ES585a - Computer Based Power System Protection

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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

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Types of A/D Converters
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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

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Recap of Terminology

• Sampling
• Sampling rate Nyquist interval
• Quantization
• Quantizer resolution
• Quantization error
• Quantization noise

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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 64fs)

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Over Sampling

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

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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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Noise Shaping

• 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.

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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

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Functional Block Diagram
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Functional Flow Chart
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X1 X2 X3 X4 X5
  0 0 1 1
0.5 -0.5 -0.5 0 -1
0.6 1.6 1.1 1 1
0.7 -0.3 0.8 1 1
0.8 -0.2 0.6 1 1
0.9 -0.1 0.5 1 1
1 0 0.5 1 1
0.9 -0.1 0.4 1 1
0.8 -0.2 0.2 1 1
0.7 -0.3 -0.1 0 -1
0.6 1.6 .5 1 1
0.5 -0.5 1 1 1
0.3 -0.7 0.3 1 1
0 -1 -0.7 0 -1
-0.2 0.8 0.1 1 1
-0.4 -1.4 -1.3 0 -1
-0.6 0.4 -0.9 0 -1
-0.8 0.2 -0.7 0 -1
-1 0 -0.7 0 -1
-0.8 0.2 -0.5 0 -1
-0.6 1.6 1.1 1 1
-0.4 -1.4 -0.3 0 -1
-0.2 0.8 0.5 1 1
0 -1 -0.5 0 -1
Data Flow

• 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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Simulation with sinusoidal input
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Simulation with sinusoidal input
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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.

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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

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Decimation
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Simulation for Decimation filter
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Simulation for Decimation filter
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Simulation for Decimation filter
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Noise shaping effect

• 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.

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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

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Sigma Delta vs. other ADC
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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

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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

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Questions