ES585a - Computer Based Power System Protection Course by Dr.T.S.Sidhu - Fall 2005 Class discussion presentation by Vij

1. UNDERSTANDING SIGMA – DELTA CONVERTERS ES585a - Computer Based Power System Protection Course by Dr.T.S.Sidhu - Fall 2005 Class discussion presentation by Vijayasarathi Muthukrishnan 25th October 2005 Department of Electrical & Computer Engineering

2. Types of A/D Converters Department of Electrical & Computer Engineering

3. Topics for Discussion • Recap of terminology • Over-sampling • Noise shaping • Introducing Sigma-Delta Converters (ADC) • Functional description & Simulations • Comparison with other converters • Applications & Relevance to Protection industry Department of Electrical & Computer Engineering

4. Recap of Terminology • Sampling • Sampling rate & Nyquist interval • Quantization • Quantizer resolution • Quantization error • Quantization noise Department of Electrical & Computer Engineering

5. Over Sampling • Sampling at a higher rate which is a larger multiple of normal Nyquist rate. • Example: • Fmax = 60 Hz • Minimum sampling rate Fs = 120 Hz (Nyquist rate) • Over sampling rate • Fs’ = 7680 Hz (Say 64*fs) Department of Electrical & Computer Engineering

6. Over Sampling • Anti-aliasing filter requirements are greatly reduced. • Reduces the quantization noise within the frequency range of interest. Department of Electrical & Computer Engineering

7. Frequency spectrum for Normal sampling condition With Sharp cut-offAnti-aliasing filter Magnitude Fmax Fs Frequency Frequency spectrum for Over-sampling condition With Wide roll-off Anti-aliasing filter Magnitude Fmax Fs ‘ Frequency Impact of Over Sampling on Anti-aliasing filters Department of Electrical & Computer Engineering

8. Impact of Over Sampling on Quantization Noise Quantization noise - Nyquist rate sampling Department of Electrical & Computer Engineering

9. Impact of Over Sampling on Quantization Noise Quantization noise – Over sampling Department of Electrical & Computer Engineering

10. Impact of Over Sampling on Quantization Noise Quantization noise after filtering Department of Electrical & Computer Engineering

11. The efficiency of Noise reduction is increased in the frequency range of interest if Noise shaping filters are used in an over sampled system. These filters reduce the quantization noise by pushing them out of the frequency range of interest. Noise Shaping Department of Electrical & Computer Engineering

12. Introduction to Sigma Delta Converters • High resolution low cost ADC. • Made possible by the chips that integrate both analog and digital circuitry. • Over sampling and Noise shaping concepts are applied. • Circuit uses Comparators (Delta) and Integrators (Sigma) and so the name :“DELTA-SIGMA or SIGMA-DELTA” Department of Electrical & Computer Engineering

13. 1-Bit stream (1 or 0) +1 or -1 volt 1 Bit DAC Functional Block Diagram Department of Electrical & Computer Engineering

14. X1 X2 = X1-X5 X3 = X2 + X3(n-1) IF X3 > 0 IF X3 < 0 X4 = 0 X4 = 1 X5 = +1 X5 = -1 Functional Flow Chart Department of Electrical & Computer Engineering

15. Data Flow • Density of ones is more when the input is more positive. • Density of zeros is more when input is more negative. Department of Electrical & Computer Engineering

16. Fs’ = 32*Fs Simulation with sinusoidal input Department of Electrical & Computer Engineering

17. Fs’ = 64*Fs Simulation with sinusoidal input Department of Electrical & Computer Engineering

18. Functional Description • The input is an analog signal over sampled at Fs’. • Use of 1-bit ADC simplifies the structure. • The output of this ADC is a stream of 1 bit data i.e. 1s & 0s generated at very high clock rate which is nothing but Fs’ • The feedback loop ensures that the average output level is equal to the input signal level. • A decimation filter is used to average and get the digital output from the stream of one bits. • The resolution at converter output i.e. no of bits is also increased after decimation. Department of Electrical & Computer Engineering

19. Decimation Filter • Everything is in Digital domain : Low pass filter + Down sampler. • Acts as a low pass filter and removes the high frequency quantization noise and other remains of high frequency components. • Averages the stream of one bits • Finally reduction to original sampling rate Fs from over sampled rate Fs’ • Higher bit resolution is also achieved Department of Electrical & Computer Engineering

20. 16:1 Decimation 16 - one bit stream Analog input 1100000110000011 Avg.= (6/16 )= 0.375 SIGMA – DELTABLOCK DECIMATION FILTER Over sampled at 16 times 0110 One 4 - bit representation Decimation Department of Electrical & Computer Engineering

21. Simulation for Decimation filter Department of Electrical & Computer Engineering

22. Simulation for Decimation filter Department of Electrical & Computer Engineering

23. Simulation for Decimation filter Department of Electrical & Computer Engineering

24. Z-domain analysis of this converter reveals that the noise is High-pass filtered [Hn(Z) = (Z-1)/Z] i.e. noise is pushed out of our range of interest. Low pass filtering in Decimation filter removes all out of band noise leading to very minimum noise within our range of interest. Noise shaping effect Department of Electrical & Computer Engineering

25. Sigma Delta - Merits & Demerits • Merits • High resolution at Low cost • Very efficient noise handling • Less stringent Anti-aliasing filter requirements • Demerits • Several clock cycles settling time or latency due to delays in digital filtering stage • Longer conversion time, typically 100000 samples/s for 16-bit resolution and 1000 samples/s for 24-bit resolution • Limited to low frequency applications as over sampling becomes tough for high frequency applications Department of Electrical & Computer Engineering

26. Sigma Delta vs. other ADC Department of Electrical & Computer Engineering

27. Applications of Sigma Delta • Process applications • Temperature measurements • Digital Audio CD system applications • Latency is the major issue which keeps the protection industry away from sigma delta ADC Department of Electrical & Computer Engineering

28. References • An over view of sigma delta converters – IEEE Signal Processing Magazine, 1996 • Motorola Sigma Delta converter – Application note • MAXIM Semiconductors Sigma delta converter – Application note • Intersil corporation Sigma Delta converter– Application note • ‘Introduction to Signal Processing’ book by Sophocles J. Orfanidis • ‘Understanding DSP’ book by Richard G.Lyons Department of Electrical & Computer Engineering

29. Questions Department of Electrical & Computer Engineering