While looking for the reason why the filter output jumps frantically between +/- max when the cutoff is low or the input is close to zero when turning up distortion (spoiler: it's the biasing capacitor), I realised that I should have a closer look at what the output biasing/centering capacitor is actually doing to the filter's response.
The cap is there to make sure the output is centered around 0, i.e. filter out any DC component (AC coupling the signal). The higher the capacitor, the longer the filter takes to change to 0V after an abrupt (DC) change. In the case of the jumping described above, I would like the change to settle as fast as possible, which means replacing the current 1uF cap with a smaller one, but what would that do to the output?
Looking online, it seems that the most common value of cap is 10uF. The Juno synths use 1uF. The cap in combination with a resistor/resistance creates a high pass filter with the cutoff frequency f=1/(2*PI*C*R). In my case, I have an 82k resistor immediately following the cap so I assume that this is R in the formula (the JP8 uses 100k and Juno 6 56k + a 20k trimmer).
The red line in the first plot here shows what our current 1uF cap does.
0.47uF
1uF 3dB
The 470uF cap clearly moves the cutoff frequency higher. Its -3dB point is at approximately 2.9Hz, compared to the 1.4Hz of the 1uFthe calculated values are 1.94Hz and 4.2Hz so 82k is at least close to the "real" resistance).
0.47uF at 20Hz
The human hearing is usually considered incapable of hearing frequencies of less than 20Hz. At this point the 0.47uF cap attenuates the signal by 90mdB. This in itself is not a lot, but it means that any sub-audible, ground shaking frequencies are filtered out. This may not be a problem as the equipment later in the chain may also have similar filtering, but it is something to think about.
10uF
In comparison, the 10uF cap gives a cutoff of less than 0.2Hz which is probably the reason why it's the more common choice.
0.047uF
I've seen some designs use a 47nF cap. This gives a -3dB cutoff at 370Hz which is a complete no-go combined with my 82k resistor.
NB: R_abc is 10k instead of the 18k found in the JOVE circuit.
Resonance
I think the resonance looks quite good
Here are some quick measurements of the resonance voltages using the JOVE resonance circuit. This seems to give approxmiately unity gain for HP/LP and self resonance (could perhaps be a bit better).
Output of trimmer 1: -2.83V
Output of trimmer 2: -10.83V
Reso CV: 0V
Output CV mixer: 2.9V
Base voltage: -52mV
Reso CV: 5V
Output CV mixer: 7.94V
Base voltage: -10mV
Cutoff
The cutoff range seems too limited, but with this, a 50Hz wave has an amplitude of approx 130mVpp. At max, the HP filter lets a 1.5kHz wave through with 180mVpp. An 8k wave has approx 5Vpp amplitude.
Cutoff trimmer 1: -8.4V
Cutoff CV 0:
Output CV mixer: 998mV
Base voltage: 100mV
Cutoff CV 5:
Output CV mixer: -1.25V
Base voltage: -100mV
Polarities
LP output, Cell 1: inverted
BP output, Cell 1: normal
HP output, Cell 1: inverted
Amplitudes
HLP Max: +/-5.25V
BP Max: +/-3.5V
HP Max: +/-5.25V
High frequency oscillations
The high frequency oscillations seen previously are completely gone (though I have not tested with higher CV), perhaps they were caused by the erroneous 3p filter cap
To get a feel of how my filter is performing, I took a closer look at the Moog Little Phatty, and how its output looks on the scope.
Waveforms
The LP does not have discrete selectable waveforms. Instead, it has a continously changeable waveform that starts as a triangle wave, goes through saw and sqare and then ends up as a pulse wave.
This is what it looks like when turning:
Here are the four variations that most closely resembles the four mentioned waveforms:
Pulse wave. Notice how it is no longer centered around 0V - instead, the TOP is at 0V.
There are two things to notice:
First of all, the wave is not straight, it curves slightly. The triangle wave is actually on its way to becoming a sine wave, and the saw wave is almost like a half sine with an abrupt but not instant fall to the bottom. These photos are taken at a rather high frequency, but the effect becomes even more pronounced as the frequency drops. This means that the perceived level of the triangle wave is significantly lower than that of the other waveforms, just like with a sine wave. It also probably introduces different overtones than the waveforms from a 'cleaner' waveshaper does, which may greatly affect the character of the synth. Interesting!
Second, the wave is not always centered around 0V. This is something I've wondered a lot about after looking at various service manuals - a lot of them use a capacitor to center the wave, which means that waves with uneven energy levels above and below 0V would end up not being sentered. This is clearly the case with the LP - look at the photo of the pulse wave above, it has its TOP at 0V. This is fine and inaudible as long as the output does not start clipping, and mixing multiple oscillators that are not synced would probably reduce the offset. Still, it's interesting to see that this is actually done in professional instruments. I worked hard on my waveshaper to prevent this, perhaps it's unnecessary.
Resonance and self oscillation amplitude
Here is a video of what happens when I turn on resonance with the cutoff set to max. I then gradually reduce the cutoff to introduce self oscillation:
As you can see, the amplitude is quickly reduced to less than 50%. Then, when adding self oscillation, the self oscillation has an amplitude closer to (but less than) the original signal. It never overpowers the original:
Original wave, no resonance
Full resonance and filter fully open
Cutoff turned down, filter is self oscillating
Resonance pot response
In my last post I explained how I found that the resonance CV for the juno filter definitely not was exponential, but not sure if reverse exponential (using a reverse log pot) or linear was the best. Here is how the LP responds:
All pics are taken with the cutoff slightly higher than middle. Self resonance becomes visible about when the pot pointing to the right. This is independent of cutoff, and is fairly similar to the linear pot in my Juno VCF circuit.
Oscillator mixing
The little phatty has two oscillators. I would expect mixing them to simply sum them up, but it seems the total is less than the sum. I did the summing by running two similar waveforms on both oscillators and synching oscillator 1 and 2. The sum reached it's peak with oscillator 1 at 100% and oscillator 2 at 50%, after this further summing only changed the shape of the output slightly. It seems to me that the synth does some soft clipping or similar, which becomes more apparent when using overload.
Overload
Overload increases the amplitude of the signal. At first it appeared that it only doubled the amplitude:
But when lowering the cutoff and then turning on overload, we see that the wave is heavily distorted:
Switching to a different waveform shows this even more. It seems that the actual amplification is much more than doubled, but that the Little Phatty uses something like a compander/limiter circuit to soft clip the output (or maybe not - it starts stretching long before the edges reach the peak) - see how the middle of the wave is much more amplified than the top/bottom:
