Hypex / Delta Sigma / Class D Technical Question

[hatvolt]

I've been looking into class D amplifiers for a while now, and the hypex / purifi amps seem to always be on top. I know they use some aggressive feedback, but the main question I have is how they get high resolution from their somewhat low frequency delta sigma modulator. I assume they are using a 1-bit delta sigma modulator that they feed into the power stage and if you use some tools like delta sigma toolbox and input some parameters with low OSR that equates to around a 500khz sample rate then you will get a SNR that is low 50-80db.
Maybe I am thinking of this incorrectly, but as far as I can tell this low SNR is proportional to the OSR and is made up of random quantization noise in band. So how are they able to get higher resolution out of a signal that has random noise? Does the negative feedback directly modify the analog signal that is coming out? Is the noise no longer random when it is within a closed loop?

In delta sigma toolbox, the SNR is also proportional to the order of noise shaping. At some point with a 1-bit signal, saturation would occur with higher order noise shaping, but maybe the control loop is noise shaping itself? So maybe the control loop causes some better noise shaping than what can be calculated by the delta sigma toolbox? Or maybe you can't really compare delta sigma toolbox to the Hypex implementation because they are just functionally different?

It seems very hard to find information on this, and I can't say I understand it too well. Any feedback would be much appreciated.

 

[boXem]

To have an idea of their working principle : the initial paper

 

[boXem]

The system has been refined a lot since then with very high order loops, but the overall idea remains the same.
More literature here : Hypex support downloads

 

[hatvolt]

Yes, I have read the paper and its more technical. Going more into circuit design rather than reasoning. It doesn't even mention delta-sigma modulation in the paper. One good video I've seen regarding self-oscillating class D is:
[#21] Self-oscillating Class-D amplifiers

Not too in depth but gives a good overview. Mentions in the video that with a self-oscillating delta sigma modulator that "Timing resolution is not limited to a clock cycle-time, Therefore -> "virtually" endless oversampling"

Maybe this is the answer to my question? I can't use delta sigma toolbox because a self-oscillating delta-sigma modulator doesn't use an external clock, and the toolbox implementation is only for classic external clock-based delta-sigma modulators?

 

[boXem]

There is a bit more math in the other papers. I didn't study them since years but I think I remember that in one of the Ncore papers, the difference with 'classical' samplig theory is explained.

 

[hatvolt]

I think maybe I see. In a traditional delta-sigma modulator using a clock the minimum pulse width would be 1/clkfreq. All pulses would be some multiple of the minimum pulse width. The SNR would be proportional to minimum pulse width so it would be proportional to clock frequency. With self-oscillating delta-sigma modulation the clock frequency isn't a set value so you can have many different pulse widths but still have an overall average frequency of say 500khz at 50% duty cycle. So, you would have this virtually endless oversampling limited by rise and fall times of the 1-bit signal? Does this sound correct?

 

[Lars Risbo]

it is not sigma-delta (despite Bruno and i are old sigma-delta guys). It’s a self oscillating Pulse Width Modulation loop with a comparator controlling the power stage. There is no clock or any discretisation of the switching events thus no quantisation effect. Very important !

Cheers

Lars/Purifi

 

[voodooless]

Two key differences to a normal digital Delta sigma modulator:

- clock is not stable due to the self oscillating nature
- the pulse width is not discrete because the modulator is fully analog

 

[hatvolt]

I see, so I guess my last comment was fairly accurate. Thanks for the replies.

This might be a dumb question, but one other thing I couldn't seem to wrap my head around was how if the output is phase shifted 180 degrees in these amplifiers, then how is negative feedback done if the input signal now differs from the output signal. This one may be more complex and go into some sort of loop theory which I don't know much about.

 

[Lars Risbo]

I see, so I guess my last comment was fairly accurate. Thanks for the replies.

sorry but not accurate. there is no clock and associated time quantisation. Hence, the the modulation process is free from quantisation noise.

This might be a dumb question, but one other thing I couldn't seem to wrap my head around was how if the output is phase shifted 180 degrees in these amplifiers, then how is negative feedback done if the input signal now differs from the output signal. This one may be more complex and go into some sort of loop theory which I don't know much about.

Yes of course it’s complex . But the simplified view is that feedback is huge and in phase in the audible band and ends up with unity gains and 180 degree shift where the loop self oscillates.

 

[hatvolt]

sorry but not accurate.

What was inaccurate about that comment? It seems to be detailing exactly what you and voodooless said, the self-oscillating modulator has no set clock rate:

With self-oscillating delta-sigma modulation the clock frequency isn't a set value

and non-discrete pulse width output:

you can have many different pulse widths but still have an overall average frequency ... limited by rise and fall times of the 1-bit signal

Was my explanation of how a traditional delta-sigma modulator's quantization noise is proportional to clock speed incorrect? Or maybe my wording was just confusing?

 

[Lars Risbo]

We can have all 2x2 combinations of self oscillating vs synchronised pulse rate and quantised (clocked aka discrete-time) versus continuous time transition edges.

The term ‘self oscillating sigma-delta’ is confusing since sigma-delta is normally discrete time. Also mentioning clock would imply quantisation in time. Appeared to me that there was still time quantisation. I am sorry if I misinterpreted that.

 

[hatvolt]

Ah I see. When I made the post, I didn't quite understand the difference between the self-oscillating modulator and the traditional delta sigma modulator. I guess mentioning there is a clock frequency to begin with is incorrect, and I had not come to the realization yet that removing the discrete time samples would also remove the quantization noise. It makes sense though. I think my post kind of implied there was still some quantization noise. Thanks for the clarification