Student Reference Manual for Electronic Instrumentation Laboratories 2nd Edition Wolf Solutions Manu

Student Reference Manual for Electronic Instrumentation Laboratories 2nd Edi F u l l D o w n lhot at pd :: / / a l i b a b a d o w n l o a d . c o m / p r o d u c t / s t u d e n t - r e f e r e n c e - m a n u a l - f o r - e l e c t r o

CHAPTER 2 Experimental Data and Errors 2.1)

Accuracy of a measurement specifies the difference between the measured and the true value of the quantity. Precision specifies the repeatability of a set of readings, each made independently with the same instrument. P. 33-34

2.2) The three classes of measurement errors are Human, System, and Random. Fig. 2.4, P. 38 2.3)

Several examples are given in Fig. 2.4, P. 38

2.4)

Error for voltmeter: ± 2% × 50V = ± 1V Percent error =

Measured Value - True Value × 100% True Value

Percent error for 15 V measurement =

Percent error for 42 V measurement = 2.5)

(15

± 1) - 15 × 100% = ± 6.67% 15

( 42

± 1) - 42 × 100% = ± 2.4% 42

Error for ammeter 0.5% × 50 mA = 0.25 mA (The error on most analog meters is usually based on full scale.

Possible error 13 mA ± 0.25 mA Limits 12.75 mA → 13.25 mA

2.6)

 1000 mA  a) 0.35 A   = 350 mA  1A   1× 106 µ A  5 0.35 A   = 3.5 × 10 µ A  1A   103 µ V  b) 0.041 mV   = 41 µ V  1 mV   1 MΩ  c) 400, 000 Ω  6  = 0.4 MΩ  10 Ω 

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Chapter 2: Experimental Data and Errors  1 mV  d) 67 µ V  3  = 0.067 mV  10 µ V  2.7) a) 2 b) 6 c) 3 d) 3 e) 2 f) 6 Note: non-technical writers commonly consider zeros to the left of the decimal point as non-significant.

2.8)

For series resistance R EQ = R1 + R 2 + ... + R n

R EQ

2.9)

14.5 ± 0.1 5.36 ± 0.01 64.2 ± 0.1 4.37 ± 0.01 = 88.43 ± 0.22 Ω

635 ± 4 −296 ± 4 339 ± 8

%Error =

8 × 100% 339

%Error = 2.36%

2.10) a) 50.2 + 50.6 + 49.7 + 51.1 + 50.3 + 49.9 + 50.4 + 49.6 + 50.3 + 51.0 AVG = = 50.31 10 d12 + d 22 + d 32 + ... + d n2 b) Standard Deviation σ = n-1 d = Deviation from the average value σ = 0.474 c) Probable error = 0.675 σ = ± 0.31995 mA 2.11) a) 21.107 V b) σ = 0.927 Probable Error = 0.675 σ = ± 0.6257 c) The deviation from the average value d 4 = 2.04 is < 3σ , so the value 19.07 should be retained.

2.12) Decibel Power Gain P  A P = 10 log10  out  dB  Pin   45 × 10-3 W  a) A P = 10 log10   = 2.23 dB -3  7.4 × 10 W 

11

Chapter 2: Experimental Data and Errors  52 × b) A P = 10 log10   14 ×  32 × c) A P = 10 log10   16 ×

10-6 W   = 1.23 dB 10-6 W  10-3 W   = 3.01 dB 10-3 W 

 1.414 V  d) A P = 20 log10   = -3.01 dB  2V  2.13) Magnitude Power Gain AP Pout A  = log10 -1  P  = 10 10 Pin  10  82 Pout  82  = log10 -1   = 10 10 = 158 × 106 Pin  10 

2.14)

-40 Pout  -40  10 = log10 -1  = 10 = 1 × 10-4  Pin  10 

2.15) a) Power gain in dB P   150 W  A P = 10 log10  out  = 10 log10   = -3.01 dB  300 W   Pin 

b) Power gain in dB

A P = 10 log10

 Pout    = 10 log10  Pin 

 Vo2  Ro  2 V  in R in 

   = 20 log10  

 Vo   Vin

R in Ro

V  A V = 20 log10  o  if R o = R in  Vin  Voltage Out = Vo = Po × R o = 150 W × 8 Ω = 34.6 V

Voltage In = Vin = 12 V  34.6 V  A V dB = 20 log10   = 9.20 dB  12 V   V 2   122  R in =  in  =   = 0.48 Ω  Pin   300  A P = A V only if R o = R in , but in this case R o ≠ R in

c) R o = 8 Ω

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  

Student Reference Manual for Electronic Instrumentation Laboratories 2nd Edi F u l l D o w n lhot at pd :: / / a l i b a b a d o w n l o a d . c o m / p r o d u c t / s t u d e n t - r e f e r e n c e - m a n u a l - f o r - e l e c t r o Chapter 2: Experimental Data and Errors

P  2.16) a) A P = 10 log10  o   Pin  Po 30 W = = 1.89 mW ∴ Pin = -1  42 dB  -1  A P  log  log     10   10  b) Vo = Po × R o = 30 W × 10 Ω = 17.32 V  17.32  A V = 60 dB = 20 log10    Vin  17.32 ∴ Vin = 60 = 17.32 mV 10 20

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