Phase Shift Oscillator question

[NPrescott]

I've been trying to wrap my head around the operation of phase shift oscillators recently and I think I've mostly got it. I was wondering though, reading the explanation by Aiken Amps (here ) - under the heading of 'design modifications for tremolo oscillator' it mentions:

The ideal method of adjusting the frequency is to use a triple pot, to control all three phase shift sections. This is not always practical, so only one section is usually adjusted. It is usually best to adjust the last phase shift section, rather than the first one after the amplifier, as it will usually afford a wider range of control.

My question is - why? What is it that affords the last phase shift section a wider range of control compared to the other?

This is the circuit we're discussing, but I would think it is the same for any phase shift oscillator.


I had intended to mock this up in the simulator but I'm pretty rusty with it and it's not working as I'd thought.

[PRR]

I'm not sure Aiken's statement is fully qualified. I suspect it depends which end has more leeway: output impedance or input impedance. With tubes, the naked grid can stand *huge* resistance, so we might favor 2Meg-5Meg pot at R3.

> it's not working

Self-oscillators take time to start. They start by random noise building-up maybe 1% per cycle until limiting. With low-freq oscillators, this can take many seconds. With perfect noiseless devices (SPICE) they may never start. Several of the better Fender etc LFOs use kick-start techniques to bang a large first-cycle so as the thing will start wobbling pretty soon, not a few bars late.

I've usually had to rig my SPICE to hold the grid or cathode several volts for the first instant of the run then disconnect the kicker after a microsecond or so.

Self-limiting oscillator action is violent, abrupt changes of voltage/current, and SPICE will often fall off the rails trying to plot this in 13-place precision rather than just plowing through roughly as a sensible person would do.

[NPrescott]

Hmm, that seems to be what I'm reading Paul. I may just wait and breadboard it, I remember the headaches that SPICE tends to give me.

I was scouring everywhere to find some explanation for that quote - if it's particular to that instance I feel a bit better. I'll have to think on it, so thanks for that.

[R.G.]

The phase-shift sections load each other. If you put a buffer after each one, it would act more ideally. As is, changing the resistor (in this circuit) affects the circuit before and after it. For the one followed by the grid, it's as Paul said: the grid has a very high input impedance. That may have been what Randall was driving at.

In the ideal phase shift oscillator, all three sections would always be equal. Hence a three-gang pot for widest range. A two-gang is better than one, but one works.

What's at work is that a "perfect" PSO would take forever to start. It has to have excess gain to start, and ideally the gain would be backed off as it got to full amplitude. The simple circuits in guitar amps with one tube don't have the complexity for variable gain, so they're given excess gain and live with the waveform distortion that happens with excess gain.

The gain is important, because a PSO (well, OK, any oscillator) will not oscillate below the amount of gain that equals the attenuation of the feedback path. In the classical PSO, that works out to be ...um? 27 or 29. Have to look that up. It's been 40 years since that class.  Adding loading to a phase shift section by mismatching them equals needing more gain to start and run.

[NPrescott]

Man, sometimes I could just kick myself. I spent quite a bit of time trying to answer my own question before I posted here but I go to look up a few things you mention and I suddenly start finding the answers I was looking for.

The phase-shift sections load each other.

This phrase in particular has led me to what appears to be an interesting resource for anyone else interested:

Op Amps Are For Everyone, by Ron Mancini at Texas Instruments

Thanks for the help R.G.

[kingswayguitar]

indeed. i found that pdf very useful in the past year!

[PRR]

> The simple circuits in guitar amps with one tube don't have the complexity for variable gain, so they're given excess gain and live with the waveform distortion that happens with excess gain.

They must start with very-significant excess gain.

But as they come to full amplitude, the grid tries to swing positive of cathode. It can't, instead the grid charges-up negative. This cuts average current. Lower current is lower gain. True "variable gain". Not just "gain-reduction" by clipping. Self-control of gain.

BJTs can do this but much less effectively because of low input Z and heavy bias loading. Opamps won't.

If well-designed (or tinkered), gain will be down to 28 (or 30?) when plate-clipping is around 3%, stabilizing at 27 (or 29?) with acceptable waveform. There's usually more low-pass on the way to whatever it is driving, so the final wave is "smooth" even if not lowest-THD.

Same trick with all tube and many JFET RF oscillators. Tubes often run a 22K or 47K grid resistor. Gain is rigged so about 10V of peak RF and 10V of negative bias happens. Gain gives about 100V of RF in the plate (if plate-loaded); OTOH 10V of grid-cathode RF will modulate another tube (or the same tube) against a signal for frequency conversion.

BTW, if the resistors are "tapered", 100K 200K 400K, the minimum gain is lower. (This still assumes the amplifier source and input impedances don't get in the way.)

BTW: this combination of gentle gain control and downright nonlinearity seems to be essential for stability in many oscillators. The H-P lamp trick does not work (it over and undershoots, never constant output) if the amplifier is VERY linear, and <5% 2nd harmonic distortion in the amp will settle it right down.

> take forever to start

In a real-world oscillator, too-closely trimmed, the start-up is substantial. Say 1% excess gain (gain is 1.01 times the 1/27 loss of the network). Say the only kick-start is thermal hiss. This might amount to 1 microvolt. To get from 1uV to say 1V, gain of 1.01 must be applied 1388 times. The start-up is 1388 cycles of the design frequency. In an LFO this may be 10Hz, 1/10 seconds. So the start-up takes 139 seconds or 2 minutes. (At 1MHz it is very much less!) There is additional randomness because we won't get a 1uV noise wobble at any given instant. Until oscillation rises well above hiss we may get conflicting noise peaks tending to put it on another phase.

So aside from the practical difficulty of hitting gain=1.01, in LFOs we probably can't live with a 2 minute start-up. 10%-40% excess gain seems to be common. 12AX7 will give gain of nearly 50, need gain of 27, gain is 1.8 times what we require for an ideal network and perhaps 1.4 times a 1-pot LFO set to an extreme. However we occasionally find 12AX7 which just do not work, apparently due to marginally low gain. Also if you forget (or undersize) the cathode cap it never works.

However if we "kick" the network with something close to its normal voltage swing, it comes into full output quickly and remarkably smoothly. The hi-end Fender kick is about 20V taken from the power stage bias supply into one of the C-R-C-R-C-R network's resistors. Grounding that kills the oscillation. Un-grounding throws 20V into one node, which propagates through the network, and gets the thing going strong. When correctly sized, the first LFO peak is within 10% of the final value.