In the early days of the personal computer (PC’s in the early 80s), sound capabilities were mostly limited to annoying beeps. Often produced by a minuscule piezo crystal ‘speaker’.
Unlike a magnet/coil driven speaker cones that can move freely up and down, the piezo crystal ‘speaker’ only permits two states: ‘UP’ or ‘DOWN’. When switched ON/OF at audiorate it can produce audible sounds…but only square or pulse wave.
At some point someone tried to abuse the PC speaker beyond its intended use, and tried to implement PWM (Pulse Width Modulation). With (limited) succes. Suddenly the PC could produce (crude) complex signals like music and speech. Way beyond the simple beeps.
So…how does that work?
PWM is a pretty common technique in synthesis. As the name Pulse Width Modulation suggests it is all about modulating (changing/controlling) the pulsewidth (or duty cycle) of a pulse wave. Generally the duty cycle is the ratio between ON and OFF for a pulsewave. For a square wave this is 50/50, 50%. The width is related to the harmonic content. Generally, simplified, every 100/duty cycle harmonic is skipped. For a square this means every 100/50 harmonic is skipped, so only odds remain (it 1/rank amplitude). This is mostly how PWM is uses in synthesis.
But as with many synthesis techniques…things change when the modulation is applied at audiorate.
I guess we all know basic Pulse Code Modulation (PCM) ‘sampling’. At some sampling rate/frequency, the amplitude of a signal is sampled and stored as a stream of values, representing the amplitudes of the signal. The original signal can be reproduced using these stored values.
In PWM the amplitude of the signal is also ‘sampled’, but instead of storing the amplitude as a number, the value is translated to a pulse of a corresponding width and stored as such in a bitstream. Basically -1 to 1 is represented by 1 to 50% pulsewidth. To represent these pulses of various widths, you obviously need more then 1 bit per sample. A ‘sample’ might need hundreds of bits to be sufficiently accurate. The ‘sampling rate’ for PWM should generally be way higher than the Nyquist frequency needed for PCM.
Sending these pulse trains / bit streams to an audio output/speaker somehow magically reproduces the original signal.
But…sharp edges and sudden jumps in amplitude in a signal results in all sorts of high frequency artefacts (think saw, square/pulse, wavefolding, oscillator sync). So, generally a steep Lowpass filter is added to reduce/eliminated these high frequency artifacts.
So…can we see this in action in VCV Rack?
Well, yes, sort of…
Basically just feed any signal into the PWM modulation input of a PWM enabled VCO. Add a steep Lowpass filter. And…well that’s basically it.
- For the source signal I would suggest 2x FM operators, where one modulates phase (or frequency) of the other so you can easily generate complex signals.
- For the PWM VCO I would suggest Venom VCO Unit. It supports audiorate PWM and up to 32x oversampling.
- For the Lowpass filter I would suggest Bogaudio VCF. It supports steep filtercurves up to 12-poles.
So…some experiments. Assuming the suggested VCO’s and VCF.
- Connect a source (e.g. a VCO or any other signal generator) to the PWM input of the PWM VCO.
- Set PWM VCO oversampling to at least 4x
- Set PWM VCO frequency to the lower limit (C4 261.63)
- Connect a VCA and a precision delay (suggestion: Sckitam WaveguideDelay) at the outputs of both VCO’s to control their (relative) amplitude levels and phase (so you can match amplitude and phase of the original wave/signal and the PWM).
- Connect the output of source VCO/Signal and PWM VCO to a VCV Scope.
- Connect the output of source VCO/Signal and PWM VCO to a Bogaudio ANALYZER-XL
- Connect the output of source VCO/Signal and PWM VCO to a Bogaudio VCF for later use
- WARNING: The PWM VCO output at low ‘sample rates’ (PWM VCO frequency) are pulses at max amplitude. Also at higher, but not high enough, frequencies, amplitudes may explode towards maximum. Also screeching high amplitude, high frequencies may occur. So START AT LOW LEVELS AND PROTECT YOUR EARS AND GEAR
- So…close the PWM VCO’s VCA, so that the initial pulsewaves are not too loud (e.g. -24dB).
Experiment 1: from PWM encoded pulsetrain/bitstream to the original signal
- Vary the source signal (e.g. change waveshape/FM/PM amounts and frequency). You should see the pulses change width on the scope.
- Now turn up the PWM VCO frequency and listen to the PWM VCO output and and watch the scope and the analyzer.
- You will notice that first, you get the impression that pitch rises. The frequency analyzer shows loads of high frequency content shifting toward the end of the audiorange.
- The scope goes crazy and fills up with high frequency pulses until all lines in the resolution are filled.
- But, when nearing the end of the audible range (for many somewhere between 10Khz and 15Khz) something strange happens. The high frequencies go out of audible range. The scope and the audible audio slowly reveals…the source wave/signal. Even the spectrum in the analyzer matches up.
- Now, it is temporary relatively safe to turn up the amplitude of the PWM VCO, match amplitudes and phases in the scope and analyzer and play with the source signal parameters (slowly, carefully, sudden high amplitudes/frequencies may occur…)
Experiment 2: Creating and correcting/filtering artifacts using a steep Lowpass filter
- Lower the amplitude of the PWM VCO output (VCA)
- Now slowly turn down the frequency of the PWM VCO, until (high frequency) artifacts appear.
- Now listen to the Lowpass filter output and connect that output to scope and frequency analyzer. Slowly close the filter, until the artifacts dissapear. We are back to a (full or close) match.
- This works ever less well until the PWM VCO frequency is too low to accurately represent the source wave at all. No amount of Lowpass filtering will help there.
I noticed that some odd behaviour can occur when lowering the source signals frequency by some octaves. Not sure what happens there.
I didn’t feel like making a video on this subject. Too many aspects to cover. Would be more of a tutorial. I might do that some other time.
Here’s a random save state to experiment with and build upon:
Kwurqx - PWM ADC DAC.vcv (2.9 KB)
I guess these PWM AD/DA concepts and quirks could be hacked into a VCV Rack plugin/module (oscillator/effect) so the various PWM artifacts can be more easily exploited.