Since yesterday I have the official permission to publish this paper wherever I want. So I decided to do it here as well.
As soon as time permits I will also post info on:
- A short "how to" for designing this loop.
- How we get rid of the first op-amp. This might be intersting for those who want to use it for a self-oscillating amp (hint: the modulator -> power-stage chain has to be non-inverting and the impedance relationships of the loop-filter have to be chosen accordingly).
- How to make the loop an integrating loop or one with a lower corner frequency (hint: make one of the OP-AMP stages a PI controller or LAG filter with a zero at fL).
- How to lay another loop around the whole thing (hint: LAG filter).
Since this is 1.) not patented and has 2.) already been officially released it can be used for commercial or private purposes by whover wants to do so (maybe the first Chinese production runs will even be released within the next 24 hours
).
But it would be nice if the ones who use it would give some feedback about what they use it for and if they are satisfied with it.
Its use is of course not restricted to audio. It might also be applied to motor controllers and power supplies and other switching power converters. It might in fact as well be used for feedback control of ANY topology that includes a 2nd order lowpass function (whether electrical or mechnaical or whatever).
Regards
Charles
As soon as time permits I will also post info on:
- A short "how to" for designing this loop.
- How we get rid of the first op-amp. This might be intersting for those who want to use it for a self-oscillating amp (hint: the modulator -> power-stage chain has to be non-inverting and the impedance relationships of the loop-filter have to be chosen accordingly).
- How to make the loop an integrating loop or one with a lower corner frequency (hint: make one of the OP-AMP stages a PI controller or LAG filter with a zero at fL).
- How to lay another loop around the whole thing (hint: LAG filter).
Since this is 1.) not patented and has 2.) already been officially released it can be used for commercial or private purposes by whover wants to do so (maybe the first Chinese production runs will even be released within the next 24 hours
).But it would be nice if the ones who use it would give some feedback about what they use it for and if they are satisfied with it.
Its use is of course not restricted to audio. It might also be applied to motor controllers and power supplies and other switching power converters. It might in fact as well be used for feedback control of ANY topology that includes a 2nd order lowpass function (whether electrical or mechnaical or whatever).
Regards
Charles
Impedance Ratios
Hi Phase-Accurate
You mention the need to watch the ratio of impedances to keep the RC(H) from being loaded by the input impedance of the differentiator. What do you think is good for the RH to R2 ratio 1:10 or 1:5? I guess I could just simulate it but if you have a rule of thumb? Also, the zero from RC(z) do you just place this where you need a little bump in the phase?
Thanks.
Eric
Hi Phase-Accurate
You mention the need to watch the ratio of impedances to keep the RC(H) from being loaded by the input impedance of the differentiator. What do you think is good for the RH to R2 ratio 1:10 or 1:5? I guess I could just simulate it but if you have a rule of thumb? Also, the zero from RC(z) do you just place this where you need a little bump in the phase?
Thanks.
Eric
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Hi Charles, I'm working in China 3nd year, trust me, man, class D is not hot topic anymore, unlike 10 years ago.
What do you mean by "class D is not hot topic anymore" ?
I also live in China and in my field (pro audio) I still have not seen any good and reliable high power class D amp coming from here... All I have seen is low power integrated ICs for hifi/DIY and bad copycats of Lab.Gruppen and Powersoft.
Class D is so hot topic that we have orders for the next 2 years as nothing is available at a cost sensitive price...
hi ArthurG,
which uses amplifiers in your field?
or you build them? (High-power I mean)
Regards
To 81bas:
I will post the original graphics as soon as I have undug them. The problem was that I had to compress the paper in order to fit it to the size restrictions of this forum.
Yes, a constant gain of the the modulator -> power-stage chain is assumed which is usually the case (within practical limits of course). This is of couse depandant on PSU voltage for a classic PWM amp with a triangular carrier. So you'd have to use a reasonably stiff PSU or use compensation. If you are doing a self-osciallting amp then the compensation is intrinsic to the working principle !
To ericbrooking:
1:10 would be nice from the frequency-response accuracy point-of-view. 1:5 would often be better regarding the loading of the first op-amp. The calculated example uses 1:5 as well. Even smaller ratios could be used if: 1.) someone either derives the exact formulae (maybe I'll do it when I am really bored !) or 2.) plays around with a simulator.
The 2nd order loop is intended to achieve additional NFB and not to compensate for any poles. I.e. the open-loop gain will start to roll off at 6dB/octave and then turn to a 12 dB /octave rolloff when going higher up the frequency axis and then return back to 6dB / octave at a frequency that is far enough below the unity-gain point.
Carrier-based amps are prone to distortion that is CAUSED BY the feedback loop (by ffeding back the carrier residual). Self oscillating topologies don't have this. There are several solutions for the problem like compensation schemes that rely on accurate dimensioning. Another solution is as so called MAE loop that doesn't fully compensate for the problem but reduces it. There is a specific dimensioning of such a 2nd order loop that has this MAE characteristic. I will post this dimanesioning a soon as I have undug it.
Regards
Charles
I will post the original graphics as soon as I have undug them. The problem was that I had to compress the paper in order to fit it to the size restrictions of this forum.
Yes, a constant gain of the the modulator -> power-stage chain is assumed which is usually the case (within practical limits of course). This is of couse depandant on PSU voltage for a classic PWM amp with a triangular carrier. So you'd have to use a reasonably stiff PSU or use compensation. If you are doing a self-osciallting amp then the compensation is intrinsic to the working principle !
To ericbrooking:
1:10 would be nice from the frequency-response accuracy point-of-view. 1:5 would often be better regarding the loading of the first op-amp. The calculated example uses 1:5 as well. Even smaller ratios could be used if: 1.) someone either derives the exact formulae (maybe I'll do it when I am really bored !) or 2.) plays around with a simulator.
The 2nd order loop is intended to achieve additional NFB and not to compensate for any poles. I.e. the open-loop gain will start to roll off at 6dB/octave and then turn to a 12 dB /octave rolloff when going higher up the frequency axis and then return back to 6dB / octave at a frequency that is far enough below the unity-gain point.
Carrier-based amps are prone to distortion that is CAUSED BY the feedback loop (by ffeding back the carrier residual). Self oscillating topologies don't have this. There are several solutions for the problem like compensation schemes that rely on accurate dimensioning. Another solution is as so called MAE loop that doesn't fully compensate for the problem but reduces it. There is a specific dimensioning of such a 2nd order loop that has this MAE characteristic. I will post this dimanesioning a soon as I have undug it.
Regards
Charles
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Well, yes, I'm also afraid this complicated schematic basically does this simple task, but I'm not sure yet.
And I think this topology is still in conflict with UcD if we apply it to self-oscillating amplifier. UcD: self oscillating amp with pure post-filter feedback, without histeresis. The controller is not defined (in 1st claim), so this schematic is also covered by it. (However I don't understand how could they get the patent for such a general thing.)
Charles! Correct me if I'm wrong!
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I wonder how it would cope in cases where the output load impedance could vary widely. I have designed a number of self-oscillating class-D designs for 100V output, with powers varying from 30W to 400W. The output loading on a 100W amplifier designed for 100V output could realistically vary from a minimum of 100 Ohms to a maximum of over 1000 Ohms, depending on the number and power-tapping of the speakers connected. Traditional class-D doesn't cope with this too well, which is one reson why there aren't all that many class-D amplifiers on the market intended for 100V output applications.
OK, sorry you lost me a bit. You still want the open loop gain to pass through unity gain with a 6 dB/oct slope for stability, correct?
Also, for practcal designs with modulator gain and closed loop gains of say 25dB would you do the calculations as shown and then just change the feed back resistor proportionately?
And lastly, for now
, what is your methodology behind picking your unity gain crossover freq? If I pick a freq higher than 120KHz in your example, other than potential aliasing, is there any other effects beyond possibly being harder to get your GM and PM?Thanks
Eric
OK, I get it. I can push the open loop gain up from DC to say 20K or so by adding the Rz Cz zero at about 10K, this seems to put the extra zero at about 40K or so. The end result is that I can up the value of R3, giving the mentioned increase in gain but the rest of the open loop response from about 40KHz and up looks the same, ie about the same GM and PM just more gain in the pass band. Very cool. This technique is much easier than the old Type 3 compensation.
Thanks so much Phase-Accurate it's been an education.
It might not be the most clever of all class-d NFB circuits but it does definitely more than just cancel a pole of the output filter.
It can cope with almost ANY 2nd order lowpass (that is including such with a very high Q value). This is something that a PID for instance can't do.
I am convinced that a dimensioning for a 100 V amp would be possible by overcompensating a little (i.e. dimensioning for a higher lowpass - Q than is actually used).
Eric:
If dimensioning for a higher gain and higher supply voltage (and the rest stays the same) then only RI and RF have to be changed.
Yes the maximum unity-gain point is determined by the sampling theorem. With weak input signals you have two samples per full switching cycle. The higher the signal amplitude the closer to each other do they move on the time axis.
That means you will have to design for sampling-rate = switching frequency. Older sources say that the unity-gain point should be 1/2 of the switching frequncy (minus some safety marging), newer literature says that it should be switching-frequency/Pi or lower.
If you want to increase gain for say 0 to 20 kHz then you would double R1 and make the RZ = R1. Cz would then be 1 / ( 2 * Pi * 40 kHz * RZ).
Regards
Charles
It can cope with almost ANY 2nd order lowpass (that is including such with a very high Q value). This is something that a PID for instance can't do.
I am convinced that a dimensioning for a 100 V amp would be possible by overcompensating a little (i.e. dimensioning for a higher lowpass - Q than is actually used).
Eric:
If dimensioning for a higher gain and higher supply voltage (and the rest stays the same) then only RI and RF have to be changed.
Yes the maximum unity-gain point is determined by the sampling theorem. With weak input signals you have two samples per full switching cycle. The higher the signal amplitude the closer to each other do they move on the time axis.
That means you will have to design for sampling-rate = switching frequency. Older sources say that the unity-gain point should be 1/2 of the switching frequncy (minus some safety marging), newer literature says that it should be switching-frequency/Pi or lower.
If you want to increase gain for say 0 to 20 kHz then you would double R1 and make the RZ = R1. Cz would then be 1 / ( 2 * Pi * 40 kHz * RZ).
Regards
Charles
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So which max loop gain can be achieved say at 10kHz using this topology with Fsw=500kHz?
Pafi
Well we could try a comparison of both and do an amplitude and phase-plot.
81 bas
I assume that you are talking about feedback factor and not loop gain as such since the latter can be made as high as one likes to.
A safe unity-gain point would be around 160 kHz and that would give a feedback factor of 16 @ 10 kHz ( 24 dB). You can of course increase that - at the cost of reduced phase-marging - by increasing the loop to 2nd order.
Regards
Charles
Well we could try a comparison of both and do an amplitude and phase-plot.
81 bas
I assume that you are talking about feedback factor and not loop gain as such since the latter can be made as high as one likes to.
A safe unity-gain point would be around 160 kHz and that would give a feedback factor of 16 @ 10 kHz ( 24 dB). You can of course increase that - at the cost of reduced phase-marging - by increasing the loop to 2nd order.
Regards
Charles
Charles!
Instead of bode I attached a step response. This describes (indirectly) amplitude+phase, but more realistic, because it contains the effects of the nonlinear PWM modulator too. This is a modell of a tri-level PWM amp with fsw=100 kHz. (Not for audio purposes.)
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