Electronic – A switching boost converter biasing a tube preamp – saturation issue

Charge pumps driven from square waves have inherent apparent series resistance based on the frequency, and the size of the pump capacitor. You expect the output voltage to drop as it is loaded with decreasing resistance.

However, your table shows the opposite. Either you measured something wrong or wrote down the data wrong, or there is something else going on here. Keep in mind that in this case you have a feedback loop that adjusts the PWM duty cycle and possibly the period to keep the 11.9 V output regulated. This may be causing various non-obvious affects on the charge pump output. The pulses are there for another purpose and the charge pump is coming along for the ride.

This probably doesn't matter much if you only want a few mA, like the negative supply of a opamp. Make sure to filter this well before using it to power a opamp. I'd put a ferrite chip inductor followed by a 20 µF or so ceramic cap to ground before the opamp power pin at least, maybe two of those filters in series. The opamp will have some supply rejection capability, but that won't work well at high frequencies. You need to filter out enough of the high frequency noise from the charge pump supply so that the active circuit in the opamp can handle the rest.

Added:

You are now measuring the negative supply voltage with a fixed 1 kΩ load on it, while varying the load on the positive supply. The relationship you measured makes sense. By increasing the load on the positive supply, the feedback mechanism increases the duty cycle and/or frequency of the switching pulses. This lowers the effective resitance of the charge pump negative supply. This is all a consequence of the pulses being produced for the purpose of regulating the positive supply, which is not necessarily optimal for regulating the negative supply. The harder the switcher has to work to maintain the positive supply, the better job it does of driving the negative supply too.

and R3 is 270k (works a lot better for some reason).

This speaks volumes.

Filaments: Using 5V on 6.3Vrms heaters isn't impossible. You'll produce less heat, which means your cathode is more likely to pit and degrade. However, it shouldn't be noticeable given the low anode voltage. Thus your tube will likely live as long as a normal tube would. You may find that is sounds more distorted than if you heated it properly.

Power: USB 5V charger for filaments - sound like a bad idea, mostly because you're much more likely to get ground loops from using two discrete chargers. So using a linear regulator would be the easiest solution. The only other solution being to use a buck circuit to take 9V down to 6.3Vdc -> 5Vdc (which ever you happen to want to use). This is about the time where someone points out that they're using a 9V battery and that means that you won't get ground loops. Except that every foot pedal design I've seen (and I've seen many) have a 9V wall Jack and a switch so that they don't need to have a battery. So when you have the wall wart plugged in, you'll likely hear ground loop hum. When you're on battery, you wouldn't hear it (assuming that you were in fact using the 5V USB charger).

If you want my honest opinion, which you're getting anyways, don't limit this design to a battery. There's a reason we don't use these tubes with batteries (they do have battery tubes, these are not those) because they take so much power to heat properly. Take the time to find a good high power 9V wall-wart (think 1.5A-2A). Create a buck circuit to drive the heaters at 6.3Vdc (heck, go nuts and drive them at 6.3Vrms some people swear that AC sine wave heating sounds best). And while you're at it, go read up on tube amp designs like from this UK website.