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
12
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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