[sdiy] Pulse Density Modulation, PDM instead of PWM (was Re: How to measure 1-bit DAC performance?)

Mon May 1 23:01:33 CEST 2017

Thanks Tom,

Very clever solution. I´ll try.

Vinicius Brazil

On Mon, May 1, 2017 at 2:01 PM, Tom Wiltshire <tom at electricdruid.net> wrote:

> It's not an original idea, but I haven't seen anything that describes
> using the PIC NCO like this. I saw that the DSPSynths JVS-01 chip claims to
> use "1 MHz 16-bit sigma-delta PDM, 66.9KHz PCM"
>
>         http://www.dspsynth.eu
>         http://dspsynth.eu/files/JVS-01%20manual%20v1.0.pdf
>
> So then I started wondering what exactly that was, and how it had been
> implemented, and whether it was actually any better than basic PWM (which
> some of the other chips use). They've done it on AVR, so the other question
> was if I could do it on a PIC, or if there was some special gizmo on those
> chips that helps.
>
> I found out what I could about Pulse Density Modulation, and found a
> couple of different algorithms for doing it. This is the complicated
> "keeping track of the errors" way:
>
>         http://wsprnet.org/drupal/node/3216//
>
> Then I found an alternative algorithm here:
>
>         https://hackaday.io/project/6356-delta-sigma-versus-pwm
>
> The executive summary version of this is you have an integrator to which
> you add the signal every clock. If the integrator overflows, the output
> goes high for a single clock.
>
> Reading about this it occurred to me that the NCO hardware is essentially
> exactly what they've done in software. Turns out it is. You can put the NCO
> in "Pulse Frequency Mode" (e.g. changing the increment changes the
> frequency of the pulses - pulse density modulation by another name) and
> then you simply stick your sample in as the increment value, left-aligned
> if you're not using the whole 20-bits.
>
> There are a couple of technical points. The earlier incarnations of the
> PIC NCO peripheral only allow you a 16-bit increment for a 20-bit
> accumulator. This is no good. The newer chips have an extra byte which
> gives you a full 20-bit increment. You need a maximum value sample (say
> 65535) to make the integrator overflow practically every single time -
> The second point is that you can set the length of the output pulses from
> a single clock upwards. I found that a single 16MHz clock was too short to
> do much due to rise time, and the net result was some distortion of the
> output waveform (a classic tube-like "squashing" actually - in other
> contacts, I'd probably be delighted..). Increasing the pulse length to 4 or
> 8 clocks and then shifting the increment down either 2 or 3 places fixed
> this problem at the cost of output frequency. But since 16MHz/8 is still
> 2MHz, that's miles above any frequency of interest and allows me to output
> waveforms and filter with a passive filter and still get a decent result.
>
> There are various advantages. One is simple speed. Whilst you might well
> run a PWM module with a clock of 16MHz, with 10-bit resolution, that gives
> you an output frequency of 15.625KHz. The worst-case for PWM is the
> midpoint value, since the filter spends longest charging and then
> discharging whilst trying to produce a smooth middle value. For PDM, the
> midpoint value is the *best* case, since the output is one pulse on, one
> pulse off at the clock frequency - so say 16MHz for our example. That's
> enormously easier to smooth than 15KHz! As the output value approaches the
> extremes, you'll get long strings of on or off filled by a brief blip of
> the opposite, but the brief blips will always be distributed rather than
> all together as they are for PWM. This is a massive advantage.
>
> It's a clever trick, and the NCO is dead handy for it. I shall probably be
> using it rather than PWM on future chip designs and projects.
>
> There's still some things I don't understand about it, like what happens
> if you output high resolution samples faster than the integrator can keep
> up. For example, if you use 16-bit samples, a value of 1 will take 65536
> clocks to overflow and produce a pulse. At 16MHz clock, that's 244Hz. If I
> send out another sample before that time has elapsed, what happens? Do I
> lose some resolution? Does it scramble the output? In practice it seems to
> work ok, so I'm betting you just lose resolution - it becomes impossible to
> differentiate two close sample values, because you don't allow the
> integrator time enough to settle accurately enough to see a single bit.
>
> Tom
>
>
> On 1 May 2017, at 15:58, Richie Burnett <rburnett at richieburnett.co.uk>
> wrote:
>
> > Tom, I'm intrigued by your mention of using the NCO module for pulse
> density modulation. Is this described in an app note somewhere or something
> you came up with yourself?
> >
> > -Richie,
> >
> > Sent from my Xperia SP on O2
> >
> > ---- Tom Wiltshire wrote ----
> >
> >> Thank very much to everyone that helped me with this.
> >>
> >> With your pointers, I was able to establish using the FFT function on
> my scope that 10-bit PWM at 31.25KHz gives me background hash at a level
> -41dB wrt my sine signal, and that 10-bit PDM pushes that down to -64dB.
> That's not bad for something that is just one IO pin on a PIC with a
> passive RC filter hanging off it.
> >>
> >> I'm now going to experiment to see if I can squeeze more resolution out
> of it too, and if that helps further.
> >>
> >> Tom
> >>
> >>
> >>
> >> On 25 Apr 2017, at 14:09, Tom Wiltshire <tom at electricdruid.net> wrote:
> >>
> >>> Hi All,
> >>>
> >>> I've been using the PWM output module on the PIC chips as a cheap DAC
> for years. It does this job reasonably well, all things considered. Whilst
> the quality and 10-bit resolution aren't great, it's cheap and convenient,
> and those are big pluses.
> >>>
> >>> However, I've been looking at using the NCO peripheral as a Pulse
> Density Modulated output instead. This would in theory produce a higher
> frequency output and allow a greater resolution.
> >>>
> >>> In order to determine if the results I can get out of it are genuinely
> an improvement, I need to be able to accurately measure the performance of
> both styles of "DAC".
> >>>
> >>> How would I do this?
> >>>
> >>> My current method is to send an incrementing count to the DAC and then
> have a look at the post-reconstruction filter output on a 'scope. How
> wiggly the line is is my measure of quality! Not very exact!
> >>>
> >>> I've got a digital oscilloscope, a multimeter, and a laptop. No other
> test equipment is available, unless I make it.
> >>>
> >>> Thanks,
> >>> Tom
> >>>
> >>>
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