PWM - natural vs uniform sampling of audio signals

[Tony]

Hello all,

All the literature I've been able to find seems to indicate that generating PWM
by natural sampling (analog input signal compared to saw or triangle wave)
produces lower distortion than uniform sampling (sample/hold the input first).
But all those same sources also use the case of "single-ended" PWM (where one
edge is fixed, and the other is modulated by the signal).

Now it seems quite logical to me that single ended uniform sampling will produce
even order distortion products, if only because the effective pulse position
varies with the signal, and natural sampling seems to partially correct this
problem.

BUT in the real world, all the natural AND uniform sampled PWM generators I have
found effectively compare the signal to the reference on both the rising and
falling edges of a triangle wave, so the pulse position does not shift with
signal. And under these conditions, it seems to me that uniform sampling should
be better.

I've googled a lot for enlightenment on this issue, but to no avail.

Can anyone set me straight?

Tony (remove the "_" to reply by email)

 

[Ban]

Hello all,

All the literature I've been able to find seems to indicate that
generating PWM by natural sampling (analog input signal compared to
saw or triangle wave) produces lower distortion than uniform sampling
(sample/hold the input first). But all those same sources also use
the case of "single-ended" PWM (where one edge is fixed, and the
other is modulated by the signal).

Now it seems quite logical to me that single ended uniform sampling
will produce even order distortion products, if only because the
effective pulse position varies with the signal, and natural sampling
seems to partially correct this problem.

BUT in the real world, all the natural AND uniform sampled PWM
generators I have found effectively compare the signal to the
reference on both the rising and falling edges of a triangle wave, so
the pulse position does not shift with signal. And under these
conditions, it seems to me that uniform sampling should be better.

I've googled a lot for enlightenment on this issue, but to no avail.

Can anyone set me straight?

Tony,
maybe it appeals to the mind but I do not think there is much difference if
the squarewave is centered or not around the sample points, with the
sampling frequency being high enough.
A dual-sided modulation allows only *half* the sampling frequency, the
question is if this is not of disadvantage. With a good 3rd order
noiseshaper you gain at least 20dB of S/N in the baseband per doubling of
the sample rate, whereas a single sided modulation will certainly not loose
that much compared to the dual sided.
If you think you do not need a sample/hold for the triangle modulation, you
are mistaken. Aliasing will be much worse and creates not a harmonic
distortion but mirrored artifacts in the baseband that are degrading the
performance.
Nowadays for better performance a sigma-delta converting scheme is used,
which reduces distortion much more than even the best pure PWM is able to
do. In this case there is a delayed feedback of several samples, so that the
question of double sided modulation becomes even less important.
I'm working on a digital amp which uses exactly these ingredients and after
a lot of research I gave up on analog triangle modulators, because it
requires much better shielding and decoupling than a A/D-conversion done in
the "dead-time", where no high-current switching occurs.

 

[Tony]

Tony,
maybe it appeals to the mind but I do not think there is much difference if
the squarewave is centered or not around the sample points, with the
sampling frequency being high enough.
A dual-sided modulation allows only *half* the sampling frequency, the
question is if this is not of disadvantage.

Could you explain why this is so?

With a good 3rd order
noiseshaper you gain at least 20dB of S/N in the baseband per doubling of
the sample rate, whereas a single sided modulation will certainly not loose
that much compared to the dual sided.
If you think you do not need a sample/hold for the triangle modulation, you
are mistaken.

My intuition told me that I DO need a S/H, but this produces "uniform sampling",
which many references claim to be inferior to "natural sampling" (ie, no S/H).

Aliasing will be much worse and creates not a harmonic
distortion but mirrored artifacts in the baseband that are degrading the
performance.
Nowadays for better performance a sigma-delta converting scheme is used,
which reduces distortion much more than even the best pure PWM is able to
do. In this case there is a delayed feedback of several samples, so that the
question of double sided modulation becomes even less important.
I'm working on a digital amp which uses exactly these ingredients and after
a lot of research I gave up on analog triangle modulators, because it
requires much better shielding and decoupling than a A/D-conversion done in
the "dead-time", where no high-current switching occurs.

I would like to explore a multi-order delta modulator (although AFAIK the
"sigma" part would not be needed). Can you suggest any good references for this,
and especially multi-order noise shapers as referred to above?

Tony (remove the "_" to reply by email)

 

[Ban]

Could you explain why this is so?

The thing is I use a counter, which limits the resolution. Obviously an
up/down counter has to run at double the frequency, to produce the same
resolution, because the on duration of the switch is always of even numbers
of count. But also the triangle wave will have to slew double and the jitter
of the comparator is higher etc. this is again the limiting factor in an
analog modulator.

My intuition told me that I DO need a S/H, but this produces "uniform
sampling", which many references claim to be inferior to "natural
sampling" (ie, no S/H).

Well, then you need a lot of filtering on the O/P

I would like to explore a multi-order delta modulator (although AFAIK
the "sigma" part would not be needed). Can you suggest any good
references for this, and especially multi-order noise shapers as
referred to above?

J.C.Candy; Use of Double Integration in Sigma Delta Modulation IEEE1985
J.C.Candy;Oversampling DS-Converters IEEE1992
K.Chao; A High Order Topology...IEEE1990
Oppenheim/Schafer; Discrete-Time Signal Processing; chapter 4.9
You'll like this one:
http://www.e-insite.net/ednmag/archives/1995/042795/09df3.htm
JAES_V52_3_PG166.pdf (is copyrighted) if you do not find it tell me via PM
This is what I have here at hand, but there is little literature to find.

 

[litw]

I once tried a design with a first order sigma-delta but without any s/h
so the result frequency was only limited by the delay in the circuit.
Such high freq will be not too good to the inductor i guess. But from
the simulation i found the harmonic distortion is lower than the
conventional sawtooth wave approach.
Those may not be relavent to what you are discussing. just my experiences.

litw