א‬‫א‬E٤ J٥F R3R1‫א‬‫א‬rth‫א‬‫א‬

 



K‫א‬‫א‬‫א‬،‫א‬‫א‬R4R2‫א‬،‫א‬‫א‬  Wrth‫א‬‫א‬ -٨٨-

‫א‬‫א‬

 ‫א‬٢٦٧

‫א‬

‫א‬‫א‬

 



 

rth =

R1 R 3 R R + 2 4 R1 + R 3 R 2 + R 4

E١١ J٥F  E٢ J٥F

 KE٥ J٥F‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  

R1 = 1kΩ E=6V

 

R2 = 1.6 kΩ

 

RG = 200 Ω

 

A

 

R3 = 3.5 kΩ

B

G

 

R4 = 7.5 kΩ

 

 KE٢ J٥F‫א‬E٥ J٥F

 ‫א‬

 W‫א‬‫א‬‫א‬‫א‬

 WE١٠ J٥F‫א‬Vth

Vth = E (

R1 R2 − ) R1 + R 3 R 2 + R 4

⎛ ⎞ 1kΩ 1.6 kΩ ⎟⎟ = 0.278V − Vth = 6 × ⎜⎜ Ω + Ω Ω + Ω 1 k 3 .

5 k 1 .

6 k 7 .

5 k ⎝ ⎠

 WE١١ J٥F‫א‬rth rth =

R1 R 3 R2 R4 + R1 + R 3 R 2 + R 4

rth =

1 kΩ × 3.5 kΩ 1.6 kΩ × 7.5 kΩ = 2.096 kΩ + 1 kΩ + 3.5 kΩ 1.6 kΩ + 7.5 kΩ

 WE٨ J٥F‫א‬IG‫א‬‫א‬‫א‬ IG =

Vth 0.278 V = = 121.4 µA rth + R G 2.096 × 10 3 Ω + 200 Ω  

-٨٩-

‫א‬‫א‬

 ‫א‬٢٦٧

‫א‬

‫א‬‫א‬

 



   

 ‫א‬‫א‬‫א‬٣ J١ J٢ J٥

Slightly unbalanced Wheatstone Bridge

‫א‬‫א‬‫א‬‫א‬‫א‬

،E٦ J٥F‫א‬‫א‬‫א‬٪٥  W‫א‬‫א‬  

R

R  E

 

A

 

Vth

R 

B R+∆R

 

 K‫א‬‫א‬E٦ J٥F

 

 WE١٠ J٥F‫א‬VthW  ⎛ R1 R2 Vth = E × ⎜⎜ − ⎝ R1 + R 3 R 2 + R 4

⎞ ⎟⎟ ⎠

⎛ R ⎞ ⎛1 ⎞ R R ⎟⎟ = E × ⎜⎜ − ⎟⎟ Vth = E × ⎜⎜ − 2 R 2 R + ∆ R 2 2 R + ∆ R ⎝ ⎠ ⎝ ⎠

E١٢ J٥F

⎛ 2 R + ∆R ⎞ 2×R ⎟⎟ Vth = E × ⎜⎜ − ( ) ( ) 2 × 2 R + ∆ R 2 × 2 R + ∆ R ⎝ ⎠

E١٣ J٥F

⎛ ⎞ ∆R ⎟⎟ Vth = E × ⎜⎜ ( ) 2 × 2 R + ∆ R ⎝ ⎠

E١٤ J٥F

،2R‫א‬،∆R‫א‬‫א‬‫א‬‫א‬‫א‬  W‫א‬‫א‬

⎛ ∆R ⎞ ⎟⎟ Vth = E × ⎜⎜ ⎝4R ⎠

E١٥ J٥F -٩٠-

‫א‬‫א‬

 ‫א‬٢٦٧

‫א‬

‫א‬‫א‬

 



 

 WE١١ J٥F‫א‬rthW  rth =

R1 R 3 R2 R4 R ⋅ R R ⋅ (R + ∆R ) + = + R 1 + R 3 R 2 + R 4 R + R R + R + ∆R

E١٦ J٥F

rth =

R R ⋅ (R + ∆R ) + 2 2 R + ∆R

E١٧ J٥F

 W،‫א‬‫א‬R∆R rth =

R R ⋅ (R ) R R + = + =R 2 2R 2 2

E١٨ J٥F    E٣ J٥F

‫א‬‫א‬‫א‬‫א‬E٧ J٥F‫א‬‫א‬‫א‬‫א‬‫א‬

 K‫א‬ 500 Ω

500 Ω  10 V

A

 

G

  125 Ω 500 Ω  

B 525 Ω

 

 E٣ J٥F‫א‬E٧ J٥F

 

 ‫א‬

 W‫א‬‫א‬W  ⎛ R1 R2 Vth = E × ⎜⎜ − ⎝ R1 + R 3 R 2 + R 4

⎞ ⎟⎟ ⎠

⎛ 500 Ω 500 ⎞ ⎟⎟ = 0.122 V Vth = 10 V × ⎜⎜ − 1000 Ω 1025 ⎝ ⎠ -٩١-

‫א‬‫א‬

 ‫א‬٢٦٧

‫א‬

‫א‬‫א‬

 



 

rth =

R1 R 3 R2 R4 + R1 + R 3 R 2 + R 4

rth =

500 Ω ⋅ 500 Ω 500 Ω ⋅ 525 Ω = 506.1 Ω + 500 Ω + 500 Ω 500 Ω + 525 Ω

 W‫א‬‫א‬‫א‬

 I G =

Vth rth + R G

 I G =

0.122 V = 193.3 µA 506.1 Ω + 125 Ω

 

 W‫א‬‫א‬W ⎛ ∆R ⎞ ⎟⎟ Vth = E × ⎜⎜ ⎝4R ⎠ ⎛ 25 Ω ⎞ ⎟⎟ = 0.125 V Vth = 10 V × ⎜⎜ 4 × 500 Ω ⎝ ⎠ rth = R = 500 Ω

 

 W‫א‬‫א‬‫א‬

 I G =

Vth 0.125 V = = 200 µA rth + R G 500 Ω + 125 Ω

 

 Kelvin Bridge٢ J٢ J٥

،‫א‬‫א‬‫א‬E٨ J٥F



‫א‬‫א‬‫א‬‫א‬K  

 K‫א‬‫א‬‫א‬

-٩٢-

‫א‬‫א‬

 ‫א‬٢٦٧

‫א‬

‫א‬‫א‬

 



 

 

 

R2

  R1

  E

A

    R3  

Ra

G

B

Rlc

Rb Rx

 

 K‫א‬‫א‬‫א‬E٨ J٥F

E ‫א‬F‫א‬‫א‬‫א‬

 ‫א‬‫א‬‫א‬K‫א‬‫א‬

‫א‬ERa, RbF‫א‬‫א‬‫א‬‫א‬

K‫א‬‫א‬‫א‬Rlc‫א‬،  K‫א‬ 1Ω1 µΩ‫א‬

  Balance of Kelvin Bridge‫א‬‫א‬١ J٢ J٢ J٥

 W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ R R1 R = 2 = a R3 R4 Rb

E١٩ J٥F

 W،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ R R Rx = 3 = b R2 R1 R a Rx =

E٢٠ J٥F

R2 × R3 R2 × Rb = R1 Ra

E٢١ J٥F

-٩٣-

‫א‬‫א‬

 ‫א‬٢٦٧

‫א‬

‫א‬‫א‬

 



 

 E٤ J٥F

 R1=5Ω،1000RbRa‫א‬‫א‬،Rx‫א‬

 K R 1 = 0.5 R 2   

 ‫א‬

 W، R 1 = 0.5 R 2 R1=5Ω R2 =

R1 5Ω = = 10 Ω 0.5 0.5

 W‫א‬‫א‬

R Rx = b R2 Ra Rx =

 W

R 2 × R b 10 Ω × 1 = = 0.01 Ω Ra 1000

 

Digital readout Bridges‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬٣ J٢ J٥

‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬KK‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬،‫א‬‫א‬ ‫א‬‫א‬

‫א‬‫א‬ E٩ J٥FK‫א‬‫א‬ ‫א‬Amplifier‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  K‫א‬

-٩٤-

‫א‬‫א‬

 ‫א‬٢٦٧

‫א‬

‫א‬‫א‬

 



 

 

 

  Rb E

R2

   

A

B  R3

Rx

 

Amplifier EF

Logic circuits ‫)دواﺋﺮ‬ (‫ﻣﻨﻄﻘﻴﺔ‬

Readout 

   

 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E٩ J٥F

 

 ‫א‬‫א‬‫א‬‫א‬‫א‬٤ J٢ J٥

Microprocessor – controlled Bridges

K  ‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬

 ‫א‬‫א‬‫א‬‫א‬‫א‬

 ‫א‬‫א‬‫א‬K‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬K ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 

Applications on D.C Bridges‫א‬‫א‬‫א‬٥ J٢ J٥

 Murray Loop‫א‬‫א‬١ J٥ J٢ J٥

‫א‬‫א‬‫א‬

‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬

K  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬

‫א‬،‫א‬‫א‬K ‫א‬‫א‬E١٠ J٥F -٩٥-

‫א‬‫א‬

 ‫א‬٢٦٧

‫א‬

‫א‬‫א‬

 



 

،‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬‫א‬ R2

R1 E

 

A

La

B

G

   



‫א‬     

Lb

‫א‬

 



Lx

 

‫א‬

 

‫א‬

 

‫א‬‫א‬

 

 ‫א‬‫א‬E١٠ J٥F  

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬KRx‫א‬Lx‫א‬

‫א‬‫א‬‫א‬‫א‬Ra‫א‬La‫א‬

 KRb-Rx‫א‬Lb-Lx‫א‬

‫א‬‫א‬‫א‬ R2‫א‬‫א‬

 K‫א‬

 W،‫א‬‫א‬W‫א‬

 

E٢٢ J٥F  E٢٣ J٥F















R 2 R a + (R b − R x ) = R1 Rx

∴ R 2 R x = R1 R a + R1 R b − R1 R x

∴ R 2 R x + R1 R x = R1 R a + R1 R b -٩٦-

E٢٤ J٥F

‫א‬‫א‬

 ‫א‬٢٦٧

‫א‬

‫א‬‫א‬

 



 

∴ R x (R 1 + R 2 ) = R 1 (R a + R b )

  E٢٥ J٥F

 

Rx‫א‬‫א‬

 E٢٦ J٥F

∴R x =

R 1 (R a + R b ) (R 1 + R 2 )

 WE٢٦ J٥F‫א‬‫א‬‫א‬‫א‬ E٢٧ J٥F

QR =

ρL a

 W

 ‫א‬‫א‬‫א‬W ρ

 ‫א‬W L

 ‫א‬W a ∴

R1 ρx Lx = ax R1 + R 2

⎛ ρa La ρb L b ⎜⎜ + a ab ⎝ a

⎞ ⎟⎟ ⎠

E٢٨ J٥F

 W‫א‬‫א‬‫א‬‫א‬‫א‬ ∴L x =

R1 2 R 1L (2 L ) = R1 + R 2 R1 + R 2

E٢٩ J٥F  E٥ J٥F

  ‫א‬،E١١ J٥F‫א‬‫א‬‫א‬‫א‬

،‫א‬1760 m‫א‬‫א‬K ‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬100 Ω‫א‬‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬،300 Ω

-٩٧-

‫א‬‫א‬

 ‫א‬٢٦٧

‫א‬

‫א‬‫א‬

 



 

 

100 Ω E

A

300Ω   G

1760 m

 B



       

1760 m Lx



     

 KE٥ J٥F‫א‬‫א‬E١١ J٥F

∴L x =

2 R 1L 2 ×100 Ω × 1760 m = 880 m = R1 + R1 100 Ω + 300 Ω

 

 ‫א‬

Alternating Current Bridges‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬٣ J٥

‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

K ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 ، ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬K

‫א‬‫א‬‫א‬‫א‬‫א‬

،‫א‬‫א‬KEE١٢ J٥F F‫א‬(detector)

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 .(Filters)‫א‬‫א‬(Amplifiers)‫א‬‫א‬‫א‬(Oscillators)

‫א‬‫א‬‫א‬‫א‬‫א‬



‫א‬‫א‬‫א‬‫א‬،‫א‬  K‫א‬‫א‬‫א‬‫א‬ -٩٨-

‫א‬‫א‬

 ‫א‬٢٦٧

‫א‬

‫א‬‫א‬

 



 

 

 

a

 

  Z1

a.c source

b  

Z2 a.c detector

 Z 3    

c Z4

d

 K‫א‬‫א‬E١٢ J٥F

 

 Balance of A.C Wheatstone Bridge‫א‬‫א‬‫א‬١ J٣ J٥

‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬

K‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬،balance

‫א‬K‫א‬ c b‫א‬‫א‬‫א‬  KE١٣ J٥F‫א‬

    I1 a.c source

a

 

Z1

 

I2

 b

Z2 c

 

I3  Z3

I4

Z4

d

 K‫א‬‫א‬‫א‬‫א‬‫א‬E١٣ J٥F  

-٩٩-

   

‫א‬‫א‬

 ‫א‬٢٦٧

‫א‬

‫א‬‫א‬

 



 

‫א‬ ‫א‬cb‫א‬‫א‬‫א‬

‫א‬ab‫א‬‫א‬K‫א‬ E٣٠ J٥F







 W‫א‬،ac‫א‬  

 I1 Z1 = I 2 Z 2

‫א‬،dc‫א‬‫א‬db‫א‬‫א‬  W E٣١ J٥F

I3 Z3 = I 4 Z 4

 W،‫א‬bc‫א‬‫א‬‫א‬ E٣٢ J٥F

I1 = I 3

E٣٣ J٥F

I2 = I4 I 1 Z1 I 2 Z 2 = I3 Z3 I 4 Z 4

 WE٣١ J٥F‫א‬E٣٠ J٥F‫א‬ E٣٤ J٥F  W،E٣٣ J٥FE٣٢ J٥F

Z1 Z = 2 Z3 Z4

E٣٥ J٥F  WE٣٥ J٥F‫א‬ E٣٦ J٥F

Z1 Z 4 = Z 2 Z 3

 W‫א‬‫א‬E٣٦ J٥FE٣٥ J٥F‫א‬‫א‬ Z1∠θ1 Z ∠θ = 2 2 Z 3 ∠θ 3 Z 4 ∠θ 4

E٣٧ J٥F  

 (Z1∠θ1 ) (Z 4 ∠θ 4 ) = (Z 2 ∠θ 2 ) (Z 3 ∠θ 3 ) E٣٨ J٥F

‫א‬،‫א‬‫א‬‫א‬‫א‬E٣٨ J٥F‫א‬  W‫א‬‫א‬

Z1 Z 4 = Z 2 Z 3

E‫א‬‫א‬‫א‬F

 ∠θ1 + ∠θ 4 = ∠θ 2 + ∠θ 3 E‫א‬‫א‬‫א‬‫א‬)

-١٠٠-

E٣٩ J٥F

E٤٠ J٥F

‫א‬‫א‬

 ‫א‬٢٦٧

‫א‬

‫א‬‫א‬

 



 

 E٦ J٥F

 J٥F ‫א‬‫א‬‫א‬‫א‬‫א‬

 WE١٤

Z1 = 300 Ω ∠30° Z 2 = 150 Ω ∠0°

Z 3 = 250 Ω ∠ − 40°

 KZx‫א‬‫א‬‫א‬

 

a

Z 2 = 150 Ω ∠0°

Z1 = 300 Ω ∠30° b

a.c source

a.c detector

c

Z4 = Zx

Z 3 = 250 Ω ∠ − 40° d

 KE٦ J٥F‫א‬‫א‬E١٤ J٥F

               

 ‫א‬

 WEE٣٩ J٥F‫א‬F‫א‬‫א‬‫א‬ Z1 Z 4 = Z 2 Z 3 Zx = Z4 =

Z 2 Z 3 150 Ω × 250 Ω = 125 Ω = Z1 300 Ω

 WEE٤٠ J٥F‫א‬F‫א‬‫א‬‫א‬‫א‬ ∠θ 4 = ∠θ 2 + ∠θ 3 − ∠θ1 = 0° + (−40°) − 30° = − 70°

 W‫א‬‫א‬‫א‬‫א‬ Z x = 125 Ω ∠ − 70° -١٠١-

‫א‬‫א‬

 ‫א‬٢٦٧

‫א‬

‫א‬‫א‬

 



 

 W Z x = 125 Ω ∠ − 70° = 125 cos (−70°) Ω + j125 sin (−70°)

Z x = 42.75 Ω − j117.5

‫א‬‫א‬‫א‬42.75 Ω‫א‬‫א‬‫א‬  W، X C = 117.5 Ω

X C = 117.5 Ω = C=

1 ωC

1 ω × 117.5 Ω

 W‫א‬60 Hz،‫א‬‫א‬‫א‬ C =

1 = 22 .58 µF 2 × π × 60 × 117 .5 Ω

   E٧ J٥F

 KZx‫א‬‫א‬‫א‬،E١٥ J٥F‫א‬‫א‬‫א‬  

R2=200Ω

 

R1=400Ω

 

E=6 V F=1 kHz

A

 

R3=300Ω     C3=0.4 µF

L2=15.92 mH B

d Zx

 

 KE٧ J٥F‫א‬‫א‬‫א‬E١٥ J٥F

-١٠٢-

 

‫א‬‫א‬

 ‫א‬٢٦٧

‫א‬

‫א‬‫א‬

 



 

 ‫א‬

 W‫א‬‫א‬‫א‬ WZ1‫א‬

E١F

WZ2‫א‬

E٢F

Z1 = 400 Ω + j0 = 400 Ω∠0°

Z 2 = R 2 + j ω L 2 = 200 Ω + j ω × 15.92 × 10 −3

 Wω

ω = 2 π f = 2 × π × 1000 = 6283.19 rad / sec  WZ2‫א‬ Z 2 = 200 Ω + j × 6283.19 × 15.92 × 10 −3 = 200 Ω + j 100 Ω

Z 2 = 200 Ω + j 100 Ω = 223.6 Ω ∠26.6°

WZ3‫א‬ Z3 = R 3 − j

E٣F

1 1 = 300 Ω − j Ω ωC 3 6283.19 × 0.4 × 10 −6

Z 3 = 300 Ω − j 400 Ω = 500 Ω∠ − 53.13°

 W‫א‬‫א‬‫א‬‫א‬‫א‬،Z4‫א‬

 W‫א‬W 

Zx = Z4 =

Z 2 Z 3 223.6 Ω × 500 Ω = 279.5 Ω = Z1 400 Ω

 W‫א‬‫א‬W  ∠θ 4 = ∠θ 2 + ∠θ 3 − ∠θ1 = 26.6° + (−53.13°) − 0° = − 26.53°

 W‫א‬‫א‬Zx‫א‬‫א‬ Z x = 279.5 ∠ − 26.53° = 250 Ω − j124.8 Ω

250 Ω‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬  W‫א‬،124.8 Ω‫א‬‫א‬‫א‬ -١٠٣-

‫א‬‫א‬

 ‫א‬٢٦٧

‫א‬

‫א‬‫א‬

 



 

X C = 124.8 Ω = C=

1 ωC

1 = 1.28 µF 6283.19 × 124.8 Similar Angle Bridge‫א‬‫א‬‫א‬٢ J٣ J٥

‫א‬‫א‬K ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 ،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 W‫א‬‫א‬‫א‬‫א‬‫א‬،E١٦ J٥F WZ1‫ א‬E١F E٤١ J٥F

Z1 = R 1

WZ2‫ א‬E٢F E٤٢ J٥F

Z2 = R 2

 WZ3‫ א‬E٣F E٤٣ J٥F

Z 3 = R 3 − j X C3

WZ4‫ א‬E٤F E٤٤ J٥F

Z 4 = R x − j X Cx

 

R2

R1

   

d

 

R3 C3

Rx Cx

 K‫א‬‫א‬‫א‬‫א‬E١٦ J٥F  

-١٠٤-

   

‫א‬‫א‬

 ‫א‬٢٦٧

‫א‬

‫א‬‫א‬

 



 

 WE٣٦ J٥F‫א‬ R 1 (R x − j X Cx ) = R 2 (R 3 − j X C3 )

E٤٥ J٥F

 W‫א‬‫א‬‫א‬ R 1 R x − j R 1X Cx = R 2 R 3 − j R 2 X C3

E٤٦ J٥F

 W‫א‬،‫א‬‫א‬‫א‬‫א‬ E٤٧ J٥F

R1 R x = R 2 R 3

Rx =

 W

R2 R3 R1

E٤٨ J٥F  W‫א‬،‫א‬‫א‬‫א‬‫א‬ E٤٩ J٥F

− j R 1 X Cx = − j R 2 X C3

 W

E٥٠ J٥F

R 1 X Cx = R 2 X C3

X Cx =

 W

R 2 X C3 R1

E٥١ J٥F  W

R2 1 = ωC x R 1 ωC 3 Cx =

E٥٢ J٥F  W

R 1C 3 R2

E٥٣ J٥F

-١٠٥-

‫א‬‫א‬

 ‫א‬٢٦٧

‫א‬

‫א‬‫א‬

 



 

 E٨ J٥F ‫א‬‫א‬‫א‬،2 kHz‫א‬‫א‬‫א‬‫א‬‫א‬  W‫א‬‫א‬

  C 3 = 100 µF & R 3 = 100 kΩ ، R 2 = 50 kΩ ، R 1 = 10 kΩ   K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬

 W‫א‬‫א‬‫א‬‫א‬،E٤٨ J٥F‫א‬ Rx =

R 2 R 3 50 kΩ × 100 kΩ = 500 kΩ = R1 10 kΩ

 W‫א‬‫א‬‫א‬‫א‬،E٥٣ J٥F‫א‬ Cx =

R 1C 3 10 kΩ × 100 µF = 20 µF = R2 50 kΩ

 Maxwell Bridge٣ J٣ J٥

 K ‫א‬ ‫א‬‫א‬‫א‬



K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 W‫א‬‫א‬‫א‬‫א‬‫א‬،E١٧ J٥F

 

R1

 

R2 C1

 

d

a.c source

 

R3

Lx Rx

 K‫א‬E١٧ J٥F

-١٠٦-

     

‫א‬‫א‬

 ‫א‬٢٦٧

‫א‬

‫א‬‫א‬

 



   

WZ1‫א‬ ⎛ j ⎞ jR 1 ⎟⎟ R 1 ⎜⎜ − − ωC1 ⎝ ωC 1 ⎠ Z1 = = j R 1ωC1 − j R1 − ωC1 ωC 1 Z1 =

E١F

E٥٤ J٥F

− jR 1 1 = R 1 ωC 1 − j 1 + jωC1 R1

E٥٥ J٥F  WZ2‫א‬

E٢F

 WZ3‫א‬

E٣F

WZ4‫א‬

E٤F

E٥٦ J٥F

Z2 = R 2

E٥٧ J٥F

Z3 = R 3

E٥٨ J٥F

Z 4 = R x + j X Lx

 WE٣٦ J٥F‫א‬ ⎛ ⎞ ⎜ ⎟ 1 ⎜ ⎟ (R + j X ) = R R Lx 2 3 ⎜ 1 ⎟ x + jω C 1 ⎟ ⎜ R ⎝ 1 ⎠

(R x

⎞ ⎛R R + j X Lx ) = ⎜⎜ 2 3 + j ω R 2 R 3 C1 ⎟⎟ ⎠ ⎝ R1

E٥٩ J٥F

E٦٠ J٥F

 W‫א‬‫א‬‫א‬‫א‬ Rx =

R2 R3 R1

E٦١ J٥F  W‫א‬‫א‬‫א‬‫א‬ E٦٢ J٥F

j X Lx = j ω R 2 R 3 C1 -١٠٧-

‫א‬‫א‬

 ‫א‬٢٦٧

‫א‬

‫א‬‫א‬

 



 

 W E٦٣ J٥F

X Lx = ω R 2 R 3 C1

 W E٦٤ J٥F

L x = R 2 R 3 C1

   E٩ J٥F

 W‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬   R 3 = 100 kΩ & R 2 = 5.1 kΩ ، C1 = 0.01 µF ، R 1 = 470 kΩ

 K‫א‬‫א‬‫א‬‫א‬

 ‫א‬

 W‫א‬‫א‬E٦٤ J٥F‫א‬E٦١ J٥F‫א‬

 WRx‫א‬W 

Rx =

R 2 R 3 5.1 kΩ × 100 kΩ = 1.085 kΩ = R1 470 kΩ

 WLx‫א‬‫א‬‫א‬W  L x = R 2 R 3 C1 = 5.1 kΩ × 100 kΩ × 0.01 µF = 5.1 H

     

-١٠٨-

‫א‬‫א‬

 ‫א‬٢٦٧

‫א‬

‫א‬‫א‬

 



 

 ‫א‬‫א‬  

 W‫א‬،E‫א‬‫א‬‫א‬F‫א‬‫א‬Rx‫ א‬E١F  R3 = 2 kΩ،R2 = 5 kΩ،R1 = 400 Ω    

R1 = 400 Ω  E

A

R2 = 5 kΩ

 

B

G

   

R3 = 2 kΩ

 

Rx

 

 W‫א‬،‫א‬‫א‬Rx‫א‬E‫א‬‫א‬‫א‬F E٢F  R3 = 18.5 kΩ،R2 = 60 kΩ،R1 = 10 kΩ

R1 = 10 kΩ E

A

R2 = 60 kΩ

G

R3 = 16.5 kΩ

B

           

Rx

     

 W‫א‬،‫א‬‫א‬Rx‫א‬E‫א‬‫א‬‫א‬F E٣F  R3 = 10 Ω،R2 = 40 kΩ،R1 = 5 kΩ -١٠٩-

 

‫א‬‫א‬

 ‫א‬٢٦٧

‫א‬

‫א‬‫א‬

 



 

  R1 = 5 kΩ E

R2 = 40 kΩ

A

G

B

       

R3 = 10 Ω

Rx

   

‫א‬‫א‬‫א‬R3‫א‬‫ א‬E٤F K100 kΩ1 Ω‫א‬‫א‬ R1 = 1 kΩ E

R2 = 10 kΩ

A

B

G

         

R3

Rx

   

‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬ E٥F K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ R1 = 1 kΩ E=3 V

 

A

R2 = 1 kΩ

G

B

       

R3=1 kΩ

R4=1050 Ω

 

W‫א‬،Rx‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬ E٦F Ig=13.6 µA, Vth= 24 mV

-١١٠-

‫א‬‫א‬

 ‫א‬٢٦٧

‫א‬

‫א‬‫א‬

 



 

 

R1 = 1 kΩ E=3 V

R2 = 1 kΩ

A

B

G

       

Rg=100 Ω R3=5 kΩ

 

 

Rx

 

K‫א‬‫א‬‫א‬،10 mm/µA‫א‬‫א‬‫א‬‫א‬‫א‬ E٧F  

 

R1 = 500 Ω E=3 V

R2 = 500 Ω

A

 

B

G Rg = 500 Ω

R3 = 1 kΩ

   

R4 = 1010 Ω

   

W‫א‬،‫א‬‫א‬‫א‬‫א‬ Rx‫א‬  Ra=1200 Ω, Ra=1600Rb, R1=800Rb & R1=1.25R2   R2

R1 E

G

A R3

-١١١-

Ra B Rb Rx

E٨F

   

Rlc

     

‫א‬‫א‬

 ‫א‬٢٦٧

‫א‬

‫א‬‫א‬

 



 

،‫א‬‫א‬‫א‬

E٩F

‫א‬،0.005 Ω/30mb‫א‬0.1 Ω/30ma‫א‬K‫א‬

K‫א‬‫א‬‫א‬ Lb ‫א‬La‫א‬‫א‬،Lx‫א‬

 

R1=100 Ω E= 6 V

A

 

R2=500 B

G

La

 

Lb

 

   

L

 

   

‫א‬Zx‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬ E١٠F K(R, L or C) 

 

R2 = 200Ω R1 = 200Ω E=6 F=1 kHz

A

C2 = 5 µF B

d

R3 = 500Ω C3 = 0.2 µF

Zx

               

W‫א‬،Zx‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬ E١١F   Z1 = 400 Ω∠0° , Z 2 = 300 Ω∠ − 40° , Z 3 = 100 Ω∠ − 20°

-١١٢-

   \

‫א‬‫א‬

 ‫א‬٢٦٧

‫א‬

‫א‬‫א‬

 



 

 

a

 

Z1 E= 6 V f = 1 k HZ

 

Z2 a.c detector

b Z3

 

c

 

Zx

   

d

  KRx, Cx‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ E١٢F  

R2= 15.3 kΩ

R1= 1.65 kΩ E=6V f = 1 kHZ

     

d

 

R3= 2.5 kΩ

 

C3= 10 µF

 

Rx Cx

   

W‫א‬،Rx, Cx‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ E١٣F

Z1 = 2000 Ω∠0° , Z 2 = 15000 Ω∠0° , Z 3 = 1000 Ω∠ − 50°

  Z1 E=6V f = 1 kHZ

 

Z2

   

d

 

Z3 Rx Cx -١١٣-

   

‫א‬‫א‬

 ‫א‬٢٦٧

‫א‬

‫א‬‫א‬

 



 

KLx, Rx‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬ E١٤F  

R1=600 Ω

R2=100 Ω

C1=1 µF

   

d

E=6V f = 1 kHZ

 

R3=1 kΩ

Lx Rx

     

‫א‬،Lx, Rx‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬ E١٥F W

Z1 = 153.8 Ω∠ − 75° , Z 2 = 100 Ω∠0° , Z 3 = 1000 Ω∠0°

Z1

Z2

d

E=6V f = 1 kHZ

 

-١١٤-

Z3

Lx Rx

 ‫א‬‫א‬‫א‬



٦

‫א‬‫א‬‫א‬

‫א‬‫א‬

 ٢٦٧

‫א‬

‫א‬‫א‬‫א‬

 



 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬W‫א‬‫א‬    W‫א‬‫א‬W‫א‬‫א‬‫א‬‫א‬ K‫א‬‫א‬‫א‬‫א‬‫א‬ • K‫א‬‫א‬‫א‬‫• א‬

K‫א‬‫א‬‫א‬‫א‬‫א‬ •  

 K٪١٠٠‫א‬‫א‬‫א‬‫א‬‫א‬W‫א‬‫א‬‫א‬

 

 KW‫א‬‫א‬

 

 W‫א‬‫א‬

K‫א‬‫א‬ •

K‫א‬K‫א‬ •  

 K‫א‬‫א‬‫א‬‫א‬W‫א‬‫א‬

- ١١٥ -

‫א‬‫א‬

 ٢٦٧

‫א‬

‫א‬‫א‬‫א‬

 



Introduction ١ J٦

‫א‬‫א‬‫א‬‫א‬

 KK…‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬ ‫א‬، ‫א‬‫א‬  ‫א‬

‫א‬  ‫א‬‫א‬‫א‬ ‫א‬K‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬

 K‫א‬

General concepts ٢ J٦

 ‫א‬‫א‬ ١ J٢ J٦

،  ‫א‬‫א‬‫א‬

 W‫א‬‫א‬‫א‬

 ‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬

E١F

E٢F

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬   KE١ J٦F،‫א‬

 

 ‫א‬

    

  ‫ﺟﻬﺎز ﻗﻴﺎس آﻬﺮﺑﺎﺋﻲ‬

   

     

 K‫א‬E١ J٦F

- ١١٦ -

‫א‬‫א‬

 ٢٦٧

‫א‬

‫א‬‫א‬‫א‬

 



 Classification of sensors and transducers‫א‬‫א‬ ٢ J٢ J٦

، ‫א‬‫א‬،‫א‬‫א‬

 K،‫א‬،‫א‬

Selection of sensors and transducers‫א‬‫א‬‫ א‬٣ J٢ J٦

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 W‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬W‫א‬

  ‫א‬‫א‬W‫א‬

 K  

E١F E٢F

‫א‬ ‫א‬W‫א‬‫א‬

E٣F

‫א‬‫א‬ ‫א‬‫א‬W ‫א‬‫א‬‫א‬

E٤F

‫א‬‫א‬‫א‬W

E٥F

‫א‬‫א‬‫א‬‫א‬‫א‬

E٦F

‫א‬W‫א‬‫א‬‫א‬

E٧F

  ‫א‬‫א‬‫א‬W‫א‬‫א‬

E٨F

 K‫א‬

 K‫א‬  K‫א‬

 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬

‫א‬‫א‬،‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ 

- ١١٧ -

‫א‬‫א‬

 ٢٦٧

‫א‬

‫א‬‫א‬‫א‬

 



Basic types of special instruments‫א‬‫א‬‫א‬‫א‬‫א‬

٣ J٦

Resistive position instrument‫א‬‫א‬‫א‬ ١ J٣ J٦

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬ K‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬

 ‫א‬

‫א‬  ‫א‬  ‫א‬‫א‬

 KE٢ J٦F،‫א‬‫א‬  

  

‫א‬

 

  ‫ﻣﻨﺰﻟﻖ‬       B

   

A

W

 K‫א‬‫א‬‫א‬E٢ J٦F   ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

W‫א‬KE٣ J٦F ‫א‬‫א‬‫א‬

 .BAW‫א‬‫א‬‫א‬

- ١١٨ -

‫א‬‫א‬

 ٢٦٧

‫א‬

‫א‬‫א‬‫א‬

 



A

VT

 

R1 

 

R 2  B

 

 

W VO

 

 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E٣ J٦F  W‫א‬‫א‬‫א‬ I=

VT R1 + R 2

E١ J٦F

VO = I R 2

E٢ J٦F

VO IR 2 R2 = = VT I(R 1 + R 2 ) R 1 + R 2

E٣ J٦F



‫א‬VO‫א‬‫א‬‫א‬‫א‬  KAB‫א‬‫א‬‫א‬

- ١١٩ -

‫א‬‫א‬

 ٢٦٧

‫א‬

‫א‬‫א‬‫א‬

 



 E١ J٦F

‫א‬،3 inches‫א‬E٤ J٦F ‫א‬KB0.9" ‫א‬VT = 5 V‫א‬‫א‬‫א‬،5 kΩ

 KVO‫א‬

3"

 

0.9 "

 

A

‫ﻣﻨﺰﻟﻖ‬

   

R1 VT = 5 V 5 kΩ B

R2

  A

5V

 

W

 

  W VO

B

 

 KE١ J٦F‫א‬‫א‬‫א‬E٤ J٦F

 

 WE٣ J٦F‫א‬W‫א‬ VO R2 = VT R1 + R 2 R2 =

0.9 × 5000 = 1500 Ω 3

VO 1500 = VT 5000 VO = VT ×

1500 1500 = 5× = 1.5 volts 5000 5000

- ١٢٠ -

‫א‬‫א‬

 ٢٦٧

‫א‬

‫א‬‫א‬‫א‬

 



Strain guage transducer‫א‬ ٢ J٣ J٦

‫א‬‫א‬‫א‬‫א‬

K‫א‬‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

E٥ J٦F ‫א‬



‫א‬‫א‬‫א‬‫א‬ ‫א‬

 K‫א‬‫א‬‫א‬

     



‫א‬‫א‬

       

‫א‬‫א‬  

 K‫א‬E٥ J٦F F‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

،   ‫א‬‫א‬‫א‬،E‫א‬  W‫א‬ ‫א‬‫א‬، E٤ J٦F

R = ρL a

 W

 ‫א‬‫א‬WR

 ‫א‬‫א‬‫א‬‫א‬Wρ

‫א‬WL

 ‫א‬Wa

 W‫א‬ - ١٢١ -

‫א‬‫א‬

 ٢٦٧

‫א‬

‫א‬‫א‬‫א‬

 



 KEF‫א‬‫א‬ K‫א‬‫א‬

E١F

E٢F

 W، G ‫א‬ L ‫א‬‫א‬‫א‬ ∆L ‫א‬‫א‬‫א‬  

E٥ J٦F

G=

∆L L

 K‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬

،‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬  W K ‫א‬

K=

∆R R ∆L L

E٦ J٦F  K1‫א‬‫א‬‫א‬

 ‫א‬‫א‬‫א‬‫א‬ (StressW ‫א‬F

‫א‬،(Modulus of Elasticity (E))‫א‬(Strain)‫א‬  W‫א‬‫א‬

E٧ J٦F

 E =

S G

 W

 ‫א‬WE  ‫א‬WS

 ‫א‬WG

 W‫א‬S‫א‬ S=

F A

E٨ J٦F  W

 kg‫א‬WF

 m2‫א‬WA - ١٢٢ -

‫א‬‫א‬

 ٢٦٧

‫א‬

‫א‬‫א‬‫א‬

 



،G ‫א‬،kg/m2‫א‬

 Kkg/m2WS‫א‬E‫א‬

‫א‬‫א‬  ‫א‬‫א‬

‫א‬  ‫א‬‫א‬،K‫א‬ ،K‫א‬

 K‫א‬EF‫א‬  

 E٢ J٦F

‫א‬ K = 2 ‫א‬  K ∆R ‫א‬‫א‬‫א‬، R 0 = 130 Ω ‫א‬‫א‬‫א‬‫א‬، G = 1× 10 −6

 ‫א‬

 W‫א‬E٦ J٦F‫א‬ K=2=

∆R R ∆R R 0 ∆R 130 Ω =  = ∆L L G 1 × 10 −6

∆R = 2 × 130 × 1 × 10 −6 = 260 µΩ 

 

 E٣ J٦F

، 33000 kg ‫א‬، 0.4 m  0.02 m ‫א‬‫א‬

 K ∆L ‫א‬‫א‬، E = 2 × 1010 kg / m 2 ‫א‬

 ‫א‬

 W A ‫א‬ πd 2 π A= = × (0.02)2 = 3.14 × 10 −4 m 2 4 4

 WE‫א‬E٧ J٦F‫א‬ E=

F× L S FA = = G ∆L L A × ∆L

∴ ∆L =

F×L 33000 kg × 0.4 m = = 2.1 × 10 −3 m = 2.1 mm − 4 10 A × E 3.14 × 10 × 2 × 10 - ١٢٣ -

‫א‬‫א‬

 ٢٦٧

‫א‬

‫א‬‫א‬‫א‬

 



‫א‬‫א‬‫א‬‫א‬

،(Transducer)‫א‬،‫א‬‫א‬  K‫א‬  

 ‫א‬‫א‬‫א‬

‫א‬F‫א‬‫א‬‫א‬‫א‬

 ،‫א‬‫א‬‫א‬‫א‬‫א‬،E Vo  KE٦ J٦F،‫א‬  

R1

R2

  E

   

R3  

Vo R4 =‫א‬

 

 K‫א‬E٦ J٦F ‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬K‫א‬‫א‬‫א‬،‫א‬

‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬ ‫א‬K‫א‬‫א‬ ،‫א‬  K‫א‬‫א‬‫א‬‫א‬،

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬KE٧ J٦F‫א‬

‫א‬‫א‬E ‫א‬‫א‬‫א‬F‫א‬‫א‬‫א‬،E ‫א‬HF  ‫א‬‫א‬‫א‬‫א‬‫א‬، - ١٢٤ -

‫א‬‫א‬

 ٢٦٧

‫א‬

‫א‬‫א‬‫א‬

 



   ‫א‬ ‫א‬‫א‬،‫א‬

 K‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬          

R1

 

E

Vo



     

R3

R2

 

R4



    ‫א‬‫א‬

     

‫א‬‫א‬

 

 K‫א‬‫א‬‫א‬‫א‬‫א‬E٧ J٦F Inductive instrumentations‫א‬‫א‬ ٣ J٣ J٦

‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬ (Tachometer)‫א‬‫א‬‫א‬

١ J٣ J٣ J٦

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E٨ J٦F

‫א‬‫א‬  - ١٢٥ -

‫א‬‫א‬

 ٢٦٧

‫א‬

‫א‬‫א‬‫א‬

 



(Voltmeter)،(10 mV/r.p.m)‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬

 K  

    North Pole

 

  South Pole

       

‫א‬

  ‫א‬‫א‬‫א‬  

 ‫א‬‫א‬‫א‬E٨ J٦F ‫א‬،‫א‬‫א‬

 

‫א‬‫א‬‫א‬‫א‬‫א‬

 KE٩ J٦F‫א‬‫א‬‫א‬        

N S

 

 K‫א‬‫א‬‫א‬E٩ J٦F ‫א‬E‫א‬F‫א‬‫א‬

 

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬

- ١٢٦ -

‫א‬‫א‬

 ٢٦٧

‫א‬

‫א‬‫א‬‫א‬

 



‫א‬، ‫א‬‫א‬‫א‬‫א‬‫א‬

 W‫א‬‫א‬‫א‬‫א‬‫א‬

 

E٩ J٦F

n=

120 f P

 W

 (r.p.m.)‫א‬‫א‬Wn

 cycle/sec = Hertz‫א‬Wf

 ‫א‬‫א‬‫א‬WP  ‫א‬‫א‬‫א‬‫א‬

Electro-magnetic transducer

٢ J٣ J٣ J٦

  ‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬

‫א‬‫א‬‫א‬،

، ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬،  ‫א‬‫א‬E١٠ J٦F   ‫א‬‫א‬،‫א‬‫א‬‫א‬  

 K V‫א‬‫א‬

   

N

  B

S

  V

       

 ‫א‬‫א‬‫א‬‫א‬E١٠ J٦F - ١٢٧ -

 

‫א‬‫א‬

 ٢٦٧

‫א‬

‫א‬‫א‬‫א‬

 



 W‫א‬‫א‬‫א‬‫א‬‫א‬ E١٠ J٦F

E=BLV

 W

 (volts)‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬WE

 (Tesla = Weber/m2)‫א‬‫א‬‫א‬WB  (m/sec)L‫א‬WV

‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

K0.5 siemens/m‫א‬‫א‬E1 foot/secF‫א‬‫א‬

،‫א‬‫א‬‫א‬ ‫א‬‫א‬   ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 K‫א‬

 E٤ J٦F

‫א‬‫א‬،D=1.25 cm ،‫א‬

 KV‫א‬‫א‬،E = 25 mV‫א‬،B = 0.2 Tesla ‫א‬

 ‫א‬

 WE١٠ J٦F

E=BLV 25 × 10 −3 E V= = = 10 m / sec B L 0.2 × 1.25 ×10 − 2

 WV‫א‬

 

Capacitive instrumentations‫א‬‫א‬ ٤ J٣ J٦

 ‫א‬ ‫א‬‫א‬‫א‬‫א‬C‫א‬‫א‬ C=

kAε 0 d

 W‫א‬E١١ J٦F E١١ J٦F

(Farads)

  - ١٢٨ -

‫א‬‫א‬

 ٢٦٧

‫א‬

‫א‬‫א‬‫א‬

 



   

d

A

   

 K‫א‬‫א‬‫א‬‫א‬E١١ J٦F

 

 W

 (Farad)‫א‬‫א‬‫א‬‫א‬WC  ‫א‬‫א‬‫א‬Wk

 (m2)‫א‬‫א‬‫א‬WA  (m)‫א‬‫א‬‫א‬Wd

،L ‫א‬‫א‬Permittivity‫א‬‫א‬ ‫א‬‫א‬Wε0   ( ε 0 = 8.854 × 10 −12 Farad / m)   ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬

Rotational movement transducer‫א‬‫א‬‫א‬‫א‬

١ J٤ J٣ J٦

 ‫א‬‫א‬ 

‫א‬KE١٢ J٦F‫א‬‫א‬‫א‬

  ‫א‬‫א‬  ‫א‬‫א‬‫א‬

 K‫א‬



 

 

‫א‬

    

‫א‬

K‫א‬‫א‬‫א‬‫א‬E١٢ J٦F  

- ١٢٩ -

‫א‬‫א‬

 ٢٦٧

‫א‬

‫א‬‫א‬‫א‬

 



Linear movement transducer ‫א‬‫א‬‫א‬

٢ J٤ J٣ J٦

‫א‬‫א‬‫א‬   

KE١٣ J٦F‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  K‫א‬

   

 ‫א‬

     

  ‫א‬ ‫א‬

‫א‬

 

 K‫א‬‫א‬‫א‬E١٣ J٦F Pressure transducer‫א‬

٣ J٤ J٣ J٦

‫א‬‫א‬

‫א‬ ‫א‬KE١٤ J٦F‫א‬‫א‬‫א‬

‫א‬K  ‫א‬  ‫א‬‫א‬  ‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬،d‫א‬‫א‬d0‫א‬‫א‬‫א‬  

‫א‬

   

d1

   

d 0 

 K‫א‬E١٤ J٦F - ١٣٠ -

‫א‬‫א‬

 ٢٦٧

‫א‬

‫א‬‫א‬‫א‬

 



 E٥ J٦F

 W‫א‬،‫א‬‫א‬

  5 × 10 −3 m 2 = ‫א‬‫א‬‫• א‬ 1 × 10 −3 m = ‫א‬‫• א‬

 ‫א‬

 W‫א‬‫א‬‫א‬E١١ J٦F‫א‬

C= C=

kAε 0 (Farads) d (1) (5 × 10 −3 m 2 ) (8.854 × 10 −12 F / m) 1 × 10

−3

m

= 44.25 × 10 −12 F

C = 44.25 pF

 Piezoelectric TransducerE‫א‬‫א‬F‫א‬ ٥ J٣ J٦ ERochelle saltquartz‫א‬‫א‬F‫א‬‫א‬‫א‬

‫א‬‫א‬،،

‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬  KE١٥ J٦F‫א‬  

‫א‬

     

 ‫א‬    

‫א‬

     

 K‫א‬E١٥ J٦F - ١٣١ -

‫א‬ ‫א‬‫א‬

‫א‬‫א‬

 ٢٦٧

‫א‬

‫א‬‫א‬‫א‬

 



‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬

 

 ‫א‬‫א‬ ٦ J٣ J٦

 W‫א‬‫א‬‫א‬‫א‬‫א‬

 KResistance thermometer‫א‬‫א‬‫א‬

KThermo Couple‫א‬‫א‬‫א‬

KThermistor‫א‬‫א‬‫א‬

EF

E F

E F

 K‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬

 

١ J٦ J٣ J٦

‫א‬ ‫א‬  ‫א‬  ‫א‬‫א‬‫א‬  

 W‫א‬‫א‬‫א‬‫א‬ R = R 0 [1 + α ∆t ] E١٢ J٦F

 W

 ‫א‬t‫א‬‫א‬W R

 E 20 ° C F‫א‬‫א‬ WR0  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬W ∆t  ‫א‬‫א‬‫א‬W α

‫א‬‫א‬ α ‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬ ‫א‬ ∆R ‫א‬‫א‬K‫א‬‫א‬‫א‬  KE١٦ J٦F‫א‬‫א‬‫א‬‫א‬

- ١٣٢ -

‫א‬‫א‬

 ٢٦٧

‫א‬

‫א‬‫א‬‫א‬

 



  R1 

R2

   

E

 

Vo

 

R4 = ‫א‬‫א‬

R3 

 

 K‫א‬‫א‬‫א‬E١٦ J٦F  

Thermo-couple‫א‬‫א‬‫א‬

٢ J٦ J٣ J٦

‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬K‫א‬،

K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬Copper‫א‬‫א‬

،‫א‬‫א‬(mV)‫א‬‫א‬،Constantan  K‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬

‫א‬Operational Amplifier‫א‬‫א‬‫א‬

 KE١٧ J٦F،‫א‬‫א‬‫א‬‫א‬ 

‫א‬

     

 

 

 

H 

J

 K‫א‬‫א‬‫א‬E١٧ J٦F

- ١٣٣ -

 EF

 

‫א‬‫א‬

 ٢٦٧

‫א‬

‫א‬‫א‬‫א‬

 



 W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ E = c (T1 − T2 ) + k (T12 − T22 )

E١٣ J٦F

mV

 W

 K‫א‬‫א‬‫א‬‫א‬ W E

 ‫א‬‫א‬‫א‬‫א‬ Wkc

 E‫א‬F‫א‬E‫א‬‫א‬F‫א‬‫א‬‫א‬ W T1

 E‫א‬F‫א‬E‫א‬‫א‬‫א‬F‫א‬‫א‬‫א‬ W T2  E٦ J٦F ‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬ k = 4.5 × 10 −5 ‫א‬ c = 3.75 × 10 −2 ‫א‬  K‫א‬‫א‬‫א‬

 ‫א‬

K T2 = 0°C W‫א‬‫א‬ T1 = 100 °C W‫א‬‫א‬‫א‬

 W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E١٣ J٦F‫א‬

E = c (T1 − T2 ) + k (T12 − T22 )

mV

E = 3.75 ×10 −2 (100 − 0) + 4.5 × 10 −5 (100 2 − 0 2 ) = 4.2 mV Thermistor‫א‬‫א‬‫א‬

 

٣ J٦ J٣ J٦

‫א‬ ‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬K ‫א‬‫א‬  ‫א‬‫א‬  ‫א‬ ‫א‬‫א‬E١٨ J٦FK ‫א‬‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬‫א‬

- ١٣٤ -

‫א‬‫א‬

 ٢٦٧

‫א‬

‫א‬‫א‬‫א‬

 



1000000 100000

(‫اﻟﻤﻘﺎوﻣﺔ )أوم‬

10000 1000 100 10 1 -100

100

300

500

(‫درﺟﺔ اﻟﺤﺮارة )درﺟﺔ ﻣﺌﻮﻳﺔ‬

   K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E١٨ J٦F ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬E١٩ J٦FK 75 MΩ  0.5 Ω      

 ‫א‬‫א‬‫א‬E١٩ J٦F

Photo – Electric Transducers  ٧ J٣ J٦

 W‫א‬‫א‬‫א‬‫א‬

- ١٣٥ -

‫א‬‫א‬

 ٢٦٧

‫א‬

‫א‬‫א‬‫א‬

 



‫א‬‫א‬

١ J٧ J٣ J٦

،‫א‬‫א‬‫א‬‫א‬‫א‬

K ‫א‬‫א‬(Cathode)‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

(Electrodes) (Anode)(Photo Cathode)

،‫א‬  ‫א‬‫א‬(Dynodes)  KE٢٠ J٦F

+100

‫اﻟﻀﻮء اﻟﺴﺎﻗﻂ‬

 

+300

 

 

+700 V

+500

‫أﻧﻮد‬

       

‫آﺎﺛﻮد‬ 0

 

+200

 

+400 V

+600

 K‫א‬‫א‬‫א‬E٢٠ J٦F  

‫א‬‫א‬  ‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬EF ‫א‬E‫א‬‫א‬F‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬  KE1mA100µAF‫א‬  

- ١٣٦ -

‫א‬‫א‬

 ٢٦٧

‫א‬

‫א‬‫א‬‫א‬

 



‫א‬

٢ J٧ J٣ J٦

‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬

‫א‬،EE٢١ J٦F‫א‬F‫א‬  E‫א‬F‫א‬‫א‬‫א‬

‫א‬،E‫א‬F‫א‬‫א‬‫א‬

 K‫א‬‫א‬

 

 

 K‫א‬‫א‬‫א‬‫א‬‫א‬E٢١ J٦F  

‫א‬،E٢٢ J٦F‫א‬‫א‬‫א‬‫א‬‫א‬

،‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬  



 

V

     

       

‫א‬

 K‫א‬‫א‬‫א‬‫א‬‫א‬E٢٢ J٦F

- ١٣٧ -

‫א‬‫א‬

 ٢٦٧

‫א‬

‫א‬‫א‬‫א‬

 



‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬E٢٣ J٦F

 K‫א‬

1000000

(‫ﻣﻘﺎوﻣﺔ اﻟﺨﻠﻴﺔ )أوم‬

100000

10000

1000

100

10 1

10 100 (ft-c) ‫اﻹﺿﺎءة‬

1000

   ‫א‬‫א‬‫א‬‫א‬‫א‬E٢٣ J٦F     ‫א‬

٣ J٧ J٣ J٦

‫א‬E F‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬K‫א‬

 KE‫א‬‫א‬F                  

- ١٣٨ -

‫א‬‫א‬

 ٢٦٧

‫א‬

‫א‬‫א‬‫א‬

 



 ‫א‬‫א‬  K‫א‬‫ א‬E١F

‫؟‬‫א‬‫א‬‫א‬ E٢F

K‫א‬‫א‬‫א‬‫ א‬E٣F

K‫א‬ E٤F

K‫א‬‫א‬‫א‬‫א‬‫א‬‫ א‬E٥F

K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫ א‬E٦F K‫א‬ E٧F

K‫א‬‫א‬‫א‬‫ א‬E٨F

K‫א‬‫א‬‫א‬‫א‬ E٩F

K‫א‬‫ א‬E١٠F

 K‫א‬‫א‬‫א‬ E١١F K‫א‬‫א‬‫א‬‫ א‬E١٢F

K‫א‬‫א‬‫א‬‫א‬‫א‬ E١٣F K‫א‬‫א‬‫א‬ E١٤F

K‫א‬‫א‬‫א‬‫ א‬E١٥F    

- ١٣٩ -

‫א‬

‫א‬‫א‬

 ٢٦٧

‫א‬

‫א‬‫א‬‫א‬

 



 ‫א‬

EF1 inch‫א‬‫א‬ E١F  W‫א‬‫א‬‫א‬‫א‬X‫א‬‫א‬‫א‬،10 V‫א‬‫א‬‫א‬  Vo =3 V EF  Vo=5 V EF Vo=8 V EF 1" X

A

‫ﻣﻨﺰﻟﻖ‬

B

10 V

 

R1

VT

W

 

‫א‬‫א‬‫א‬،5 inches‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬ E٢F

W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬،10 V  Vo = 2 V EF  Vo = 4 V EF  Vo = 6 V EF ‫א‬‫א‬ ‫א‬‫א‬،k = 4‫א‬   E٣F G =   ‫א‬،R0 = 100 Ω‫א‬‫א‬‫א‬‫א‬K

K‫א‬‫א‬‫א‬‫א‬،2×10-5

‫א‬K  ،k = 4‫א‬ E٤F

‫א‬‫א‬‫א‬،10.2 inches10 inches‫א‬‫א‬ ‫א‬،R0 =120 Ω‫א‬‫א‬‫א‬‫א‬‫א‬K ‫א‬‫א‬ K‫א‬‫א‬

،R0 =120 Ω ‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬ E٥F

  ‫א‬‫א‬‫א‬‫א‬،k = 12‫א‬

K1%

- ١٤٠ -

   

R2

W

A

 

 

‫א‬‫א‬

 ٢٦٧

‫א‬

‫א‬‫א‬‫א‬

 



،R0 = 250 Ω‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬ E٦F ،G=1.5×10-4‫א‬∆R = 0.15 Ω

Kk‫א‬‫א‬

‫א‬‫א‬،A=4×10-3 m2‫א‬،  ‫א‬

W‫א‬‫א‬‫א‬‫א‬‫א‬،d=5×10-4 m

 (k = 1000)‫א‬‫א‬‫א‬‫א‬‫א‬  (k = 4)‫א‬‫א‬‫א‬‫א‬

E٧F

EF

E F

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬،  ‫א‬  W‫א‬

E٨F

 K‫א‬‫א‬‫א‬‫א‬‫א‬ EF

K‫א‬‫א‬‫א‬‫א‬ E F F K‫א‬‫א‬k‫א‬‫א‬ E

‫א‬،0.02 m ‫א‬

‫א‬K0.5 m/sec ‫א‬،0.1 Tesla ‫א‬‫א‬

E٩F

 K‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬،0.02 m ‫א‬ E١٠F

‫א‬‫א‬‫א‬‫א‬‫א‬،0.5 Tesla ‫א‬‫א‬ K‫א‬‫א‬K0.03 V

،T1=80°C‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫ א‬E١١F K‫א‬‫א‬‫א‬ k = 5 × 10 −5 ‫א‬0.05 mV/°C‫א‬

‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫ א‬E١٢F

‫א‬‫א‬ k = 5 × 10 −5 ‫א‬ c = 4 × 10 −2 ‫א‬  K‫א‬‫א‬‫א‬‫א‬

 - ١٤١ -

‫א‬‫א‬

 ‫א‬٢٦٧

‫א‬

 



(References) ‫א‬‫א‬

[1] "Electronic Instruments And Measurements."

Larry D. Jones, A. Foster Chin.

Prentice-Hall, Inc. A Division of Simon & Schuster Englewood Cliffs, New Jersey, 1991.

[2] "Electrical Measurements and Calibration: Fundamentals Applications."

Lawrence M. Thompson Instrumentation System & Paperback – June 1994.

[3] "The Measurements, Instrumentation and Sensors Handbook."

J. G. Webster Spring -Verlag Berlin and Heidelberg GmbH & Co. KG Hardcover- December 1998.

[4] "Sensors for Measurement and Control."

Peter Elgar Longman Paperback – 19 January 1998.

- ١٤٢ -

 

and

‫א‬

 ‫א‬٢٦٧

‫א‬

 



 ‫א‬ ١ ........................................................................................................................................ ‫א‬‫א‬‫א‬‫א‬ ٣ ......................................................................................................................................................... ١ J١ ٣ ................................................................................................................................................. ٢ J١ ٤..................................................................................................................... ‫א‬‫א‬‫א‬٣ J١ ٤............................................................................................ ‫א‬‫א‬‫א‬١ J٣ J١ ٦ ......................................................................................................................... ‫א‬‫א‬٤ J١ ١١ ........................................................................................................... ‫א‬‫א‬‫א‬٥ J١ ١٥ ........................................................................................................................................... ‫א‬‫א‬٦ J١ ١٦ ......................................................................................................................... ‫א‬‫א‬٧ J١ ١٧ ................................................................................................................ ‫א‬‫א‬‫א‬‫א‬‫א‬٨ J١ ١٨ ........................................................................................................................................‫א‬‫א‬  ٢١ .................................................................................................................................... ‫א‬‫א‬‫א‬‫א‬  ٢٠ ....................................................................................................................................................... ١ J٢  ٢٠ ..................................................................................................................‫א‬‫א‬‫א‬٢ J٢  ٢٠ ............................................................................................................ ‫א‬‫א‬‫א‬١ J٢ J٢  ٢١ .................................................................................................... ‫א‬‫א‬‫א‬٢ J٢ J٢  ٢١ .................................................................................‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬٣ J٢ J٢  ٢٠ ............................................................................. ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬١ J٣ J٢ J٢  ٢٣ ........................................................................................................................ ‫א‬‫א‬١ J١ J٣ J٢ J٢  ٢٧ ................................................................. ‫א‬‫א‬‫א‬‫א‬‫א‬٢ J١ J٣ J٢ J٢  ٢٨ ............................................................................ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬٢ J٣ J٢ J٢  ٣٢ ................................................................. ‫א‬‫א‬‫א‬‫א‬‫א‬١ J٢ J٣ J٢ J٢  ٣٣ ........................................................................... ‫א‬‫א‬‫א‬‫א‬‫א‬٣ J٣ J٢ J٢  ٣٥ ................................................................................. ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬٤ J٢ J٢  ٣٥ ........................................................................... ‫א‬‫א‬‫א‬‫א‬‫א‬١ J٤ J٢ J٢  ٤١ ........................................................................... ‫א‬‫א‬‫א‬‫א‬‫א‬٢ J٤ J٢ J٢  ٤٥ ...................................................................................................................................... ‫א‬‫א‬ ٥٧ .................................................................................................................................... ‫א‬‫א‬‫א‬‫א‬ ٥٨ ...................................................................................................................................................... ١ J٣  ٥٩ ............................................................................................................................... ‫א‬‫א‬٢ J٣ ٥٩ ....................................................................................................... ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬١ J٢ J٣ ٥٩ ...................................................................................................... ‫א‬‫א‬‫א‬‫א‬‫א‬٢ J٢ J٣

‫א‬

 ‫א‬٢٦٧

‫א‬

 



٦٦ ................................................................................................................ ‫א‬‫א‬‫א‬٣ J٣ ٦٩ ..................................................................................................................................... ‫א‬‫א‬ ٧١ .................................................................................................................................... ‫א‬‫א‬‫א‬‫א‬‫א‬ ٧٢ .................................................................................................................................................... ١ J٤ ٧٢ .......................................................................................................................... ‫א‬‫א‬‫א‬‫א‬٢ J٤  ٧٥ ...................................................................................................................... ‫א‬‫א‬‫א‬‫א‬٣ J٤ ٧٥ ................................................................................................. ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬١ J٣ J٤ ٧٥ .........................................................................................................................

‫א‬‫א‬‫א‬٢ J٣ J٤

 ٧٠ .........................................................................................................................

‫א‬٣ J٣ J٤

 ٧١ .................................................................................................................................... ‫א‬٤ J٣ J٤ ٨١ ...................................................................................................................................... ‫א‬‫א‬‫א‬ K‫א‬‫א‬> ................................................................................................ ‫א‬‫א‬‫א‬‫א‬ ٨٤ ....................................................................................................................................................... ١ J٥  ٨٤ .............................................................................................................. ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬٢ J٥ ٨٤ ...................................................................................................................................... ١ J٢ J٥  ٨٤ .................................................................................................................... ‫א‬‫א‬١ J١ J٢ J٥ ٨٤ ........................................................................................................................................... ٢ J٢ J٥ ٨٥ .............................................................................................................................. ‫א‬‫א‬١ J٢ J٢ J٥  ٨٦ ................................................................................................................... ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬٣ J٢ J٥ ٨٧ .................................................................................................‫א‬‫א‬‫א‬‫א‬‫א‬٤ J٢ J٥  ٨٧ .............................................................................................................. ‫א‬‫א‬‫א‬٥ J٢ J٥ ٨٧ .................................................................................................................................... ‫א‬‫א‬١ J٥ J٢ J٥  ٩٨............................................................................................................... ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬٣ J٥ ٩٨....................................................................................................................... ‫א‬١ J٣ J٥ ٩٨............................................................................................................................. ‫א‬‫א‬‫א‬٢ J٣ J٥ ٩٨..................................................................................................................................... ٣ J٣ J٥ ١٠٩ .................................................................................................................................... ‫א‬‫א‬ K‫א‬‫א‬> ................................................................................................ ‫א‬‫א‬‫א‬‫א‬  J١١٦ J ............................................................................................................................................. ١ J٦  J١١٦ J ...................................................................................................................................... ٢ J٦  J١١٦ J ................................................................................................................ ‫א‬‫א‬١ J٢ J٦  J١١٧ J .............................................................................................................. ‫א‬‫א‬٢ J٢ J٦  J١١٧ J ................................................................................................................ ‫א‬‫א‬‫א‬٣ J٢ J٦  J١١٨ J ........................................................................................................‫א‬‫א‬‫א‬‫א‬‫א‬٣ J٦

‫א‬

 ‫א‬٢٦٧

‫א‬

 



 J١١٨ J ................................................................................................................ ‫א‬‫א‬‫א‬١ J٣ J٦ ١١٣ .............................................................................................................................. ‫א‬٢ J٣ J٦ ١١٧ .............................................................................................................................. ‫א‬‫א‬٣ J٣ J٦ ١١٧ ...................................................................................................................... ‫א‬‫א‬‫א‬١ J٣ J٣ J٦ ١١٧ ......................................................................................‫א‬‫א‬‫א‬‫א‬٢ J٣ J٣ J٦ ١٢٠ ............................................................................................................................. ‫א‬‫א‬٤ J٣ J٦ ١٢١ .....................................................................................................................‫א‬‫א‬‫א‬‫א‬١ J٤ J٣ J٦ ١٢١ .......................................................................................................................‫א‬‫א‬‫א‬٢ J٤ J٣ J٦ ١٢٢................................................................................................................................ ‫א‬٣ J٤ J٣ J٦ ١٢٣........................................................................................................................‫א‬٥ J٣ J٦ ١٢٤ ...............................................................................................................................‫א‬‫א‬٦ J٣ J٦ ١٢٤ .......................................................................................................... ‫א‬‫א‬‫א‬١ J٦ J٣ J٦ ١٢٥ ............................................................................................................................. ‫א‬‫א‬‫א‬٢ J٦ J٣ J٦ ١٢٦ ............................................................................................................................. ‫א‬‫א‬‫א‬٣ J٦ J٣ J٦ ١٢٧ .......................................................................................................................... ٧ J٣ J٦ ١٢٧ ..................................................................................................... ‫א‬‫א‬١ J٧ J٣ J٦ ١٢٨ .................................................................................................... ‫א‬٢ J٧ J٣ J٦ ١٣٠ .....................................................................................................‫א‬٣ J٧ J٣ J٦  J١٣٩ J .......................................................................................................................... ‫א‬‫א‬  J١٤٢ J .................................................................................................................................................... ‫א‬‫א‬

             