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

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

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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

Types of A/D Converters

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- Recap of terminology
- Over-sampling
- Noise shaping
- Introducing Sigma-Delta Converters (ADC)
- Functional description & Simulations
- Comparison with other converters
- Applications & Relevance to Protection industry

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- Sampling
- Sampling rate & Nyquist interval
- Quantization
- Quantizer resolution
- Quantization error
- Quantization noise

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- 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)

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- Anti-aliasing filter requirements are greatly reduced.
- Reduces the quantization noise within the frequency range of interest.

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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

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Impact of Over Sampling on Quantization Noise

Quantization noise - Nyquist rate sampling

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Impact of Over Sampling on Quantization Noise

Quantization noise – Over sampling

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Impact of Over Sampling on Quantization Noise

Quantization noise after filtering

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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

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Introduction to Sigma Delta Converters frequency range of interest if Noise shaping filters are used in an over sampled system.

- 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”

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1-Bit stream frequency range of interest if Noise shaping filters are used in an over sampled system.

(1 or 0)

+1 or -1 volt

1 Bit DAC

Functional Block Diagram

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X1 frequency range of interest if Noise shaping filters are used in an over sampled system.

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

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Data Flow frequency range of interest if Noise shaping filters are used in an over sampled system.

- Density of ones is more when the input is more positive.
- Density of zeros is more when input is more negative.

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Fs’ = 32*Fs frequency range of interest if Noise shaping filters are used in an over sampled system.

Simulation with sinusoidal input

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Fs’ = 64*Fs frequency range of interest if Noise shaping filters are used in an over sampled system.

Simulation with sinusoidal input

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Functional Description frequency range of interest if Noise shaping filters are used in an over sampled system.

- 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.

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Decimation Filter frequency range of interest if Noise shaping filters are used in an over sampled system.

- 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

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16:1 Decimation frequency range of interest if Noise shaping filters are used in an over sampled system.

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

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Simulation for Decimation filter frequency range of interest if Noise shaping filters are used in an over sampled system.

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Simulation for Decimation filter frequency range of interest if Noise shaping filters are used in an over sampled system.

Department of Electrical & Computer Engineering

Simulation for Decimation filter frequency range of interest if Noise shaping filters are used in an over sampled system.

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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

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Sigma Delta - Merits & Demerits is High-pass filtered [H

- 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

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Sigma Delta vs. other ADC is High-pass filtered [H

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Applications of Sigma Delta is High-pass filtered [H

- Process applications
- Temperature measurements
- Digital Audio CD system applications
- Latency is the major issue which keeps the protection industry away from sigma delta ADC

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References is High-pass filtered [H

- 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

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Questions is High-pass filtered [H

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