Design IV. E232 Spring 07

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1 Design IV Spring 07 Class 8 Bruce McNair bmcnair@stevens.edu 8-1/38

2 Computerized Data Acquisition Measurement system architecture System under test sensor sensor sensor sensor signal conditioning signal conditioning signal conditioning signal conditioning S e l e c t o r Analog-todigital converter(s) Computer Computercontrolled test equipment GPIB/HPIB/IEEE-488 signals controls 8-2/38

3 Analog-to-digital converters Computerized Data Acquisition MSB Analog input signal (e.g., 0-10V) A/D converter N-bits 2 N levels LSB 8-3/38

4 Digital-to-analog converters Computerized Data Acquisition R - + V out b 3 b 2 b 1 b 0 Summing 2R 2R 2R 2R junction -V ref R R R 2R V = K( b 2 + b 2 + b 2 + b 2 ) out /38

5 Computerized Data Acquisition Successive approximation A/D converter Comparator V in Approximation of input + - Input > < approx. Reference voltage D/A converter Control logic Output logic Adjust digital signal to input 8-5/38

6 Today s topics Computerized Data Acquisition Quantization effects Sampling Anti-alias filtering Reconstruction filtering 8-6/38

7 Quantifying Error How well does output represent input signal? Input Output 8-7/38

8 Quantifying Error Peak error Input Output max(i i O i ) Peak error 8-8/38

9 Quantifying Error Peak error Input Output max(i i O i ) Peak error What if output is only rarely different from input? 8-9/38

10 Quantifying Error Root-Mean-Square (RMS) error RMS error 1 N N 1 i= 0 ( I O ) i i 2 Input Output max(i i O i ) Peak error What if output is only rarely different from input? 8-10/38

11 Computerized Data Acquisition Systems Quantization effects Original analog signal 8-11/38

12 Computerized Data Acquisition Systems Quantization effects Original analog signal Error 1 Digital representation with 1 bit rms(error) = /38

13 Computerized Data Acquisition Systems Quantization effects Original analog signal.328 Error Digital representation with 2 bits rms(error) = /38

14 Computerized Data Acquisition Systems Quantization effects Original analog signal Error.142 Digital representation with 3 bits rms(error) = /38

15 Computerized Data Acquisition Systems Quantization effects Original analog signal Error.067 Digital representation with 3 bits rms(error) = /38

16 Quantization Error 0.2 error( n) QE..( n ) =.5 2 n 8-16/38

17 Quantization Error 0 error( n) error.db ( n) QE..( n ) =.5 2 n QE.. ( n) n 6 db 8-17/38

18 Sampling Time-varying Signals Quantization - restriction of amplitude to discrete values 8-18/38

19 Sampling Time-varying Signals Sampling at discrete points in time 8-19/38

20 Sampling Time-varying Signals These are samples of an analog signal what is the waveform? 8-20/38

21 Sampling Time-varying Signals T Is it a sinusoid with a period T? 8-21/38

22 Sampling Time-varying Signals What if we provide more samples? 8-22/38

23 Sampling Time-varying Signals This is what the actual signal looked like: The first set of samples was at too low a frequency 8-23/38

24 Nyquist Sampling Theorem f max f s >= 2f max A signal that has energy to f max must be sampled at a rate (2 x f max ) or greater 8-24/38

25 Nyquist Sampling Theorem f max f s >= 2f max A signal that has energy to f max must be sampled at a rate (2 x f max ) or greater Sampling creates an alias copy of a signal 8-25/38

26 Nyquist Sampling Theorem f max f s < 2f max A signal that has energy to f max must be sampled at a rate (2 x f max ) or greater Sampling creates an alias copy of a signal If the sampling rate is less than twice the highest frequency, the alias overlaps the original, creating distortion 8-26/38

27 Nyquist Sampling Theorem f s/ /2 f s Consider f s = 1000 Hz with two signals, f 1 = 5 Hz, f 2 = 990 Hz. 8-27/38

28 Nyquist Sampling Theorem f s/ /2 f s Consider f s = 1000 Hz with two signals, f 1 = 5 Hz, f 2 = 990 Hz. Sampling creates a reflected signal (alias) around the sampling frequency. Aliased signal at f s f 2 = 10 Hz cannot be distinguised from a real signal at 10 Hz. 8-28/38

29 Nyquist Sampling Theorem Actual 5 Hz signal Alias of 990 Hz signal 8-29/38

30 Practical Sampling Considerations Signal Source Sampled Data Acquisition System Recorder/ Indicator Sample rate f s 8-30/38

31 Practical Sampling Considerations Signal Source Sampled Data Acquisition System Recorder/ Indicator Sample rate f s Noise 8-31/38

32 Practical Sampling Considerations Signal Source Sampled Data Acquisition System Recorder/ Indicator Sample rate f s Noise Are all input signals bandlimited to f s /2? 8-32/38

33 Practical Sampling Considerations Signal Source Sampled Data Acquisition System Recorder/ Indicator Sample rate f s Noise Are all input signals bandlimited to f s /2? Sampled, quantized signal 8-33/38

34 Practical Sampling Considerations Signal Source Sampled Data Acquisition System Recorder/ Indicator Sample rate f s Noise Are all input signals bandlimited to f s /2? Sampled, quantized signal Is a signal that abruptly changes value at discrete points of time appropriate? 8-34/38

35 Practical Sampling Considerations Signal Source Anti-aliasing filter Sampled Data Acquisition System Analog reconstruction filter Recorder/ Indicator Sample rate f s Noise Sampled, quantized signal 8-35/38

36 Practical Sampling Considerations Signal Source Anti-aliasing filter Sampled Data Acquisition System Analog reconstruction filter Recorder/ Indicator Sample rate f s Noise Bandlimited signal and noise Sampled, quantized signal Reconstructed analog signals 8-36/38

37 Next time Computerized Data Acquisition Fourier Transform and frequency domain analysis 8-37/38

38 Homework 4 Read Chapter 5 Problems 4.2, 4.5, 4.10, 5.14, /38

Design IV. E232 Fall 07

Design IV. E232 Fall 07 Design IV Fall 07 Class 7 Bruce McNair bmcnair@stevens.edu 7-1/27 Example Low-Pass Filter Design (like HW2 Problem 3.18) A(f) db f Cutoff (corner) frequency 7-2/27 Transmission Systems Analog signal transmission