| Pierre |
As an experimenter with Class-D amplifiers, I have found that it is not easy to properly design the feedback network when you want to include the LC output filter on it, and make the amp remain estable.
I think that some designs (self-osc or UCD) use positive or "hysteretical" feedback, but I am not interested on that, but on designing the compensation network for a basic PWM (triangle based) amplifier with negative feedback, including a single LC network (2nd order lowpass).
I have seen that there is a so-called "leapfrog" method, but I am not able to extract the phisical sense and design procedure for that case from the PDF. Are there some basic guidelines or simple explanations?
Phase_accurate, I have seen you are kind of an expert in these issues, can you help me, please?
Thanks! |
|
|
| phase_accurate |
Salut Pierre
Sorry for not responding earlier. I have been on holiday. In the meantime also my hotmail account was erased due to not using it.
If you have e-mailed me you message might have got lost.
There are many ways to build the triangle-based modulator itself. Could you tell us something about the ciscuit decisions that you have made so far ? Are you willing to share the final design ? If so I am of couse willing to assist.
Regards
Charles |
|
|
| Pierre |
Thanks for the help offering and don't worry for the delay, Charles.
My set-up is, by the moment, a simple experiment:
An error opamp configured as inverting amplifier, the signal enters via a resistor to the inv. input. The output goes to a comparator, and the other input of the comparator receives the triangle.
The output filter values are 20uH and 440nF.
What I would like is to include a 2nd order filter (LC) into the loop so the output impedance is reduced and the freq. response is made almost independent on the load, and the overall response is similar to a 1st order lowpass, while reducing distortion due to non-linearities of the ouput filter.
If you could give general design guidelines on how to design the feedback network to compensate for the filter phase shift, I think it could be very useful for any Class-D amp designer.
thanks! |
|
|
| phase_accurate |
Before we try to close the loop around everything: Does everything look fine open-loop. I.e. no ringing on the switching signal (with and without load) ?
How does it look like if you close the loop around the the switching stage (what this topology is meant to be used like) ?
If everything is working fine so far (important, if you don't want to do annoying debugging) we need to know the component values of your integrator and the gain of the switching stage (basically the PSU/trinangle-amplitude voltage-ratio).
Then we are able to rearrange the loop filter to take the output filter into consideration.
Regards
Charles |
|
|
| Pierre |
Thanks for your help, Charles.
Well, by now I have a 68k resistor between mosfet's output , with input resistor to the error opamp of 2k. (looking for a 30dB gain).
The output stage gain is 15, aprox. (6Vpp triangle with +/-45v supply rails).
The error opamp (integrator) capacitor is 470pF, and a 100K resistor in parallel, to improve DC offset, etc.
Now the loop is closed aroung switching stage. With this setup and a 10ohm in series with 330n zobel network, the -speaker- output has ringing only with light loads (above 20 ohms or so), overshoot for 8 ohms and very clean below that.
Is this a good start point? |
|
|
| phase_accurate |
| quote: | | With this setup and a 10ohm in series with 330n zobel network, the -speaker- output has ringing only with light loads (above 20 ohms or so), overshoot for 8 ohms and very clean below that. |
What I meant was the PWM signal itself. Things like ringing etc can lead to interesting effects like increased THD when the loop is closed (instead of the contrary). The output-signal of the comparator must also look clean, without glitches etc, since this can lead to premature death of mosfet-drivers.
One important thing I forgot to ask: What is your carrier frequency ?
And another point: We are free to change the actual closed-loop cutoff frequency within some limits. Do you want to do this ?
Regards
Charles |
|
|
| Pierre |
Ah, ok.
The PWM signal looks very good. The rise and fall times are about 70ns and there is almost no overshoot. So does the comparator output.
About the operating frequency, I feel comfortable with 260-300KHz, although I can vary this. (after all, this is an experiment!)
About the cutoff frequency, I would like to have about 30KHz at -3dB for 2ohm to 8ohm loads.
What do you think about my Zobel network? In my simulations it actually helps damping things when there is no load.
If I have time I will try to post some photos of the PWM and play a bit with the feedback network so I can give more details. My primary concern when closing the loop around filter is estability.
Thanks, Charles, for helping us in demystifying the "feedback after filter" problem! |
|
|
| phase_accurate |
| quote: | | What do you think about my Zobel network? In my simulations it actually helps damping things when there is no load. |
I also think that it is a good idea to use it but I would maybe lower the capacitor's value. One critical situation with after-filter NFB takeoff is the no-load situation. Though it might not be as severe in practice as in simulations, since practical filter parts are always lossy. But it would be a good idea to switch the thing on for the first time (i.e. the first time using after-filter NFB when it worked beforehand using before-filter NFB) WITH a resistive load connected.
As a start I would use the following:
1.) A 47 pF cap in parallel with your 68 k feedback resistor. This gives a phase-lead in the closed-loop and determines the overall upper cutoff-frequency.
2.) Decrease the Integrator cap to 330 pF since this will give you more NFB. With this value there is still some marging, so you won't get into problems when lowering the carrier-frequency below 260 kHz.
3.) Use a resistor of 10 k in series with said integrator cap. This will make your integrator (actually a PT1) into a PI. The FR of this "turns flat" at the output-filter pole frequency at said dimensioning.
4.) Play around with the integrator's parallel resistor. A larger one will lead to more NFB and lower THD at low frequencies. Smaller values however will lead to a more constant NFB factor throughout the audio range (and therefore more constant THD behaviour over the input- frequency) and faster overload recovery. Your 100 k is about the largest I would recommend. Maybe you will try with 47 k as an alternative.
You might actually try it first on the simulator.
And one more thing: Have fun !
Regards
Charles |
|
|
| Pierre |
Thanks!
It's funny! Just this afternoon I was playing with the simulator a little bit. Although my model doesn't include the switching nature of the amplifier (it is just an opamp -the integrator- , then a linear gain -the switching stage gain-, and then the filter), I hope the results can be extrapolated.
Before reading this, I have tried by adding a 82pF capacitor in parallel with the 68k resistor, and it has solved almost all the problems. I haven't currently added 10k in series with the integrator cap, but I will try your suggestion to see its effect. I had also lowered the 100k to 47k and I now I like it more.
Let's see if I can try this in real life as soon as possible, and let's see also if the pulse response is as good as in the simulation, as well as the freq. response, that has become almost load independent!
Thank you very much for your help. Should I find any more optimizations, I will publish them here, no doubt.
I think that these guidelines can help a lot of Class-D designers.
Cheers |
|
|
| Pierre |
Hi, Charles.
I added a resistor in series with the integrator cap as you suggested, and now the simulated freq. response is better (no ringing) with no load, so it does improve things.
A last question before putting hands into the lab: how can I measure phase margin in the simulation? Sorry, but I have forgotten the details since I studied it, so if you want to remind me... can I measure it in open loop or is it necessary to introduce an excitation while maintaining it close-loop, as it is done when designing power supplies compensation?
What is a good phase margin figure for these kind of amps?
If you are so kind to explain the procedure I (and many others) would be very pleased.
Thanks! |
|
|
| phase_accurate |
Phase marging can be measured (i.e. simulated) by opening the NFB loop, grounding the input and feeding the signal into the feedback branch.
If you then simulate the frequency response and display it as phase and gain plot, you can look at the phase of the output signal at the unity-gain point (you can of course also measure it on the real amp that way). The phase-difference between the actual output signal and 180 degrees is the phase-marging. One is trying to have more than 90 degrees, but this would be in a perfect world, in reality it is usually less. Even many excellent-sounding linear amps out there have only about 45 degrees !!! But values between 60 and 90 degrees can be achieved with properly designed switching amps.
Regards
Charles |
|
|
| Pierre |
Wow, that's a fast response!
So, in an inverting setup like mine and many others, that means that I should break the loop by disconnecting the output from the feedback network, and then insert a test voltage in the feedback input (where before was the output), then ground the input, and compara the output with the test signal, that is?
Thanks! |
|
|
| Pierre |
Well, there's where my small mess comes: if the setup I have explained before is correct, the simulator gives a DC shift of +180 degrees (that's logical, it's inverting), and a DC gain of about 23dB.
Phase is going down until it is +77 degrees where the gain is 0dB.
What is the phase margin there?
My reasoning is this: Gain should be less than 0dB when phase is 0 degrees, so the output has gone round from +180 degrees to 0 degrees and hence it is in phase (oscillation occurs), so phase shift in my case is 77 degrees (in the simulation, of course ;-)
That's with 8 ohm load. The funny thing is that with 2 ohms load, the phase at 0dB is +105degs. That is too good. Am I doing something really bad?
Cheers. |
|
|
| phase_accurate |
Ouch !!
I made a mess myself. Since you already have 180 degrees by the inversion (that is actually necessary for NFB) it is the difference to 360 degrees (where oscillation would start to occur) that is relevant. So you have 77 degrees now which is quite cool !
If you load your filter more heavily two things happen: It is damped more and its phase-change gets less steep. Secondly the amplitude response is also less steep with an earlier rolloff. Both these things together may get you the effect you described. The unity-gain frequency will not be the same again however (from a first guess it is lower now), but who bothers as long as the overall outcome is a stable frequency response for all load conditions ?!
Regards
Charles |
|
|
| Pierre |
| Here is the bode plot (for 4 ohm load): |
|
|
| phase_accurate |
Hi Pierre
That looks nice but it seems as if I made a calculation error because it should reach unity gain at less than 0.5 * fcarrier. I.e. at less than 130 kHz. What happens if you decrease the series resistor of the integrator ?
Regards
Charles |
|
|
| Pierre |
Well, if I reduce it to 4.7k then it crosses 0dB at 110KHz (4 ohm load), so ok.
Please, could you explain why did you wanted that condition? And how did you do the calculations? (if you are willing, of course ;-) I did some drawings and inserted the zero to lead phase shift and compensate the loop, but these subtle details escape to my (present) knowledge.
This figure is the speaker vs input freq. response at 4 ohms. It looks almost exactly the same for other loads. Do you think that the strange phase / gain change at about 10 MHz is worrying? I suppose it is due to the hf pole of the opamp.
Thanks. |
|
|
| phase_accurate |
| quote: | | Please, could you explain why did you wanted that condition? |
Because a class-d amp is a discrete-time control system the loop gain has to be lower than unity at the Nyqvist frequency. IMHO the assumption that the Nyqvist frequency is half the carrier frequency (that many sources mention) is not completely valid, since we make two decisions per carrier cycle. As long as there is no drive signal the Nyqvist frequency (i.e. half the rate at which decisions are taken) is the same as the switching signal. With increasing modulation index, the two instances where decisions are taken, move closer together until they happen at the same time for 100% (or 0 % ) duty-cycle and is therefor reduced to the switching frequency. The only practical solution to expliot this fact is a self oscillating class-d amp (at least to my knowledge).
The only case when the values can be simply and elegantly determined mathematically is the case with an output filter with a Q of 0.5 but this is not very practical.
So the only values that were actually exactly determined is the integrator C and the parrallel capacitor for the feedback branch.
As soon as I have time and I am motivated enough I will put it on paper (er word document) and post it here.
Regards
Charles
Edit: I wouldn't worry about the phase-change at 10 MHz. |
|
|
| Pierre |
Well, I am very happy with the results of the simulations. Let's see if they reproduce as well in the reality. At least I (and I am sure that many more people) have gained a little bit of "sensibility" on the issue.
Let's see if I can post some related useful schematics or oscilloscope images when the measurements are done.
Thanks, Charles, sincerely. |
|
|
| Pierre |
Well, now some real-world results:
I have implemented the changes in one of my prototypes (although the coil is 33uH and the cap is 1uF instead of 20uH+440n, so they are not identical to the simulations conditions).
The system works quite well, with very good transient (square wave) response (check the image: no overshoot and fast response). The gain and bandwidth are as expected also.
However, I have found slightly more distortion with a sine wave input than before, when the feedback was taken before the filter. Check the image.
On the other hand, the waveform doesn't degrade with high power levels. In fact, the image shows 72Vpp on 5 ohms, but it was the same with 70Vpp at 2.65ohm (230W rms). It is present in the whole audio band.
I think I should try with more feedback, perhaps reducing the 68k resistor (and recalculate the comp. capacitor in parallel accordingly). Do you have any suggestions?
Thanks! |
|
|
| phase_accurate |
Difficult to see where this distorion is generated, from this trace alone, but it seems to be of quite high order. (i.e. neither 2nd nor 3rd).
How is the open loop performance of your amp ? Diy you ever test it (careful when doing so because of DC offset and subsequent supply pumping) ?
Don't forget that the loop was designed for a filter whose cutoff frequency was almost an octave higher than the present one. You now have an unnecessarily low unity-gain frequency.
I'd suggest that you either use the output filter as determined or that we recalculate the components around the integrator.
The rectangular looks indeed cool, congrats ! How does the amp behave without load ?
Regards
Charles
Edit: What type(s) of OP-AMPs are you using and why did you go for 6 V pp for the triangular ? |
|
|
| Pierre |
Thanks (and sorry for the delay)!
Yes, you are right, I will correct the filter values so everything is as calculated.
About your question on the triangle amplitude, well, I chose a value not too low in order to more noise inmunity and not too high in order to have a smaller slew rate and less distortion in the circuit that generates it.
I use a low noise LM833 opamp for the error amplifier and a MAX038 for the triangle generator.
Best regards. |
|
|
| classd4sure |
Hi,
Great thread guys. I'm looking forward to that paper on feedback too, there's some information to be found online about it of course but it's such a vast subject it's hard if not impossible to find a good spot for jumping in.
Cheers |
|
|
| phase_accurate |
It is basically ordinary control theory but I know that many people would be grateful to have at least some guideline.
Regards
Charles |
|
|
| Pierre |
I agree with you, this info can be very useful to any Class-D designer. I think Charles is the most helpful member in the forum. Congratulations. I hope that my experiments are helpful to somebody, too.
Pierre |
|
|
| phase_accurate |
With 6 Volts pp @ 260 kHz you have 3.1 V/us slew-rate which might be a little large (with respect to the 7 V/us capability of the LM833) for comfort.
Regards
Charles |
|
|
| Workhorse |
| quote: | Originally posted by Pierre
I agree with you, this info can be very useful to any Class-D designer. I think Charles is the most helpful member in the forum. Congratulations. I hope that my experiments are helpful to somebody, too.
Pierre |
Charles is an extraordinary Element in CLASS_D Active Discussions. He simply accurate the phase of problem by applying its Indepth knowledge.
I regard and respect him as "Nelson Pass of Class-D"
He is extremely helpful as an active source of Information.
Without him I won't able to design some Class-D designs.
ThanX Charles for helping us.
regards
ampman |
|
|
| Pierre |
Do you think that the triangle amplitude/freq. is a bit high?
What would be the benefits of using a very high speed opamp as the error amplifier?
I think that, as the error signal is integrated and taken after the output filter, there is no need to have a very fast error opamp, at least with a very high slew-rate, right? (remember that, in my setup, the triangle goes directly to the comparator, it is not mixed with the signal and then the output is quantized like in other designs).
Thanks
PS: Charles, I can see that you are very appreciated in this forum. I didn't know because I am very new here, now I appreciate that I can feel lucky to count with you help. |
|
|
| fr0st |
It's probably better to take the feedback before the output fiter in a carrier type. In my simulations the phase shift of the output filter puts some nasty artifacts on the output waveform and also allows any switching risidule into the error amp so it spends it time correcting that aswell as the audio.
I got better results with a RC filter taken before the filter. I managed to obtain a 0.02% THD at 1kHz @ 1v in the simulation using this (I was using balanced modulators aswell... atleast I think thats what its called). This was done using the TL072 as my difference amp and error amp.
If you want to see the schematic just ask.
Good luck
Matt |
|
|
| phase_accurate |
| quote: | | In my simulations the phase shift of the output filter puts some nasty artifacts on the output waveform and also allows any switching risidule into the error amp so it spends it time correcting that aswell as the audio. |
This artifacts are a general problem in carrier-based class-d amps. They can indeed be exagerated by after-filter feedback-takeoff. Thats why I asked Pierre if everything else was working nicely in the first place.
| quote: | | If you want to see the schematic just ask. |
Yes please !
Did you also build it ? Keep in mind that you can have differences between simulations and real-life. In a simulation people usally use linear inductors, what they definitely aren't in real life.
I had better sonic results when playing around with post-filter feedback.
An alternative would be a mixed solution with pre- and post- filter NFB.
I used the TL 072 in a design 14 years ago (using a 250 kHz and 2V pp carrier) and it showed to be quite good for that purpose, although there would be better ones around nowadays.
Keep in mind that a class-d amp is a precision RF circuit used to process an audio signal.
Pierre wrote:
| quote: | | I think that, as the error signal is integrated and taken after the output filter, there is no need to have a very fast error opamp, at least with a very high slew-rate, right? (remember that, in my setup, the triangle goes directly to the comparator, it is not mixed with the signal and then the output is quantized like in other designs). |
The fact that we differentiate the output signal (parallel C on the feedback resistor) and that the response of the NFB integrator turns flat above a certain frequency, will lead to a triangular signal at the output of the NFB op-amp as before, when it was a simple integrator fed by the output stage directly.
One does not necessarily need to differentiate the feedback signal up to infinity. One can play with a series resistor on the capacitor of the feedback branch that is between 1 and 10% of the NFB resistor's value. That's another option I would suggest to Pierre to try out.
And never forget that a class-d amp is somewhat an "EMC-hell" which can also lead to unexpected problems sometimes.
Regards
Charles |
|
|
| Pierre |
Well, I have added a 4.7k in series with the 56pF capacitor that was in parallel with the 68k fb resistor.
I have noticed no difference in the simulation, only a decrease of the phase margin from 65 degs to 59 degs. But I will have to test in real-life to see if distortion is reduced at least "by eye".
I re-checked the switching waveform of the amplifier and it looks simply perfect, with 50ns rise/fall time and no overshoot at all (all this measured with load connected and no signal).
Then should I really expect a smaller distortion with feedback after filter than with feedback before filter? Are there any other things to check?
Cheers. |
|
|
| fr0st |
Keep in mind the 0.02% THD was using a 10u cap accross the output and using ideal components. Having 10u accross the output attenuates signals above about 5k I think, lowering it to 1u gave it a wider response at the cost of THD. Right now it measures at 0.047% at 1v and 0.1% at full swing (1.9v input). swithcing frequency is about 190kHz.
I recently changed the error amp to an OPA627, I had it spare so it saves buying a TL071.
I havn't built it yet :(
National rejected my sample request for its half bridge driver so I'll have to get a different one from farnell *shudder*
I hope it helps
Matt |
|
|
| Pierre |
That seem quite good figures. I hope it can be the same or even better with feedback after filter, anyway. Are that results of simulations or real-life tests?
Cheers. |
|
|
| fr0st |
Thats just in simulation
Good luck with your design |
|
|
| IVX |
fr0st,
if you'll set some dead time in the simulation, THD will be worse, but closer to the reality. |
|
|
| Pierre |
I have just realized that I have input coupling capacitors that are tantallum, hence with polarity, while the opamps are fed at +/-10V, so there is no DC bias at the amplifier input, only that I want to remove it from the source.
That's not very good, but can this capacitors -really- have a bad influcence on distortion (they even get reverse-biased in the - cycles of the input signal)?
Perhaps it would be nicer to use ceramic SMD non-polarized capacitors, right?
Thanks! |
|
|
| phase_accurate |
Salut Pierre
Yes, tantalum caps in the signal path can increase distortion, though not in the orders of magnitude that you can clearly see it on the CRO.
And don't use ceramics as audio frequency coupling caps, use polypropylene instead.
Regarding the missing D.C. path: It depends on the circuit and place, whether you have to use a path to ground. On an inverted input you usually don't (the NFB is already building a path to ground in this case) and on the non-inverting input you usually have to add a path to ground.
If you are unsure about that you can post the schematic.
Regards
Charles |
|
|
| Pierre |
Of course I will post the schematics (although they are quite simple and I have revealed the details in this thread before), please let me time to draw them in the PC (I have it currently drawn by hand) and I will be very glad to post it here.
.| quote: | | Regarding the missing D.C. path: It depends on the circuit and place, whether you have to use a path to ground. On an inverted input you usually don't (the NFB is already building a path to ground in this case) and on the non-inverting input you usually have to add a path to ground. |
There is not a problem with DC, what I wanted to say is only that with the current design there is no DC in either pin of the input capacitors, so when the signal goes positive it gets reverse biased, nothing more.
What most puzzles me is the increase in distortion with respect to when I had feedback before filter (at least I couldn't clearly see it in the oscilloscope). The same input capacitors are there, and as I supposed and you have confirmed, they shouldn't have a visible influence. Perhaps the different L and C output filter values can have a lot to say there, but I sincerely doubt that's the only cause. And the PWM waveform looks great! Do you have an opinion on this, Charles?
Thanks! |
|
|
| phase_accurate |
Salut Pierre
Is the problem persistent with the filter values the loop was originally designed for ?
Regards
Charles |
|
|
| Pierre |
Wow! that's a fast response!
I haven't changed the values yet (I avoided it at a first start as they are heavily soldered and I didn't have the right soldering iron), but I will do for sure, hopefully this afternoon, and I will keep you updated!
Now it is 33uH + 1uF.
Thanks,
Pierre |
|
|
| phase_accurate |
I guess it would be easier for you to change the feedback network than the output filter, isn't it ?
In this case we could redesign the loop.
Regards
Charles |
|
|
| Pierre |
Yes, it is, but I will finally use the 20uH + 440n filter, so sooner or later I have to live with that values. Thanks for the offering, anyway!
I'll keep you posted.
BTW: I know it is very difficult, but what order of magnitude in THD should I expect from the figures I showed? In the order of 0.5-1% or much more? Just to have an idea ;-) |
|
|
| Pierre |
Well, components changed: Now L=22uH and C=470uF. I hope that helps, this afternoon I will be able to test it and hopefully I can post some images tomorrow.
I am also drawing the sch. in the PC to post it here, as my scanner is broken. Please have some patience. (this way it will be updated with the last changes ;-)
About the distortion, is it possible to know more or less the distortion level I should expect with the waveform I shown?
Thanks! |
|
|
| phase_accurate |
Salut Pierre
Did you succeed ?
The posted waveform shows more than 1% THD I fear. But let's first see what happens with the changed output filter.
Regards
Charles |
|
|
| Pierre |
I still haven't got the time for the test. Arrrggjjj!
Another possibility I have thought of is that the DC cancellation network (a 20k pot with 100k in series with its lets, one connected to +5Vcc and another to -5Vcc, the wiper of the pot joined with 100k to the - input of the error opamp) is causing some mismatch. I will remove that for testing.
Pierre |
|
|
| Pierre |
Well, I tried this morning but, unfortunately I connected something wrong, so I blew up my mosfets (they did a good job protecting my fuses ;-). So it will take me a while to change them and try seriously to see if I get a better waveform with the new values, as by the moment I can only get small periods of time to dedicate to this.
I will be out for a few days, so I expect to have some useful results on tuesday or so.
Thanks for your unvaluable help and merry xmas!
Salut,
Pierre |
|
|
| Pierre |
Well, back again!
I tried with the corrected filter values and removing the DC offset correction potentiometer. The result is almost the same, the distortion in the waveform is still visible.
Maybe the cause is that there is not enough feedback? How could I correct this, any ideas?
It is strange, as the PWM waveforms look ok and the fidelity was better with fb before filter...mmmm
Thanks and happy new year! |
|
|
| phase_accurate |
Salut Pierre
There should be enough feedback atr the given dimensioning, although there are possibilities to increase NFB.
Is the amp stable without load ? I yes, then you could do the following test (without load, your PSU will be grateful !):
Feed a very low frequency signal into the amp and watch the signal at the output of the integrator, the output of the comparator, the output of the switching stage and the output filter. Is there anything peculiar happening when the voltage sweeps over approx +- 90 % of the max output voltage ?
Some points one has to watch out for: How is the feedback wired ? Could there be any unwanted pickup from the switching stage.
One has to be aware that there is not only the possibility of unwanted pickup of voltage and magnetic spuriae but also current. It is therefore better to have a differential feedback takeoff.
You could try using an opamp as differential amp for takeing the NFB at the very output. If the situation improves then we have found the problem but still not an optimal solution.
Better would be to make the whole forward path differential, since we want to avoid op-amps in the feedback branch.
Regards
Charles |
|
|
| Pierre |
Thanks, Charles, your willingness to help is always surprising.
I assume you mean using a very low (i.e. visible) sine, for example 1 Hz or less, to see how the PWM moves. And I suppose you request to disconnect load to avoid PSU pumping, right?
My amp doesn't work properly without load, it doesn't oscillate but the output sticks at an arbitrary negative DC level. If you remove the load once it has started, no problem however. And it starts up ok with a load <1.5Kohm or so. Is that ok for the test?
About noise pickup, well, it is possible, but it is strange to me that the distortion is present with any power level, even low ones (where the currents and spikes are quite low to disturb compared to high power levels). It looks the same for 10W and 250W rms . What do you think of this?
The fb path goes by one corner of the board where the output is located by the edge to the middle, so no excessive noise should be picked.
I will observe more deeply with very light loads, let's see how it looks like, and I will tell you.
Thanks! |
|
|
| phase_accurate |
Salut Pierre
| quote: | | I assume you mean using a very low (i.e. visible) sine, for example 1 Hz or less, to see how the PWM moves. And I suppose you request to disconnect load to avoid PSU pumping, right? |
Exactly !
| quote: | | My amp doesn't work properly without load, it doesn't oscillate but the output sticks at an arbitrary negative DC level. If you remove the load once it has started, no problem however. |
That is a very strange behaviour, I am wondering where this could come from.
With 1.5 k load PSU pumping might not be a problem (depending on the PSU) and you could leave it like that.
| quote: | | About noise pickup, well, it is possible, but it is strange to me that the distortion is present with any power level, even low ones (where the currents and spikes are quite low to disturb compared to high power levels). It looks the same for 10W and 250W rms . What do you think of this? |
I first understood that the distortion was always the same, independant of load impedance. But it seems to be independant of level as well, isn't it ? Do you want to say that even the shape of the signal stays the same independant of its height ? If the latter is the case, how does the input signal look like ?
Regards
Charles |
|
|
| Pierre |
I have been observing a bit more now.
The distortion is a bit higher at high power levels, but the signal is not perfect either at low power levels. I will take some photos and show you. To do that, I will put the scope in averaging mode and the signal measured with a 220ohm + 33nF low pass filter to remove some of the ripple.
This way the waveform should show up as it is, with only the constant distortion (no noise or artifacts due to the switching residue).
About the load, yes, even worse, it doesn't start until the load is about 750 ohms, and even then you need to put some input signal for it to start. mmmm, strange....
Ah, the input signal is quite good, at least it doesn't show the visible distortion. I also suspected of that! ;-)
Best regards. |
|
|
| Pierre |
Well, photos taken.
Using average mode of the scope really improves things ;-)
These photos are taken with 256-cycle averaging and a RC filter from the load with a -3dB cutoff freq. of about 32 KHz.
When the signal is small you can still see some ripple, of course.
The input signal is quite good but not perfect, specially in the peaks (it tends to have a little peaky top/bottom)
What do you think of these signals? Do you think that measuring this way is honest? (I think so as you remove noise and carrier and you end only with the amplified signal)
Here you are some photos, I will post the rest in sucesive posts. |
|
|
| Pierre |
The photo in the previous post is 40Vpp, 3KHz, 2.65ohm load.
This is 4Vpp, 1.2KHz, 2.65 ohms load (still some remaining ripple): |
|
|
| Pierre |
Now some low freq. ones:
60Vpp, 30 Hz, 5 ohm load: |
|
|
| Pierre |
| This is 5Vpp, 30 Hz, 5 ohms: |
|
|
| Pierre |
Now, this is 60Vpp, 1.2KHz and 5 ohms load.
Compare with next one, that is at 2.65 ohms load. |
|
|
| Pierre |
| Now with 2.65 ohms load. No, it is not the same photo ;-) |
|
|
| phase_accurate |
How does the 60 V pp one look like with no load (or a high-impedance one) ?
Regards
Charles |
|
|
| Pierre |
For the tests shown, I have used a +/-44V supply (no load) with 3x6800uF capacitors per rail, that may have caused an improvement.
About the feedback network: I have reduced the gain, now it has a 47K resistor in parallel with 56pF. The Resistor in the error opamp is 47K also, in parallel with 3k3+330pF. Input resistor is 2K, so gain is about 27dB.
I think that reducing the gain has also improved things, what do you think?
The output filter is 20 uH and 440nF now.
Thanks for your help. I Hope that this discussion is being useful for a lot of people, not only me!
Pierre |
|
|
| Pierre |
Wow! That's a fast response, Charles!
I will measure it and post the photo as soon as I can (this afternoon, I am afraid). I will use a 220ohm or so resistor (high enough?)
Pierre |
|
|
| Pierre |
Here you are!
330 ohms load (the first time I had to input some signal for it to start...)
The slighty smaller waveform is the input signal (in other scale, of course).
The output is 60Vpp at around 1KHz.
Salut |
|
|
| phase_accurate |
A test with 220 ohms should be O.K. IMO.
In the meantime I checked the phase-gain plot of your NFB network and it didn't look bad.
Just out of curiosity: How do things change as soon as you increase the open-loop gain at the low end by increasing the parallel resistor of the integrator, like from 47 k to 150 k ?
Regards
Charles |
|
|
| phase_accurate |
:o
Ouch, I see you were posting while I still had the posting window open. That happens when one is slow with finishing posts !!!
Regarding your pictures I see two things (or do at least think so):
1.) there seems to be a small load-dependancy of the effect as the last output waveform is a little cleaner than the one with 2.65 Ohms load.
2.) even the input signal doesn't look totally clean.
To 1: This might be due to a ground-loop problem, i.e.differential feedback would help in this case. How does your ground look BTW, is it a ground-plane ? Or it could also be due to the changeing properties due to the different output filter damping. Maybe it would be beneficial to increase the phase-marging, I will do some brainstorming on this.
To 2: What is your signal source ? How does the sinusoidal look like if the amp isn't running and nothing else than the scope is connected to the source ?
Regards
Charles |
|
|
| Pierre |
My source isn't definitively too good. It is a function generator I built at least 8 years ago, based on a ICL8038, so you can imagine! I will post some photos of the waveform with the generator and oscilloscope alone for you to see it, but I am sure that its THD is no better than 0.1%.
Now that things are better I will try to use my work's generator, a much better HP, or at least a PC with a good soundcard.
Yes, there is a little dependency on the load, but have in mind that we are comparing 170W versus 1.36W!
I will try also your suggestion about increasing the resistor from 47k to 150k.
Thanks, and please don't spend too much of your time on me, that's not fair!
Pierre |
|
|
| classd4sure |
Hi,
I have to say, sorry for posting this!
Have you simulated this, in particular, the change from pre to post filter feedback? If you can that might really help to rule out alot of things, like EMI RFI situations, spice doesn't do that, and if you see the same kind of distortion changes after going post filter feedback in spice, we know we have to look someplace else, and you'll be able to rip through the simulation alot quicker than with the real circuit to weed out any oversights.
Also, instead of just going with a slow test signal, (less than 1 HZ was mentioned) why not just use DC with a pot?
Thanks |
|
|
| phase_accurate |
No need for being sorry.
In a simulation (using ideal elements) the circuit behaved well, with THD below 0.1 %. It does show some ultrasonic hash between 20 kHz and 150 kHz though.
You can of course also do a DC sweep with a pot. I just suggested the slow AC signal because I by myself would do it like that out of lazyness ! :angel:
Regards
Charles |
|
|
| classd4sure |
Hi,
I had to say sorry as I figured the questions I asked were already answered up in the thread someplace and I just had to read it.
That's funny because I would have been tempted to use DC out of lazyness:)
Ultrasonic hash? Not sure .. what would that look like, extra residual ripple?
Maybe if that's the case once we throw some real world components in it no longer remains ultrasonic?
It shouldnt' be too hard to add some parasitics into the simulation and find out how it could twist things around, (you probably have a good idea how it would already, but I don't) add some ESR in the filter components, some ESL and parallel capacitance for the resistors involved, might very well bring that hash down to 10Khz yeh?
If that's the case how would you fix that, different values or better parts, of course no parts are ideal but some are better than others, this could be a really good reason why the pro's insist on SMD and double layer boards.
I've read that some types of resistors start looking like caps at 50Khz~100Khz..
RANT: You know in this day and age with the PC's we've got such parasitics should really be included in spice already, at least for the passive components, especially when you consider the kind of price tag most of these come with.
Anyway, this is really the "proper" use for spice, try to get it to replicate what the real world circuit is doing and it should give a good indication how to cure it. What a pain though :xeye:
Hmmmm, to that end, maybe we could add what the scope probes might be doing to it in the simulator as well.
Thanks for your patience :) |
|
|
| Pierre |
Well, I will try to start constructing a proper model of the circuit, although I am afraid that reproducing the same effects I have observed will be quite difficult, as all the layout parasitics should be included as well, not only the components non-idealities.
Meanwhile, I think it still worths the pain to play a bit more with the circuit, anyway.
Thanks for your help and happy new year!
I will keep you posted. |
|
|
| Pierre |
Although this is not related to the issue of this thread, I am a bit worried because last night one of my test amplifiers (that had NFB before filter, btw), failed in a party. The output devices got shorted causing the PSU fuses to blow.
I use 150V mosfets with a +/-45V supply, and the drive circuit is a quite typical IR2113, with some dead-time, the PWM waveform looks good... I don't think the failure was unchained due to overcurrent, as it was playing very good and quite cool for hours with music, with much less demanded power than the lab tests. (about 100W peaks).
Perhaps a spike in the gate caused one of them to fail, what produced a failure in the other due to overcurrent? Should I put a 15v zener in parallel with Vgs?
My mosfets are OnSemi's NTP35N15, following the suggestion of someone in the thread.
Any other possible cause of failure of the mosfets, from your experience, like uncontrolled spikes from the output coil, or whatever?
Thanks! |
|
|
| Pierre |
Hello all.
I will be out for some days, but be sure that the thing is not forgotten! ;-)
When I am back, I will continue with the feedback network optimization, with your wise help, and let's see if I can post some measurements of THD, etc, also.
Best regards,
Pierre |
|
|
| Pierre |
mmm.
One question more before leaving:
When I simulate the circuit open loop (disconnect the feedback takeoff from the output, input to gnd, and test signal at the feedback takeoff), we spoke about measuring the phase marging by measuring the phase when the gain of that is 0dB, right?
And what about the -3dB bandwidth? Shouldn't it be the whole 20KHz audio band?
With the values Charles suggested me, the open loop transfer function has a DC gain of about 22dB, and a -3dB point at about 8KHz. Is that enough?
If I increased the integrator parallel resistor from 47k and lower the integrator cap, I can get 36dB of gain with -3dB at about 5.5KHz.
For example, the image shows what I get with 10k+150p || 220k in the integrator, and 68k || 68p as feedback network. (22uH+440nF LC filter). Is this any better (theoretically)? |
|
|
| phase_accurate |
| quote: | | With the values Charles suggested me, the open loop transfer function has a DC gain of about 22dB, and a -3dB point at about 8KHz. Is that enough? |
This is a question of taste. Some people prefer more NFB and a lower -3dB point of the open-loop gain. You can achieve this by incresing the parallel resistor of the integrator and leaving everything else untouched.
| quote: | | If I increased the integrator parallel resistor from 47k and lower the integrator cap, I can get 36dB of gain with -3dB at about 5.5KHz. |
But now you have a unity-gain frequency of more than 1 MHz ! => Edit: I misinterpreted your diagram, forget about this statement !
Regarding the discussions of circuit non-idealities: I almost forgot that the output-filter itself might not behave like an ideal 2nd order filter due to inductance and capacitor losses. Is there any possibility for checking its response up to some MHz ?
Regards
Charles |
|
|
| Pierre |
Thanks for the fast response.
But at a given frequency, increasing NFB should reduce distortion, right?
About the filter measurements, yes, it is possible, I can use a network analyzer.
I suppose you mean the response of the filter loaded with, say, 4 ohms, right?
However, it is easier for me to check the components separately with a component analyzer. For example, magnitudes of inductance and series resistance for the coil, and capacitance and series resistance for the capacitor. Is that enough?
I can do the measurements but with small signal, so the saturation effects won't be seen.
However, I don't think the filter is the cause for the increase in distortion, as it is the same filter that I use for feedback BEFORE filter.
Best regards,
Pierre |
|
|
| classd4sure |
Hi Pierre,
It might help if you found out what the self resonance frequency of your coil is, then you can deduce a value for parallel capacitance, even your resistors have some parallel capacitance and ESL. Depending what type of resistors you're using you should be able to look up those values easily enough.
I'd only concern myself with the feedback and filter components for this exercise, possibly even ESL / ESR of the wires themselves (best guess)... it only takes a few seconds right.
When you have the parasitics in you can quickly swap from pre filter to post filter feedback and see how it reacts.
Even if it shows little or no difference, we'll all learn something from it and it's well appreciated.
BTW are you using shielded wire for your feedback line (kind of hard to model that).
Regards |
|
|
| Kenshin |
Pierre:why the error opamp is a integrator one?
when using feedback from the switching stage,a integrator is needed for lower down the high amplitude of switching (square)waveforms and change it into triangle.
but the LC filter's output signal is already filtered,why there's need for a integrator? Is it designed for "delay" mode phase compensation as in a (chip) OP AMP?
| quote: | Originally posted by Pierre
The error opamp (integrator) capacitor is 470pF, and a 100K resistor in parallel, to improve DC offset, etc.
|
|
|
|
| phase_accurate |
| quote: | | But at a given frequency, increasing NFB should reduce distortion, right? |
Yes, but sometimes people prefer to have almost constant NFB throughout the audio range in order to get constant THD over the audible frequency range. It is a matter of taste however.
| quote: | | I suppose you mean the response of the filter loaded with, say, 4 ohms, right? |
Yes. Deviations from the 2nd order behaviour would mean that the loop would have to be redesigned. I am not talking about the range around cutoff but frequencies above. You have to take into account that the coil is behaving less like an inductor the higher you go with frequency (rising core losses, winding capacitance etc). Similar problems exist for the capacitor.
| quote: | | I can do the measurements but with small signal, so the saturation effects won't be seen. |
That's O.K. in this case.
| quote: | | However, I don't think the filter is the cause for the increase in distortion, as it is the same filter that I use for feedback BEFORE filter. |
Even though we try to decrease distortion by the post-filter NFB I could imagine that there are possibilities that the contrary may be caused.
But let's first sort out the frequency-domain problem.
BTW: What is the tech data of your inductor, apart from the inductance, which we already know ?
Regards
Charles |
|
|
| Pierre |
No, the feedback is taken with a track around the edge of the board to the integrator.
I will try to post the measurements of the components, better than just relying on the datasheets. I suspect that this is not the problem, however, but worths a try, as classD4sure points.
About the integrator, well, the design was first intended to take feedback from the switching stage, where it was needed. Then I played a bit myself, asked here and Charles suggested me the component values. The integrator limits the open loop gain at high frequencies, so it is 0dB at about half the sw. freq.
I tried to remove the cap and series resistor across the opamp (only a 100k resistor around it) and simulations are much worse (strong load dependency, ringing at low loads, small phase margin, etc).
Thanks and best regards. |
|
|
| classd4sure |
Hi Pierre,
Have you done this on a PCB or Protoboard? If it is on a protoboard it may not be worth trying to model parasitics.
I have seen others (Charles for one) recommend taking feedback with coax when taking post filter feedback, with the shield grounded or terminated somehow, might be worth a shot too. |
|
|
| Kenshin |
Pierre:
with the integrator, now it's a lag-lead compensation --something classical.
try to do it as in an classical (linear) lag-lead compensation system.
BTW:
a op amp -- either in the error amp or in triangle wave generator-- running at such a high ripple frequency,its internal frequency compensation network may generate some TIM. this may be the cause of some distortions. |
|
|
| Pierre |
No, for god's shake! It is not done on a proto-board! I did it in a double-sided handmade PCB.
BTW: All my simulations results are from a linear model of the amp, with no switching at all. I think I have said so before, but just in case we are leading to some confusion or the model is not suitable by principle. Kershin, is that what you propose?
I understand what Charles says about having constant NFB gain or higher at low frequencies. It is a matter of testing which of them gives better results.
See my sim. model in the attached figure. |
|
|
| Pierre |
The set-up as it is in the drawing is open-loop. Note that I use a pulse generator (that behaves like a AC source for freq. domain analysis) as the input to the FB network, while attaching the input to GND. This way I can see both the freq. response (AC analysis) and the transient (ringing, etc) with a single source.
BTW: Shielding the feeback can be a good idea.
Kenshin: about TIM caused by hi freq switching, it seems strange to me that distortion was slightly better (by eye) when nfb was taken before filter, as the bare switching waveform is there, and that should enworse things instead.
Cheers,
Pierre |
|
|
| Kenshin |
Pierre:
I'm not proposing that the model is not suitable by principle--on the countrary, I meant that you can optimize the feedback like a linear lead-lag compensation.
about how much THD will be caused by the switching nature--I have really no idea.
about TIM:
you said that feedback directly from the switching stage has relatively low THD. This may because you are using only resistor in feedback. When connecting NFB from the total output, a capicitor is paralleled to generate a positive phase shift.The resistance of the cap at high frequency is very small,so the EMI spikes can flow directly into the OP AMP and cause TIM.
try serial a small resistor with the capicitor to suppress the high frequency noise.
| quote: | Originally posted by Pierre
BTW: All my simulations results are from a linear model of the amp, with no switching at all. I think I have said so before, but just in case we are leading to some confusion or the model is not suitable by principle. Kershin, is that what you propose?
I understand what Charles says about having constant NFB gain or higher at low frequencies. It is a matter of testing which of them gives better results.
See my sim. model in the attached figure. |
|
|
|
| Pierre |
Thanks , I will try.
Of course, the simulations are excellent, before and now, yielding distortions in the order of 4.5e-7 %, the problem, as always, is real life!
The fb. resistor is 68k and the cap is 56pF. A resistor of 2.2k in series is enough? Following the simulations, if I go higher, the freq. response deteriorates or is made more dependent on the load.
Best regards
Pierre |
|
|
| Pierre |
Perhaps it is the same thing to add a resistor in series with the R||C. What about 2.2k + (68k || 56pF) ?
This way, at low freqs, you have a feedback resistor of 70.2k, while at high freqs, the cap. is not directly bypassing all the EMI to the opamp. But... is 2.2k enough?
Pierre |
|
|
| phase_accurate |
Aah....... here we are again at the series resistor !!
Depending on the OP-AMPS slew-rate capabilities I'd go for 1 to 10% of the "main" feedback resistor. So your 2.2k might not be a bad choice for a start.
Regards
Charles |
|
|
| Kenshin |
56pf, 2.2k...the cutting off frequency is 1.29MHz,above the switching frequency. so it seems available.
A larger resistor up to 6.8K may also be available,now the pole is at 418 KHz.
if you use two poles at this frequency cascaded to produce enogh phaseshift( of course,the phaseshift of output LPF is considered) and ensure reliable oscillation,it may become a good self-oscillating one.
| quote: | Originally posted by Pierre
Thanks , I will try.
Of course, the simulations are excellent, before and now, yielding distortions in the order of 4.5e-7 %, the problem, as always, is real life!
The fb. resistor is 68k and the cap is 56pF. A resistor of 2.2k in series is enough? Following the simulations, if I go higher, the freq. response deteriorates or is made more dependent on the load.
Best regards
Pierre |
|
|
|
| Pierre |
Let's see how far can we get before I leave...
Well: that's the open loop simulation with the following values:
Series fb resistor: 4.7k
Comp. network: 68k || 56pF
Integrator: 220k || (10k+330pF)
With this setup, the feedback -3dB bandwidth is 2K, and phase margin is about 60 degs. However, I can get a wider feedback bandwidth (althogh less open loop gain) by reducing 220k to, say, 100k and 330pF to, say, 100pF.
Closing the loop, seems right, at least as before.
Charles, do you agree with Kenshin in that the series resistor can help reducing EMI in the integrator and that this can be the cause? Seems sensible, isn't it? (you don't seem to be pleased with the idea...) |
|
|
| classd4sure |
| quote: | | Charles, do you agree with Kenshin in that the series resistor can help reducing EMI in the integrator and that this can be the cause? Seems sensible, isn't it? (you don't seem to be pleased with the idea...) |
UCD does it.
Mind if I ask what program that came from?? Has a nice look to it. |
|
|
| phase_accurate |
| quote: | | Charles, do you agree with Kenshin in that the series resistor can help reducing EMI in the integrator and that this can be the cause? Seems sensible, isn't it? (you don't seem to be pleased with the idea...) |
From:
http://www.diyaudio.com/forums/show...4362#post534362
| quote: | | One does not necessarily need to differentiate the feedback signal up to infinity. One can play with a series resistor on the capacitor of the feedback branch that is between 1 and 10% of the NFB resistor's value. That's another option I would suggest to Pierre to try out. |
Regards
Charles |
|
|
| Pierre |
Thanks for your soons responses today!
But UcD is based on a completely different concept, it is self oscillating, indeed.
I use Protel for my boards, captures and simulations, it is a very complete package.
A bit more info: The difference in open loop response with 10k series resistor vs. without it is:
0dB point: 140KHz (10k resistor) vs. 176KHz (no resistor).
Phase margin: 58.6º vs. 77º
Response at 275KHz: -8dB vs. -3.6dB
So the only benefit is a <5dB attenuation more at the sw. frequency, will that be really noticeable?
Cheers! |
|
|
| phase_accurate |
This phase-marging of around 60 degrees is not world-record but there is rumours that there are linear amps with only 45 degrees of phase marging.
As long as we still have approx the same frequency response up to about 100 kHz we will be fine IMO.
You mention that we only decrease the level by about 6 dB at the switching frequency. This is true, but don't forget that it is much more for the higher spectral content of the switching waveform, which is where the op-amps are challenged and where transient overshoot etc is located.
Regards
Charles |
|
|
| Pierre |
Then I suppose that using a very fast error opamp should help a lot too...
Well, let's see when can I test all this in real-life.
Best regards,
Pierre |
|
|
| Kenshin |
my Simpw has only poles on the real axis -- does that means the phase margin is bigger than 90 degrees? | quote: | Originally posted by phase_accurate
This phase-marging of around 60 degrees is not world-record but there is rumours that there are linear amps with only 45 degrees of phase marging.
As long as we still have approx the same frequency response up to about 100 kHz we will be fine IMO.
You mention that we only decrease the level by about 6 dB at the switching frequency. This is true, but don't forget that it is much more for the higher spectral content of the switching waveform, which is where the op-amps are challenged and where transient overshoot etc is located.
Regards
Charles |
|
|
|
| phase_accurate |
For me - being an audiohead - it is much simpler to look at the bode diagram (I don't like pole-zero diagrams).
Are you talking about Pierre's circuit BTW ? At least the output filter should cause a complex pole-pair as a quick shot from the hip.
We could of course completely eliminate their effect by the use of a transfer function of the form
s^T^2 + sT/Q + 1
So we actually hopped into the thread "creating a positive phase-shift".
Regards
Charles |
|
|
| Pabo |
Sorry for not reading the entire thread before posting.
My experience with triwave classd is that switch ripple fed back from the output is very bad for THD. This means that a zero as the one you have introduced is causing THD at the same time as it is increasing phase margin.
My solution was to apply a series notch filter in paralell with the filter capacitor. For example using a 3uH coil, 220nF cap and 0,1ohm resistor gave med 14dB attenuation at 200kHz. This makes it possible to lower the filter caps in the output filter at the same time as it decreases the ripple in the feedback loop enabling the use of a zero in the feedback path. A tip is also to have a resistor in series with the zero in order to limit the bandwidth of the zero and the ripple at the switching frequency. |
|
|
| Pierre |
Thanks, Pabo.
Could you please draw the filter with the notch you propose? (I can't follow you)
Best regards,
Pierre |
|
|
| Pabo |
I have no possibility to draw where I an right now.
You simpky place a series notch across the output filter capacitor. A series notch is the one with the three components in series. |
|
|
| Pierre |
Ok, see what you mean. No problem.
I will try a simulation.
I have tried a similar notch setup in practice, I think someone in the forum suggested that some time ago: a second stage LC filter (outside the loop), with a capacitor and a resistor in parallel with the inductance. That works very well in reducing the switching residue, but can't be included in the feedback loop easily.
Does the coil need to be rated at the output current?
Thanks |
|
|
| phase_accurate |
| quote: | | This means that a zero as the one you have introduced is causing THD at the same time as it is increasing phase margin. |
It won't do that to a higher degree than taking NFB from the switching stage directly and using an ordinary integrator.
The notch-filter aaproach does indeed look convincing from a first glimpse (I once built a class-d amp with a cauer filter and pre-filter NFB that had a carrier suppression of 80 dB !) but it worsens the phase-marging.
If the reduction of the main output filter cap is an advantage is debatable. An amp with a lower cap value will be more susceptible to capacitive loading for instance.
I once made simulations with a notch filter in the forward path of the amp, which should achieve the same advantage (but could be done without another inductor) but the results weren't convincing.
As an addition to the aforementioned series resistor an LPF could be used in the feedback branch further removing glitches.
Regards
Charles |
|
|
| Pierre |
Well, simulation done!
I see a big problem in that configuration: the filter shows a notch at the calculated frequency, BUT followed by a peak in its response in a very short frequency displacement, so you can move from a very good situation to a very bad one if the clock frequency moves a little bit, or if the tolerances of the clock or notch components vary sligthly.
Do you think that only the resistor in series with the zero is enough to make it work well?
This is what I get for the filter (only the filter) response with the notch filter proposed by Pabo (approx. values) |
|
|
|
