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what is delta sigma modulation?

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a_ronagh

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delta sigma modulation

Hi
Can anybody explain a little about Delta Sigma Modulation?
Do you know a good book about it?
thanks.
 

It's about the property of relaxation that oversampling offers. This is achieved by the use of sigma-delta modulator. Such relaxation basically relaxes cutoff frequency or -3dB bandwidth.

We musn't forget that quantisation noise is caused by quantisation error always inherent in ADC because quantisation can only linearly approximate a digital equivalent to represent an analog value over an analog dynamic range.

In a layman terms, oversampling is to sample an analog value many times, to minimise deviation error or quantisation error. The higher sampling frequency, the more accurate.

Sigma-delta suppresses quantisation noise by spreading the quantisation noise energy over the wider sampling bandwidth defined by the oversampling frequency, therefore the higher the sampling frequency, the wider the sampling bandwidth, the greater the noise suppression.

In addition, with the use of noise-shaping such as a HPF, this noise reduced to the minimum or almost removed.

Thus SNR of a sigma-delta modulator is increased to 6.02N + 1.76 + 10log(OSR), where the oversampling ratio, OSR is fs/2fo, where 2fo = nyquist-rate or minimum sampling frequency.

SNR of sigma-delta with 1st order noise-shaping = 6.02N + 1.76 - 5.17 + 30log(OSR)

SNR of sigma-delta with 2nd order noise-shaping = 6.02N + 1.76 - 12.9 + 50log(OSR)

These properties of bandwidth relaxation and removal quantisation noise offer relaxation or greater tolerance in mismatches and offsets.
 

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you can find the theory in any book about delta sigma DAC or sigma delta ADC.
 

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