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-   -   Coldn't resist: feedback from 4th order lowpass !! (http://www.diyaudio.com/forums/class-d/42540-coldnt-resist-feedback-4th-order-lowpass.html)

phase_accurate 14th October 2004 05:12 AM

Coldn't resist: feedback from 4th order lowpass !!
 
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Because there are still many out there who think that it is almost impossible to build PWM amps using post-filter NFB takeoff - I made an attempt to calculate such an NFB loop. I went to the extreme and took a fourth order output filter (f3=50 kHz, Bessel). I publish it here even at the risk that someone will go and patent it. ;)

Just some remarks:

1.) I actually know that real life is real life and simulations are just simulations so I don't want any discussions on that subject.

2.) I know the advantages of self oscillating topologies. I used a carrier-based one because "I come from there" and also because there are many ICs and other solutions for carrier-based class-d around that still use the same boring old NFB topologies.

3.) The same transfer functions can be achieved with alternative circuits. I just used the second topology that crossed my mind. These may even perform better in real life than the one here because they would need less op-amps or put less stress on them. I think I don't have to mention that careful choice of op-amps would be critical in real life.
Because my version of P-SPICE is very restricted I used the voltage-controlled voltage-source model insted of op-amps. It is of course possible to use multiple nested feedback loops instead of the single-loop topology presented here.

4.) I by myself would most probably not build a class-d amp with fourth-order filter because all the component tolerances are much tighter than they would be with a 2nd order filter. Carrier suppresion of 2nd order filters is also sufficient in most cases.

If you have a look a the schematic you can see a classic PID around E1. This one is responsible to build a first-order behaviour, together with one pole-pair of the output filter (ca 70 kHz, Q=0.52).
The second pole-pair (approx 80 kHz, Q=0.8) is dealt with by the circuit around E37 and E10 with the transfer function s^2T^2 + sT/Q + 1.

Because the transfer-function of the feedback-branch is a PD the closed-loop frequency response is a first-order lowpass. I tried with different loads between 2 Ohms and 1 k (nominal = 6 Ohms) and the response deviation was around 0.3 dB at 20 kHz. Deviations were a little "adventurous" above 30 kHz, but this wouldn't be that much of a problem with "normal" loads and clever choice of Zobel values.

On the open-loop gain diagram one can see that the whole loop has a first-order behaviour (well, almost) and the unity-gain point is 200 kHz approx. Phase-marging is 80 degrees approx !

The simulation I would trust the least is the transient analysis (i.e. the THD part to be exact). One can see the output signal when driven 20 dB below full output. There is not very much of the carrier left over ! The FFT shows that all harmonics of the "payload" are suppressed by more than 80 dB.

While the topology as such would theoretically work it is still not complete and it would show a "dangerous" restriction, depending on the input signal. I will elaborate on this later. Everybody is invited though to find that one out by himself in the meantime !

Regards

Charles

Jaka Racman 14th October 2004 06:30 AM

Hi Charles,

Thank you very much for sharing your effort. Can I suggest two other tests to try with your circuit?

First is a single unipolar square pulse response. I usually simulate with 0V to 1V 100us or 200us wide pulse. You might change output load resistance and add some load capacitance to see susceptibility of your design to the real loudspeaker loads.

Another test would be to put 1mA AC generator in parallel with the load and plot the AC transfer function from output back to the input of the PWM modulator E23. The reason for the second test is that I found my past design vey susceptible to the switching spikes that were induced in the filter itself and in the feedback path. Good layout might have prevented that, but I was forced to put six channels on a single Eurocard.

BTW, is the problem with your circuit related to the possible clipping of the opamps?

Best regards,

Jaka Racman

phase_accurate 14th October 2004 06:33 AM

Quote:

BTW, is the problem with your circuit related to the possible clipping of the opamps?
Yes and no ! It also has something to do with the first test that you suggested !

Regards

Charles

subwo1 14th October 2004 01:20 PM

Hi phase_accurate

I think it was great that put together this simulation. I too may use a carrier-based approach because I have not decided on the best set-up for my situation.

phase_accurate 14th October 2004 05:36 PM

The secret:
 
2 Attachment(s)
The circuit uses zeoes to cancel the output filters poles in advance. The closed loop has a behaviour of a 1st ordee lowpass after the bottleneck of a 4th order filter.
This is asking for trouble with fast transients and/or strong high-frequency content. Therefore one has to consider an additional lowpass filter before the amp, depending on application (a CD player wouldn't mean real danger but DVD-A and SACD probably could).

Regards

Charles

phase_accurate 15th October 2004 10:24 AM

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Thats how it would behave with a lowpass filter "in front". The filter is designed such that the overall response of the amp would be the same as the output filter alone would give.
One can see that the transient overload problem is significantely reduced (10 kHZ rectangular).

Regards

Charles

skippy 15th October 2004 11:12 AM

What max and min delays are you assuming through the amplifier's forward path?

phase_accurate 15th October 2004 12:42 PM

Quote:

What max and min delays are you assuming through the amplifier's forward path?
Are you actually talking about the open-loop behaviour of the forward-path itself or do you want to know the behaviour of the complete topology with the loop closed ?

Regards

Charles

skippy 15th October 2004 12:44 PM

I want to know about the open-loop behaviour of the forward path.

phase_accurate 15th October 2004 01:08 PM

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Here you can see the linear simulation of the forward path with the input of the feedback branch shorted to ground. The PWM modulator would of course introduce some additional dead-time delay.

Regards

Charles


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