Nth order noise shaping

[sovadk]

I here present a scheme that can be used for Nth order noise shaping suitable for Class D amplifier feedback.
In the example here, I’ve made a 4th order feedback, but more blocks can easily be added or removed.



The cut-off frequency is controlled by the ratio between the four capacitors and R6, R8, R9 plus R10.

The ratio between R6, R8, R9 and R10 controls the poles. I have not optimized the ratio. By doing so, it’s possible to get a flat output magnitude and phase response.
As long as the opamp open loop amplification is large, this resistor ratio has no influence on the order of feedback. Only stability and the magnitude ripple around cut-off will be affected.


Opamp U1 dominates the noise generated by the feedback system. Therefore only one low noise opamp is necessary to construct an outstanding feedback system.


Bode plot

FFT analysis



I've olso made good progress in making feedback after a 2nd order LC output filter. I'll write a post about this later. Happy noise shaping.

[fr0st]

looks great to me

A few quesitons though....
Are there 7 opamps used in that diagram??

Have you tried simulating using 'real' component models?

[phase_accurate]

It shouldn't be too difficult to take NFB from an output filter even with SD (I wonder why Sharp didn't do it).

At what sampling frequency do you want to run it ?

I am aware that this topology here is the one that makes it easier to take an output filter into account.
OTOH I like the loop topology with only one feedback path because you would have to change only one resistor if you want to adapt for different supply voltages.

Be aware that you might need much better noise suppression in practice than theory predicts (just think of that Sharp amp with a 7th order modulator that only achieves 100 dB of SNR).

Have you ever run it as a discrete-time model (like the one that I posted within the "Analog devices thread"). Since my version of SPICE is very limited I did have to use a trick to do it.

Regards

Charles

[sovadk]

A few quesitons though.... Are there 7 opamps used in that diagram??

Yes, the opamp usage i 7, but I'm sure that it's possible to modify the configuration so that all the inverters can be avoided or reduced. I might look into that.

Have you tried simulating using 'real' component models?

The opamps have a gain of 1E6 and are limited to a -/+15 supply. As far as I know the model dosn't contain slew rate, GWB nor poles.
Resistors and capasitors are linear and they have no deviation.

It shouldn't be too difficult to take NFB from an output filter even with SD (I wonder why Sharp didn't do it).

It's reasonable easy cancel out poles in a LC filter and make feedback possible. But if you take deviation and different load conditions into account (no load, 1ohm or 8ohm), stability and plenty of feedback becomes hard to achieve. Also the load might contain complex components at high frequencys, which gives you more poles that those you've taken account for.

At what sampling frequency do you want to run it ?

This is only a model of the analog feedback system. But I'm working on a 350kHz Class D. For that I want to make beedback up to arround 125-150kHz (Neuquest allowes 175kHz in theory, but getting to close to this frequency gives aliasing = added noise)

... only one resistor...

You might have a point there. On the other hand, changing the supply voltage eg. with a factor 1/2, only worsen the feedback with 6dB, witch is almost nothing. You really have to make a big change in supply voltage, for this to be a real matter. B&O ISEpower change their supply voltage with a factor 10, when the signal is detected low. This 20dB factor, with accounts for a change in the feedback path. Therefore they have done so.
If you want to change to feedback often anyway. You could place a noninverting amplifier first in the feedback path and use it's gain to compensate for different supply voltages. This can be done with only one resistor.

Sharp amp

100dB SNR is good I think, but 7. order feedback sounds like a lot. Maby they should increese the switching frequency and also work on open loop noise sources. Looking into the ratio between MOSFET Ron and Cds ratio, it's fairly to go for a high Ron (50mohm+) and the enclosed low Cds, with respect to P losses. With the right ratio, theres fairly no difference i loss between 100kHz switching and 400kHz.

Have you ever run it as a discrete-time model

No. I don't know much about how to do so.

[phase_accurate]

Do I get it right that you want to use PWM and not delta-sigma then (because you are talking of a switching frequency of 350 kHz?) ?

You could place a noninverting amplifier first in the feedback path and use it's gain to compensate for different supply voltages. This can be done with only one resistor

I must admit that I didn't think enough. You are right in that the circuit can be rearranged that only one resistor has to be changed in order to adapt for different voltages. But please do it passively and don't use active components in the feedback branch.

I once tried the topology intended to be used as SD modulator, as a feedback network for a PWM amp (on the simulator only), and the results looked indeed promising.

Regards

Charles

[sovadk]

Yes I'm talking about a PWM. In a PWM configuration my carrier frequency is know and I'll be able to suppress it with an passive LC filter. I'm not sure how this will work out in a delta-sigma configuration.

[phase_accurate]

If you have a PWM modulator with good linearity you would not necessarily need such a high order of NFB loop (though in simulations at least one can achieve fantastic THD values).
you would not need to remove the carrier signal completely either.

And yes, also a delta-sigma amp would show some switching residual. The difference is that the SD amp's residual is noise-like (see attached simulation) and the PWM's resembles something like a distorted sinusoidal.

Regards

Charles

[sovadk]

Do you have a picture of a nonfiltered delta-sigma sinus and also a FFT analysis of it?

[phase_accurate]

At your service:

[phase_accurate]

Et voila the modulator output:

I did intentionally use 10 kHz because the modulation pattern is much easier to recognise (I would just look like a green lump on the screen), though the performance would be better at 1 kHz input.

Regards

Charles