Delta-sigma modulation: Difference between revisions

Those qualities are combined to yield high accuracy in amplitude, using some form of time averaging.

 

Delta-sigma modulation is one type of low-bit oversampling method. A different related earlier method that also uses [[negative feedback]] is called [[delta modulation]]. Delta modulation only encodes the signal's change (its delta) rather than its [[amplitude]]. The result is a stream of pulses representing up or down, as opposed to a stream of amplitude numbers as is the case with [[pulse-code modulation]] (PCM).

 

Decimation did not initially exist, and oversampled data was sent as is. The proposal to decimate oversampled delta-sigma data before converting it into PCM audio was made by D.&nbsp;J.&nbsp;Goodman at Bell Labs in 1969.<ref name="analog">{{cite web |url=https://www.analog.com/media/en/training-seminars/design-handbooks/Data-Conversion-Handbook/Chapter3.pdf |title=Data Converter Architectures: Chapter 3 |access-date=October 27, 2018}}</ref>

 

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| image1 = Simple Circuit for Delta-Sigma Modulation.svg

Because of the integrator's ''negative'' sign, when '''{{font color|#bf0404||Ɛ(t)}}''' next gets sampled to produce '''{{font color|#8c9100|Q(t)}}''', the +'''{{font color|#8c9100|Q(t)}}''' in this integral actually represents ''negative'' feedback from the previous clock cycle.

 

An ideal [[D flip-flop]] samples '''{{font color|#bf0404||Ɛ(t)}}''' at the clock rate of 1&nbsp;[[㎒|MHz]]. The scope view (Figure 1b) has a minor division equal to the [[sampling period]] of 1&nbsp;μs, so every minor division corresponds to a sampling event. Since the flip-flop is assumed to be ideal, it treats any input voltage greater than 0&nbsp;V as logical high and any input voltage smaller than 0&nbsp;V as logical low, no matter how close it is to 0&nbsp;V (ignoring issues of sample-and-hold time violations and [[Metastability (electronics)|metastability]]).

 

The delta-sigma configuration as described by Inose et al. in 1962 was devised to solve problems in the accurate transmission of analog signals.<ref name="Inose" /> In that application it was the pulse stream that was transmitted and the original analog signal recovered with a lowpass filter after the received pulses had been reformed. This low pass filter performed the summation function associated with Σ. The highly mathematical treatment of transmission errors was introduced by them and is appropriate when applied to the pulse stream but these errors are lost in the accumulation process associated with Σ.

 

 

It is worth noting that if no decimation ever took place, the digital representation from a 1-bit delta-sigma modulator is simply a [[Pulse-density modulation#Digital-to-analog conversion|PDM signal, which can easily be converted to analog]] using a [[low-pass filter]], as simple as a [[RC circuit|resistor and capacitor]].<ref name=":1">{{Cite web |last=Ellsworth |first=Jeri |author-link=Jeri Ellsworth |date=2012-11-05 |title=One Bit ADC - Short Circuits |url=https://www.youtube.com/watch?v=DTCtx9eNHXE |url-status=live |access-date=2023-06-29 |website=[[YouTube]] |language=en-US}}</ref>