Sigma - Delta Modulation (ADC & DAC) - Negative Feedback Loop

[John 11]

Hello,
recently I was reading about Sigma - Delta Modulation that it's commonly used in DAC and ADC. Undoubtedly, two crucial things are oversampling and noise shaping for this modulation.
The most interesting thing that paid my attention was negative feedback loop. The overall idea of it is the self‑correcting system. In the case of amplifiers, the suitable portion of output signal (inversed polarity) is fed back to input to correct any errors (distortion, stabilize the gain and so on).

My question that is referring to Sigma-Delta Modulation in ADC and DAC is:

Is it possible to negative feedback loop can feed back the output signal without any errors entirely to input? I mean if the input signal with any errors can be fully replaced with the corrected output at the negative feedback stage.

Good point is DAC when the input signal is oversampled with high bit-depth and at the negative feedback loop stage this high bit-depth is reduced to low bit resolution. For example, the high bit-depth in input signal firstly was 24 bit, but at the final output it should be 16bit (we have reduced a word length + dither, then). So the corrected new output (16 bit) without any errors that is fed back to input should be replaced entirely to get desired final output, and that 24 bit signal, that was originally, should be gone.
In my meaning, they cannot exist each other as it is in an amplifier (distorted input signal + a portion of corrected one in inversed polarity to create the final output). If it was like that, in DAC our 24 bit signal would be summed up with the new one with new output (16 bit) during the negative feedback loop and this makes no sense.

Understanding the negative feedback loop as self-correcting system, the new corrected output that is fed back to input can be entire or just a suitable portion to get the desired result and there is no rule if this output should be just a portion or whole to correct errors of the input signal - but I am not sure if I think correctly.

To be honest, I am not an engineer, but I want to simply know if my meaning of negative feedback loop of Sigma- Delta modulation is correct and if there is no rule of how much the corrected output is fed back to input.

I would be grateful for your help.

[Hugh Robjohns]

The negative feedback (NFB) loop in delta-sigma converters is used only to linearise the delta-sigma modulation stage, not the overall converter.

As this Wiki page shows, the NFB is only around the actual modulation section of the process and is only correcting (linearising) the re-quantising element.

[John 11]

Thank you for your response.
Should I understand that, there is no absolute rule how much new output signal is fed back to input (referring to DAC & ADC) at the NFB stage?

Basing on the example to estimate the possibility how NFB loop works:

The input signal was originally 24bit. Then at the next stage, the requantizer changes it to 16bit at the output, then this new output signal is fed back (NFB) to the input to get the final result (desired bit-depth), but in this case that 24 bit input signal simply cannot exist any longer, after the requantizer replaced it entirely with new 16 bit output signal at NFB loop stage. Logically, they would deny each other.
Is it possible?

The reason I want to know that is I have read the term for NFB loop that claims, the only a portion of the corrected output signal (whatever it's amp or DAC/ADC) is fed back to input, which made me confused how it actually might work for DAC/ADC.

[Wonks]

Have a read of this Analog Devices explanation of delta sigma circuitry

https://www.analog.com/media/en/trainin ... MT-022.pdf

And this step by step interactive guide to how the basic circuit works in terms of signal levels:
https://www.analog.com/en/design-center ... orial.html

[John 11]

Have a read of this Analog Devices explanation of delta sigma circuitry

https://www.analog.com/media/en/trainin ... MT-022.pdf

And this step by step interactive guide to how the basic circuit works in terms of signal levels:
https://www.analog.com/en/design-center ... orial.html

Thank you.

[John 11]

Can you help me understand something else in the context of this topic?
I have just found, as it was previously said, the negative feedback is the part of SDM, but there is also something called 'feedforward' that is happening from the very beginning.

Here is the example (Fig. 1. at the right corner):
https://www.eecis.udel.edu/~vsaxena/cou ... lators.pdf

According to Feedforward term:
'A feed-forward system measures errors in an early part of the system and applies a correction in a later part of the system. If it is a true feed-forward system, the correction is not fed back to the stage that is causing the error.'

If I understand it correctly the feedforward is the path between input at early stage with errors and a quantizer is fixing the quantization errors. Then the negative feedback loop is the path when this new fixed output by quantizer (comparator) is fed back to the input to make the final output without any errors.

So in SDM there are feedforward and negative feedback loop, does it make a sense?

If so, what about amplifiers that also use negative feedback loop?
It means there is also feedforward, and it should be interpreted as the stage of inverting polarity of the signal inside amp (error measurement), then the feedback loop transfers a portion of this new output to the input to make the final output?
My meaning is the feedback loop cannot exist alone in such audio systems without feedforward path, but I am not sure if I am correct.

[Hugh Robjohns]

In the paper you've quoted the feed-forward path is, in reality, just a topological restructuring of the SDM.

Instead of combining the NFB with the source signal at the input to the loop filter (Hz), it adds the source signal to the loop filter output. This is done for practical manufacturing reasons to reduce the signal amplitude at the input to the filter, easing headroom constraints.

I'm afraid I don't know if this technique is in widespread use today. The world of converter technology evolves constantly — the latest ESS Sabre converters are very different beasts to previous generation converters, for example.

[John 11]

In the paper you've quoted the feed-forward path is, in reality, just a topological restructuring of the SDM.

Instead of combining the NFB with the source signal at the input to the loop filter (Hz), it adds the source signal to the loop filter output. This is done for practical manufacturing reasons to reduce the signal amplitude at the input to the filter, easing headroom constraints.

I'm afraid I don't know if this technique is in widespread use today. The world of converter technology evolves constantly — the latest ESS Sabre converters are very different beasts to previous generation converters, for example.

Thank you Hugh.
Does it mean SDM simply doesn't use feedforward and this example provided by me is kind of evolution/extension of the previous idea of SDM basing on just NFB?
If so, it would also mean amplifiers don't use feedforward and negative feedback loop in their own system simultaneously to correct some errors. They use either FF, or NFB (however, reading some information on Benchmark they say their amplifiers use both: https://benchmarkmedia.com/blogs/applic ... correction).
In my meaning it doesn't make a sense to use two ways of error corrections in one audio system when FF and NFB do this, but in different ways. Which is why I don't see the common relationship between them in order to stabilize the audio signal in amplifiers.

[Hugh Robjohns]

Does it mean SDM simply doesn't use feedforward and this example provided by me is kind of evolution/extension of the previous idea of SDM basing on just NFB?

I've no idea what specific converter designs are doing. There are lots of ways of implementing delta-sigma conversion when you get down to the detail circuit design and maths...

If so, it would also mean amplifiers don't use feedforward and negative feedback loop in their own system simultaneously to correct some errors.

Different system use different solutions. They all have pros and cons and the devil is always in the detailed engineering. Also, manufacturers often misuse terminology for marketing purposes, and over simplify their explanations, so be careful of making assumptions!

Fundamentally, though, a feed-forward system is anticipatory. It employs a 'model' of the nonlinearities inherent in the system as a whole, and uses that model to predict and create the expected error signal for a given input signal. That error signal is then fed into the system's output in the hope of correcting its inherent system errors.

A (negative) feedback system doesn't use a model, it uses the system itself. So it compares the system output with the input signal and looks for any differences. The resulting difference or error signal is then fed back in at the beginning of the system to correct the output. The speed of the feedback loop is critical, especially in very high frequency applications.

Both feed-forward and negative feedback approaches are useful in maintaining system linearity, but both have pros and cons. Sometimes using both together can improve upon the results of using either on its own.... but at greater expense and higher risk of unstable conditions if not designed perfectly.

In my meaning it doesn't make a sense to use two ways of error corrections in one audio system when FF and NFB do this, but in different ways. Which is why I don't see the common relationship between them in order to stabilize the audio signal in amplifiers.

Well, it must make sense or no one would do it... but you're deep-diving into what is — in it's practical realisation — a very complicated technology with a lot of relatively complicated maths.

If you want to really get to grips with specific applications and implementations of these kinds of control systems you're going to have to work through electronics fundamentals and on into their advanced applications. It's a major topic all of its own and while I studied it all 40 years ago at uni, the science (and the maths, actually) has evolved enormously since then.

[John 11]

Does it mean SDM simply doesn't use feedforward and this example provided by me is kind of evolution/extension of the previous idea of SDM basing on just NFB?

I've no idea what specific converter designs are doing. There are lots of ways of implementing delta-sigma conversion when you get down to the detail circuit design and maths...

If so, it would also mean amplifiers don't use feedforward and negative feedback loop in their own system simultaneously to correct some errors.

Different system use different solutions. They all have pros and cons and the devil is always in the detailed engineering. Also, manufacturers often misuse terminology for marketing purposes, and over simplify their explanations, so be careful of making assumptions!

A feed-forward system is anticipatory. It uses a 'model' of the nonlinearities inherent in the system as a whole, and uses that to predict and create the expected error signal which it then feeds into the output in the hope of correcting inherent system errors.

A feedback system compares the output with the input and the resulting difference or error signal is fed back in at the beginning of the system to correct the output.

Both approaches are useful, but both have pros and cons, and they are sometimes used together.

In my meaning it doesn't make a sense to use two ways of error corrections in one audio system when FF and NFB do this, but in different ways. Which is why I don't see the common relationship between them in order to stabilize the audio signal in amplifiers.

You're deep-diving into what is — in it's practical realisation — a very complicated technology with a lot of relatively complicated maths. If you want to really get to grips with specific applications and implementations you're going to have to work through electronics fundamentals and on into advanced applications. I studied it all 40 years ago at uni but the science (and the maths, actually) has evolved enormously since then.

Thank you so much Hugh!