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U130421 2nd January 2021 05:40 AM

Analog Delta-Sigma interpolation DAC
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What is Delta-Sigma? In quantified math is the same as derivative-integral in linear math. In electronics with limited frequency is simply high pass-low pass. The most known is the recording-playback RIAA curve. As on records the high frequencies which have much smaller amplitudes than the lowers, physically the groove will contain very little information about high frequencies, besides the hiss of the stylus friction noise. If the signal is recorded with the derivative function, the high frequencies are better described and on the playback the integrator cleans the hiss of the stylus bringing back the initial spectrum.
This is to be applied on the DAC to eliminate noises created by switching spikes internal R2R noise and due to step character of the analog converted signal.
The Delta hence is the difference in level between the actual and the preceding sample. I only need to delay the signal one clock and subtract with the actual and I get the derivative function

The left circuit shows this, the signal from the sampler 44khz is delayed 22us and the subtracted signal now is a cosine derivative of the input.
Now, if I integrate back the signal all the DAC noises will be attenuated and the step cosine will become ramped sine wave. The signal with 1khz becomes too clean sinusoidal , I increased to 8khz to be compared with the step wave. You can remark that very little filtering is necessary.
All is not bright, instead of sigma (accumulating discreet values) as I integrated it, the high frequency information in step is eliminated and the DAC has -3db response about 11khz. Band pass filter might re equalize but the lost information is not valuable, better can be done by interpolation that I explain in few.
To remark that the Delta is described with double precision than the signal occupying 17 bits.

NickKUK 2nd January 2021 06:03 AM

Worth checking out: Valve DAC from Linear Audio volume 13 as an implementation. In the thread there’s quite a bit of information which may help you.

MarcelvdG 2nd January 2021 06:07 AM

The circuits of post #1 are actually more similar to a delta modulator than to a sigma-delta (or delta-sigma) modulator.

NickKUK 2nd January 2021 06:07 AM

Also have you looked at the “alternate solver” in LTSpice? Numerical precision is higher.

U130421 2nd January 2021 06:29 AM


Originally Posted by MarcelvdG (
The circuits of post #1 are actually more similar to a delta modulator than to a sigma-delta (or delta-sigma) modulator.

May be I should call it delta-integral, but it is not single bit DAC.

U130421 2nd January 2021 06:34 AM

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Originally Posted by NickKUK (
Also have you looked at the “alternate solver” in LTSpice? Numerical precision is higher.

This circuit is only to show the principle of the theory.
I am a novice in LT, I don't know why I can't get ac analysis work.

U130421 2nd January 2021 07:11 AM

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This is PCM1794, 15khz, before and after filter.

Markw4 2nd January 2021 12:56 PM

Try here: Delta-sigma modulation - Wikipedia
That make sense?

Also of possible interest:

U130421 2nd January 2021 02:18 PM

I started my R&D engineer career in 1979 designing CVSD digital military communication in French company LMT.
This circuit has nothing to do with delta modulator. Instead of transforming the 16bit data into analog, the delta is transformed into analog and integrated. In fact the delay is made of 64bit shift register MC14517 and feeds inverted to a second DAC TDA1387 whose output current is tied with the first TDA1387 which receives the direct data. The delta is obtained at the current node to feed an integrator.

MarcelvdG 2nd January 2021 04:00 PM

The circuits of post #1 also have absolutely nothing to do with delta-sigma (or sigma-delta) modulation. They consist of a DAC followed by filters. If I understand post #9, you have actually implemented the delay digitally and used a kind of FIRDAC structure to make the first filter.

The analogy with delta modulation and with DPCM is that at the output of the first filter, you have a discrete-valued signal (with lots of possible values, but still discrete) that depends on the changes in the input signal.

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