In order to analyse a complex waveform the data acquisition system shown in Fig. ex.7.16 is used. The error sources and average errors in percentage are given in Table 7.1. The systematic errors due to temperature change and power supply variation can be neglected. Assuming that the random errors

Question

In order to analyse a complex waveform the data acquisition system shown in Fig. ex.7.16 is used. The error sources and average errors in percentage are given in Table 7.1. The systematic errors due to

Table 7.1

Systematic error
		Average	Random
		errors	errors	Temperature	Power supply
Elements		%	%	Δ=±25°C	Δ=±5%
1	Amplifier Ax:
Bias current		+0.005	±0.01	±0.01	±0.01
Offset voltage		+0.05	±0.01
Noise		+0.048
Amplitude error		+1.9	± 0.04	± 0.005
Gain non-linearity		+0.437
2	RC LPF:
Amplitude error		0.5	±0.05	±0.01
3	Multiplexer:
Leakage current		-0.0015	±0.02	±0.02	±0.005
Offset voltage		0.0014	±0.01
4	Amplifier A2:
Bias current		0.001	±0.01		±0.01
Offset voltage		0.001	±0.01	±0.01
Noise		0.001
Amplitude error		1.3	±0.01	±0.01
Gain non-linearity		0.0052
5	Band-pass filter:
Amplitude error		1.7	±0.01	±0.01
Crosstalk		0.006
Feedthrough		0.002
6	A-to-D converter:
Bias current		0.007	±0.01	±0.01	±0.01
Offset voltage		-0.03	±0.01
Non-linearity		0.39
Quantization error		0.2

temperature change and power supply variation can be neglected. Assuming that the random errors are approximately 10% of the average errors, compute the system accuracy and express it in the form of (7.23).

Total error = [latex]\sum\limits_{k=1}^{k}{\varepsilon _{ak} } +[\sum\limits_{l=1}^{l}{\varepsilon ^{2} _{pl} } + \sum\limits_{m=1}^{m}{\varepsilon ^{2} _{rm}} ]^{1/2}[/latex]

Accepted Answer

Add the average errors algebraically.
[latex]0.005 + 0.05 + 0.048 + 1.9 + 0.437 + 0.5-0.0015 + 0.0014 + 0.001 + 0.001+0.001 + 1.3 + 0.0052 + 1.7 + 0.006 + 0.002 + 0.007 -0.03 + 0.39 = 6.32 \%[/latex]
Add all systematic errors due to specific causes algebraically.
Due to temperature: -

[latex]\varepsilon _{pt}= \pm 0.01 \pm 0.005 \pm 0.01 \pm 0.02 \pm 0.01 \pm 0.01 \pm 0.01 \pm 0.01 = \pm 0.085 \%[/latex]

Due to power supply variation:

[latex]\varepsilon _{pps}= \pm 0.01 \pm 0.005 \pm 0.01 \pm 0.01 = \pm 0.035 \%[/latex]

Root sum square all random errors with the parametric systematic errors: -

[latex]\sqrt{ [(0.085)^{2} + (0.035)^{2} + (0.01 )^{2} + (0.01 )^{2} + (0.04)^{2} + (0.05)^{2} + (0.02)^{2} + (0.01)^{2} + (0.01)^{2} +(0.01)^{2} + (0.01)^{2} + (0.01)^{2} + (0.01)^{2} + (0.01)^{2}]}=[/latex]

[latex]\sqrt{[0.01385]}=0.117 \%[/latex]

Total error [latex]= 6.32 \% \pm 0.117 \% \pm 0.2 \%[/latex]

[latex]\uparrow \uparrow \uparrow[/latex]

average random quantisation

and
systematic

Question 7.16: In order to analyse a complex waveform the data acquisition ...

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