Pulse Width Modulation Circuits

[Pafi]

wakibaki!

The difference between UPWM and NPWM is in the sampling. I don't see anything in your post about sampling.

See fig. 3 on page no. 34, here:
http://www.icepower.bang-olufsen.com/files/convention/4446.pdf

About your bit-cutting: you have turned UADS PWM to UADD PWM by post-process (which causes delay as side-effect, which makes feedback more problematic). What's the point? OK, UADD is much better then UADS, but you could do UADD directly also.

 

[Gyula]

not full-band PWM process, so they are incapable of making calculations... ...Despite of the extremely simple input they are already doubly infinite series!

(Every) signal can be composed of orthogonal base functions.

so they are incapable of making calculations in fed back amplifiers, since there is an infinitely complex spectra on the input

For example, a sampled signal has periodic infinite spectra. Just think about how to calculate a discrete-time fed-back system.

 

[Pafi]

(Every) signal can be composed of orthogonal base functions.

And this can be used for analysing LINEAR systems! There F(a+b)=F(a)+F(b). But: do you really think this is a linear system??? (Is PWM a linear operation?) If yes, then what could cause distortion? Nothing. So this is a nonlinear system, what is more: the object of research is the nonlinearity itself, so trying to use superposition here is one of the biggest mistake you could make. Here F(a+b)<>F(a)+F(b)!

I am stupid in math (proven by Serény), but I think there can't be any audio fan (not to mention electrical engineer!) without knowing perfectly linearity (conditions too, not only consequences)!

Ahogy régebben mondták: kérd vissza a tanulópénzt! Nekem még a technikumban megtanították a szuperpozíció helyes használatát. Volt egy srác, Kenyeres, neki nagyon nem ment a híradástechnika, de egyetlen dolgot még neki is a fejébe vertek: a szuperpozíciót. Mindig amikor ezt kellett használni, és senki nem mondta magától, a tanár (Nagy Ferenc Csaba) csak annyit mondott: Kenyeres! Õ felállt, és bemondta, hogy "szuperpozíció". Na de most senki sem mondta, hogy Kenyeres! Te se mondd, mert nincs meg az elégséges feltétel!

Siralmas a magyar felsõfokú mûszaki oktatás - azt kell hogy mondjam - de ezt eddig is tudtam.

Dont tell me how to think! Do the calculations, if you can! (Then I will point to the neccessarily occuring errors!) I can't do these calculations, neither do Omar Hawksford, this is why he used matlab simulations instead of analytical calculations. And obviously you can't do them either, thats why you are trying to make me do.

For example, a sampled signal has periodic infinite spectra.

Yes, periodic (and symmetrical)! The same value in every domain! Thats why you have to deal with only one domain of spectra (as long as you make linear operations)! For sinusoidal signal, it's a single complex number! Not infinite different numbers (and most of the numbers are calculated by a sum of infinite numbers), as in case of PWM, and this is only no-fed-back case! With feedback it becomes mind-blowingly complicated.

Don't pretend you didn't know this, you are more clever then this!

Just think about how to calculate a discrete-time fed-back system.

By time-domain analysis or by Z-transformation. But Z transformation of PW Modulation does not exist! (Since PWM signal is in continuous time.)

 

[wakibaki]

Thanks Pafi, good link.

I don't see anything in your post about sampling.

No, this is because I am primarily interested in the reconstruction of existing samples e.g 44k1 16-bit PCM.

What I am suggesting is that an analog signal, digitised using PCM and played back using UADD will be trivially different from one sampled using NADD and played back using NADD. We use PCM all the time despite sin x/x distortion. UADD at a sufficient sample rate is identical to NADD, as long as the risetime of the sampled signal is insufficient to offset the OFF/ON transition 1 bit-time.

w

 

[Pafi]

Thanks Pafi, good link.

Not at all! It was originally linked by Gyula, I just copied it! He (and phase_accurate) found really good articles indeed.

We use PCM all the time despite sin x/x distortion.

Yes, but this is a very nice, linear distortion. What we talked about is a nasty nonlinear distortion!

UADD at a sufficient sample rate is identical to NADD, as long as the risetime of the sampled signal is insufficient to offset the OFF/ON transition 1 bit-time.

Yes (almost), but this is true only for extremely low freq (or small amplitude) signals (for example under 60 Hz, 0 dB, for 16 bit, 352.8 kHz PWM), so we can say never. And for such a low freq. all PWM methods are perfect. The problem allways occured only at relatively high modulating freq.

 

[wakibaki]

Cool, I think we're on the same page.

Back when I first made the suggestion about converting UADS to UADD you were arguing about the mathematical analysis of naturally sampled PWM, so I was thinking that if you can analyse UADS, then you can analyse UADD, then you only have to think about the difference between UADD and NADD.

Anyway, now I read that paper I don't have to think about it any more...

I am interested in PWM DACs.

An algorithm to convert Linear PCM to Linearised PWM can't be too difficult, it doesn't have to be done in realtime. Just a bit of geometry. If I straight-line connect the PCM samples on a graph and then find the x-coordinates of the intersections with the triangle that'll be good for a first approximation.

w

 

[Gyula]

Õ felállt, és bemondta, hogy "szuperpozíció"

Did you ask Kenyeres about this problem?

as long as the risetime of the sampled signal is insufficient to offset the OFF/ON transition 1 bit-time

When the signal's slew rate is insufficient to step at least one bit in every cycle, the quantising noise will not be undersampled and will not be spreaded in the spectra. So in that way you will hear the noise depending on the input signal. I think this is one of the particular reason for the high sample-rate audio D/A converters are made with large word-length.

 

[phase_accurate]

Look here:

http://v3.espacenet.com/textdoc?DB=EPODOC&IDX=US2007052478&F=0

and here:

http://v3.espacenet.com/textdoc?DB=EPODOC&IDX=US2006279357&F=0

regards

Charles

 

[inventor]

Distortion in PWM Class-D amplifiers

Hi to everyone in this thread,

I am a new member - please see:

http://www.diyaudio.com/forums/showthread.php?s=&threadid=128592

http://www.diyaudio.com/forums/showthread.php?s=&threadid=128594

I am trying to learn by reading the discussions in various threads. This thread on "Pulse Width Modulation" sounds interesting.

I cannot follow or understand fully the messages or information exchanged in this thread so far. I need some clarification regarding the following.

My understanding so far is:

An open-loop PWM Class-D amplifier inherently produces distortion (however small) owing to various causes including the pulse-width modulation process, imperfections in the power output stage etc. etc.

In a closed-loop PWM amplifier, negative feedback may eliminate some of the distortion mentioned above, but negative feedback itself gives rise to further distortion (that did not exist in the open-loop case and may be even worse than the distortion of the open-loop case).

My question is:

Until now, hasn't anybody been able to eliminate (or compansate for) all possible distortion modes in a closed-loop PWM amplifier via negative feedback (regardless of how you close the loops)?

If negative feedback cannot cure this situation, what can?

Thanks.

 

[wakibaki]

Hi inventor

I read your other posts. What is your background?

Highly successful class D implementations have proliferated in recent years with the improvement in materials technology and chipscale integration and wider understanding of sampling techniques. Indeed the technology is so mature that a leading producer (Tripath) has recently gone out of business. Try googling Sonic Impact T-amp.

Amplifiers of all classes are so highly developed that an amplifier easily exceeding the 'Hi-Fi' standards of yesteryear can readily be obtained at very low cost, and the choice is as much likely to be influenced by the purchaser's own particular 'enthusiasm' as any audibly perceptible difference, although this is hotly debated.

While amplifiers and sources remain objects of fascination for many audio enthusiasts, the principal remaining obstacle to perfect reproduction is the speakers.

Class D amplification is being actively developed by a number of manufacturers for reasons of economy and efficiency particularly with a view to distributed amplification.

As you have noted there are many sources of information on the web, and quite a lot of insight can be gained from datasheets and application notes. As with other classes of amplification, class D is a simple idea complicated in the implementation.

I'm sorry, I don't know of a book.

w

Some places to get up to speed:-

ESP

The Self Site

Historical perspective:-

The Audio Critic

 

[Pafi]

Hello inventor!

An open-loop PWM Class-D amplifier inherently produces distortion (however small) owing to various causes including the pulse-width modulation process, imperfections in the power output stage etc. etc.

In a closed-loop PWM amplifier, negative feedback may eliminate some of the distortion mentioned above, but negative feedback itself gives rise to further distortion (that did not exist in the open-loop case and may be even worse than the distortion of the open-loop case).

Yes, this is true, however the feedback-induced distortion can be higher then open-loop distortion in very rare cases! Basically feed-back distortion arises with significant amplitude at quite high modulation freq (or in other words: too low carrier freq). In the example of Omar Hawksford IMD is somewhere around -80...-90 dB (not clearly visible) with 17 and 20 kHz audio signal, and 705 kHz carrier freq.

Until now, hasn't anybody been able to eliminate (or compansate for) all possible distortion modes in a closed-loop PWM amplifier via negative feedback (regardless of how you close the loops)?

Zero distortion cannot be achieved by any kind of amplifiers, but all distortions can be decreased, so we can say: no, exact elimination haven't been done, but there are many possibility to reduce.

If negative feedback cannot cure this situation, what can?

NFB is OK for reducing "normal" distortion, just you have to avoid its extra distortion. Eg. by isolating carrier components from PWM input. It's described in first document linked by phase accurate!

 

[inventor]

Hi Wakibaki and Pafi,

Thank you for your comments and the web links from Wakibaki.

I am a retired academic with electrical engineering background mostly in electrical machines and their controls.

However, I am a "time-domain" (more specifically 'real-time') person rather than a "frequency-domain" person, and I am inclined more to "digital" things rather than "analog".

In a sense, I am looking for new challenges or yet-unsolved problems that I may give a go at finding some practical solutions if I can.

[ What I mean is not like in the commercial slogan "If anyone can, Cannon can!". Mine is: "If anyone cannot, I will try and see if I can!". ]

From reading the earlier discussions in this thread, I thought "distortion in Class-D PWM amplifiers" may be a subject or problem still in need of solutions or improvements.

Again from this thread, I thought "PCM to PWM conversion" may be another such subject.

What are other problems relating to Class-D amplifiers that people are trying to solve but have not been able to solve properly as yet?

Any suggestions?