department of electrical & computer engineering 1 es585a - computer based power system...

Department of Electrical & Computer Engineering

1

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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• 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)

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02-1

-0.5

0

0.5

1

Time

Mag

nitu

de

60 Hz signal sampled at 600 Hz ( 5 times Nyquist rate )

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02-1

-0.5

0

0.5

1

Time

Mag

nitu

de

60 Hz signal sampled at 7680 Hz ( 64 times Nyquist rate)


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• Anti-aliasing filter requirements are greatly reduced.

• Reduces the quantization noise within the frequency range of interest.


7

Mag

nit

ud

e

Frequency

Frequency spectrum for Normal sampling condition

Fs

With Sharp cut-off Anti-aliasing filter

Fmax

Mag

nit

ud

e

Frequency

Frequency spectrum for Over-sampling condition

Fs ‘

With Wide roll-off Anti-aliasing filter

Fmax


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Quantization noise - Nyquist rate sampling


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Quantization noise – Over sampling


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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.


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• 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 DAC

1-Bit stream

(1 or 0)

+1 or -1 volt


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X2 = X1-X5

X3 = X2 + X3(n-1)

IF X3 > 0 IF X3 < 0

X4 = 1 X4 = 0

X5 = +1 X5 = -1

X1


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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

• 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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0 20 40 60 80 100 120-1

-0.5

0

0.5

1In

put

0 20 40 60 80 100 120-1

-0.5

0

0.5

1

DA

C

0 20 40 60 80 100 1200

0.2

0.4

0.6

0.8

1

Sig

ma

Del

ta O

utpu

t

Fs’ = 32*Fs


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0 50 100 150 200 250 300 350 400 450 500-1

-0.5

0

0.5

1

Inpu

t

0 50 100 150 200 250 300 350 400 450 500-1

-0.5

0

0.5

1

DA

C

0 50 100 150 200 250 300 350 400 450 5000

0.2

0.4

0.6

0.8

1

Sig

ma

Del

ta O

utpu

t

Fs’ = 64*Fs


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• 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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• 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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SIGMA – DELTA BLOCK

DECIMATION FILTER

Analog input

1100000110000011 Avg.= (6/16 )= 0.375

0110

16 - one bit stream

One 4 - bit representation

16:1 Decimation

Over sampled at 16 times


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0 100 200 300 400 500 600 700 800 900 1000-1

0

1

Inp

ut

Decimation from fs' = 30720 Hz to fs = 1920 Hz (16:1)

0 100 200 300 400 500 600 700 800 900 10000

0.5

1

Sig

ma

De

lta O

utp

ut

0 10 20 30 40 50 60-1

0

1

Decim

ate

d o

utp

ut


22

0 50 100 150 200 250 300 350 400 450 500-1

0

1In

pu

tDecimation from fs'=15360 Hz to fs= 960 Hz (16:1)

0 50 100 150 200 250 300 350 400 450 5000

0.5

1

Sig

ma

De

lta O

utp

ut

0 5 10 15 20 25 30-1

0

1

De

cim

ate

d o

utp

ut


23

0 50 100 150 200 250-1

0

1In

pu

tDecimation from fs'=7680 Hz to fs=480 Hz (16:1)

0 50 100 150 200 2500

0.5

1

Sig

ma

De

lta O

utp

ut

0 5 10 15-1

0

1

De

cim

ate

d o

utp

ut


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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.


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• 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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• 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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• 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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