Determining frequencey roll-off imposed by PI capacitor

[anson]

Hey guys,

I've got a question about the small-value capacitor that some guitar amp manufacturers put in between the push-pull out put stages at or around the phase inverter. Look at the phase inverter on this Sunn Model T schematic and you'll see what I mean. It's 270 pF in value here:


http://www.schematicheaven.com/newamps/sunn_model_t.pdf


AFAIK, the larger the value of that capacitor is, the more effective it is in rolling off high frequencies at that point in the signal path, and typically this is done to eliminate parasitic oscillations.

My question is, how can one calculate the roll-off frequency that exists because of that capacitor? It seems intuitive that greater capacitance will lead to greater high frequency roll-off, but at what rate? Does this equation apply to this situation?:

f = 1/(2*pi*R*C)

I've used this equation with success for figuring out frequency roll-offs when dealing with grid resistors, coupling capacitors, and output impedances, but I don't know how to apply it to the situation where a capacitor bridges tewo plate resistors in a phase inverter.

Thanks for any help/guidance you can provide. I know this is probably the nerdiest of nerdy questions dealing with amps.


Anson

[Steve Conner]

I'd take R in the formula to be twice the output impedance of a PI triode, which is roughly the plate resistance of a 12AX7 in parallel with the plate load resistor, so about 50k or so.

Of course the actual result is changed greatly by the NFB loop wrapped round everything, and calculating what that does is an advanced topic. As you decrease the capacitor value with NFB present, the amp's response will start to peak at high frequencies, until it finally bursts into the high-frequency oscillations (Nyquist, not parasitic, if you want to be really nerdy) that the capacitor is there to prevent.

The frequency of peaking/oscillation depends on a lot of things including the design of the OT. In one amp I worked on, it was around 100kHz, well above the audio range, and took about 150pF to stop it.

[Bruce / Mission Amps]

Any value capacitor will roll highs off and any AC above that to a point.
That's why you see 47pF to 470pF used there.
But, a small value cap like 47pF to 100pF will start to "not be able to" roll much signal off below it's Xc frequency point.
In other words, the cap has a low frequency limit and will look like a very high impedance at low freqs but very low impedance at higher freqs.
A larger value will still effect all the highs because it still has very low Xc impedance at high freqs but now it effects the lower freqs too.... right down to the point where at around .02uF to .1uF the cap is killing almost all the audio freqs.
This is how a cross cut master volume works.... it is a modified Hi Cut control using a larger value capacitor that will kill all the freqs, turning it into a master volume control.
Using Steve's comment, at around 38K the -3dB point of that 270pF circuit would be about 15,500Hz.
If there is an oscillation in the preamp or PI, the 270pF cap would always be feeding a fairly strong NFB signal at +15KHz and above into the opposite grid of the power tubes, thus limiting the ability of the PA to amplify those oscillations at or above that frequency.
Side note:
I can't hear much above +14KHz anymore myself but when tweaking up a new amp, my son use to come down to the shop and say... "what's the whining squealing sound"... I only heard hiss.... only to find out the PA was oscillating at 16-18KHz.... obvious on my scope and the PA was making like 5 or 6 watts too.
Those snubbers would have stopped a lot of that.

[jrfrond]

OK, so I use a decidely more low-tech approach to this (somewhat).

I will monitor the PI on my scope for oscillation, to determine whether or not a "snubber" cap is actually required. I will even attempt to cajol it into oscillation by using high-frequency bursts, sweeps, etc. to see if it will oscillate at a particular resonant frequency. If no cap is need, I simply will not use one, or else use the smallest value possible, usually between 47-100pF. Nothing bigger than that, or the long-gradual rolloff starts to reach into the upper audio frequencies. Granted, the frequencies are not actually heard, but intangible harmonics are part and parcel of every guitar amp. A lot of an amp's character is determine by intermodulation.

[pdf64]

I wonder if there isn't another complicating factor with this arrangement, in that at high frequencies, the voltage or current source we are considering is not only getting shorted to ground via the source impedance of the other device of the pair, but additionally a mirror image signal is being mixed with it from that device.
I'm thinking that this might cause the roll off to be steeper than the regular -6dB/octave that f = 1/(2*pi*R*C) would normally give. I'll have to try to see if I can get some test results to dis/prove this theory, as the maths is tricky, and college was a long time ago. Peter.

[Steve Conner]

Well, if we assume both sides of the PI are giving equal and opposite signals, and assume the capacitor to be two capacitors, each twice the value, in series, then there will be no signal at the midpoint of the two capacitors. Therefore, we could ground that midpoint without changing the operation of the circuit.

This proves that hanging a capacitor of value "C" between the PI plates is no different than placing 2C from each plate to ground, and this is why I said to use twice the value of R in the formula. I could have said to double C instead: as long as you double something, you get the right answer.

[Enzo]

I'll just make my whiskey a double, thanks. Seems like the right answer to me.

[anson]

The description that you gave Steve seems pretty solid. It would have been 100 years before I would have looked at the situation that way! I'm curious about "Nyquist" oscillations. What's that?


I've had the best success using the capacitor under discussion just where the grid stoppers are soldered to the output tubes, on the PI side of the grid stoppers. If I take the same capacitor and bridge the PI plates somewhere else in the chassis, physically closer to the PI, I'd get shrill squeeling. Then when I use a larger cap, the squeeling goes away, but the frequency response sounds like it suffers because of it. I'm very happy with the results I get with a 150 pf mica cap next to the grid stoppers. Thanks for all the input, most informative!!

Anson

[Steve Conner]

Nyquist oscillations is an informal term used in audio amp design. It refers to instability in the global feedback loop, as opposed to parasitic oscillations which usually just happen in one single tube. (Or transistor: solid-state amps suffer from them just the same.)

It's an important distinction, since they are two independent kinds of instability. Grid stopper resistors stop parasitic oscillations, but don't really touch Nyquist oscillation: the capacitor across the PI plates is what stops that.

The reason for the name is that the feedback loop can be analyzed just like any other servomechanism, so Nyquist's stability criterion can be used to determine whether it'll oscillate or not.

http://en.wikipedia.org/wiki/Stability_criterion

In practice, with tube amps at least, the slide rule stays in the drawer and everyone just does what jrfrond did: find the right value of compensating capacitor by trial and error. (A square wave is another good test signal to check for stability.)

Note that if you're designing an amp to take multiple tube types, the gain of the PI tube and power tubes affects stability, since they're inside the NFB loop. You need to make the cap big enough for stability with the highest gain tubes, which might be a 12AX7 in the PI and 6550s, say. If you prototyped it with a 12AU7 and 6V6s, you could get a nasty surprise.