Avoiding Oscillation - Do's and Don'ts?

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So driving a trace with a low source impedance or loading it with a low load impedance cuts oscillation issues by allowing much higher gain without oscillation issues.

I'm not too familiar with the nyquist criterion as such (only just finished 2nd year of EE), but I'm a little confused about where you take the frequency of interest to be, to determine impedance from stray capacitance. That being said, at a frequency of 10kHz a stray capacitance of 10pf would have an impedance of almost 16 million ohms so I see sort of see how this theorem plays out.

I'm guessing there's no easy way to calculate stray capacitances due to the electric field geometry present on PCB traces (unless they're literally sitting on top of one another), though I would think they'd be greatly reduced with a ground plane shunting everything (I'm sort of worried about the current return paths in this case...). Guess I'll just have to build the damn thing and find out! No damage done if it doesn't work... just have to spend another day etching and drilling. Designed by brute force

[R.G.]

I'm not too familiar with the nyquist criterion as such (only just finished 2nd year of EE),

You'll get to it if you ever get to take and analog controls course. That used to be in every EE curriculum, but I suspect by now it's not in many of them. The Nyquist Criterion is pretty simple once you think about it.

Let's ignore variable phase shifts for a moment, and only consider inverting and noninverting. An amplifier can have either nominally inverting or noninverting gain. If you feed back a fraction of the output to the input through some attenuation, then the amplifier can provide some of its own input. When the gain through the amplifier is (a) noninverting and (b) equal to or larger than the feedback attenuation, then a signal at the input of the amplifier not only goes through the amplifier and provides a bigger signal from the output than the original input signal. At that point, the original signal is no longer needed, and the amplifier will continue to amplify its own recirculating signal more and more. It oscillates. Since there is always noise present, you don't even need an original signal. As long as the loop gain from the amplifier input through the amplifier, and through the feedback network is greater than unity, a noninverting amplifier will always oscillate. Below unity loop gain, the effective gain is increased but it does not oscillate.

If we think of an inverting amplifier, the output is always in a direction opposite the input, so feedback will decrease the effective gain by subtracting the output signal from the input signal, giving a lower output.

Mostly. At this point we can no longer ignore non-integral phase shifts. A frequency response falloff/rise is **always** accompanied by a phase shift, because only reactances can cause frequency response changes, and they inherently introduce phase shifts to do it. The series and shunt capacitances and inductances in the signal path cause phase shifts and frequency response variations in the amplifier, and in the feedback path as well. So the gain of the amplifier will vary from its nominal value, and so will its phase shift. The feedback network can do this as well. We can (and every linear controls guy does) plot the magnitude of the gain versus the phase shift of the output with respect to the input signal.

This is what tells the tale and where the Nyquist Criterion comes in.

If we consider only resistive (non-phase shifting) feedback networks to simplify things, then we can check for stability easily enough. If the amplifier has a gain of less than unity at every frequency where its phase shift (plus any phase shift added in the feedback network, which we're ignoring) is less than 180 degrees, it will be stable under feedback. That's the simplest statement of the Nyquist Criterion.

Notice that noninverting amplifiers already have a phase shift of 0 or 360 degrees, so any stable feedback arrangements require the feedback network to attenuate so much that it reduces the loop gain (forward gain times feedback attenuation) to less than unity to be stable.

but I'm a little confused about where you take the frequency of interest to be, to determine impedance from stray capacitance. That being said, at a frequency of 10kHz a stray capacitance of 10pf would have an impedance of almost 16 million ohms so I see sort of see how this theorem plays out.

Aye, there's the rub. It's **all** frequencies. If there is a gain of above unity through the amplifier and feedback attenuation, then any frequency where the phase shift adds up to 360 degrees **will** oscillate. If your amplifier has useful gain out to 100HMz (like almost every garden variety NPN does these days), and it hits 360 degrees of shift anywhere in there, if there's loop gain above unity, it will oscillate. Period. So the frequency where it oscillates may be so high your oscilloscope can't see it. FETs complicate this by having useful gains well up into the hundreds of megahertz, so that 10pf cap may be an impedance of Xc = 1/(2*pi*10E-12*5E9) = 31.8 ohms at 500MHZ. Then 318 ohms at 50MHz, 3180 ohms at 5MHZ, 32k at 500kHz. Tubes have higher capacitances internally than solid state stuff, so they have worse high frequency gains, but they also have much higher impedances, especially on grids. It's easy to get oscillations that you can't easily see. The same thing can happen, by the way, on the low end. It's called "motorboating" there from the distinctive "put-put-put" sound.

I'm guessing there's no easy way to calculate stray capacitances due to the electric field geometry present on PCB traces (unless they're literally sitting on top of one another), though I would think they'd be greatly reduced with a ground plane shunting everything (I'm sort of worried about the current return paths in this case...).

The geometry gets complicated. But not as complicated as true point-to-point, where conductors are anywhere in the three-space volume. That's complicated. Ground planes do affect the capacitances, shunting the trace-to-trace stuff. But they add capacitance (and phase shift) to the forward gain of the amplifiers, so they can make a deliberately fed-back amplifier unstable by introducing more phase shift as well.

Guess I'll just have to build the damn thing and find out! No damage done if it doesn't work... just have to spend another day etching and drilling. Designed by brute force

Welcome to engineering.

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Thanks for the incredibly useful information! One last question (I promise )... Does gain-phase oscillation actually occur in stages without negative feedback? I know it's certainly possible to somehow get an additional 180 degrees of phase (some op-amp oscillators use RC networks to achieve this), but does it tend to cause problems in guitar amps?

[R.G.]

Thanks for the incredibly useful information!

You're welcome. I'm happy to confuse you any time you want.

Does gain-phase oscillation actually occur in stages without negative feedback? I know it's certainly possible to somehow get an additional 180 degrees of phase (some op-amp oscillators use RC networks to achieve this), but does it tend to cause problems in guitar amps?

Stages without intentional negative feedback?

Gain-phase oscillation lives in the crack between theory and practice in most cases. For instance, one way you can get gain-phase oscillation is for the power amp to share a ground wire with preamp stages. The current from the power amp - or worse: the speaker return - can cause a significant voltage drop in the resistance of a wire. Or if you run a grid wire too near the plates of the phase inverter or the output tubes where the hundreds of volts of signal on those places can couple through stray capacitance to the high impedance grid wire. It can bite you.

However, the number of stages gets into it. Generally, unless you make a many-time-constant feedback network, one or two gain stages don't have one of enough gain or enough phase shift internally at high frequencies to oscillate. For simple resistive feedback, you generally only run into oscillation with three or more gain stages, where each stage's high frequency rolloff contributes up to 90 degrees of shift.

One exception is in transformer coupled stages - like tube power amps - where the transformer all by itself gives you two out of the three time constants needed to get gain-phase oscillation. The power tube(s) give you a third, and you can get gain-phase oscillation in a tube output stage all by itself if its gain is too high or the feedback network lets too much output signal back through. This is one reason tube amps never get to the low distortion figures of solid state. They can't stand to have as much forward gain and as much feedback to correct the internal distortions without oscillating. This is even with tubes in general being more linear per amplifying device than transistors.

One way to look at it is that there are no amplifiers without feedback. There are only amplifiers where there is no deliberate feedback and the unintentional feedback paths have such a high attenuation that they can be ignored.

It's this plethora of unintentional feedback and crosstalk paths that make grounding and signal wire layout critical in some amps. The higher the gain, the more the unintentional feedback paths are important. Mesa Boogie, for one, has run into some problems with this.

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Okay I lied. I have still more questions!

How well does the the grounding strip between parallel signal traces actually work? I'm wondering because I have a strange design in mind, where each gain stage has it's own 'bus' so to speak, which can be routed to other buses, hence allowing the swapping of gain stages, or paralleling of stages. These buses would be parallel to each other, and depending on what signal you route where, you could end up with the input and output signal buses right next to each other (which I imagine wouldn't be too great). The routing is done before the coupling capacitor of each stage, so I'm considering swamping the whole routing apparatus with a ground plane on both sides of the board, due to the somewhat reduced effect capacitance has on circuit behaviour (as opposed to capacitance to ground at the grid).

I've included a little block diagram, and if anyone can follow it, I applaud you! The 'router' devices are really just jumper pins mounted on some veroboard , which is then mounted perpendicular to the signal buses (ie, vertically mounted like bus components in a computer). Two shielded wires then exit from these router modules to whatever gain device I want.

I guess what I'm asking is, can the ground ever become such a large distraction to the signal lines, that they simply won't interact with each other to a degree that causes oscillation? I'm also assuming no one has been insane enough to try something like this either...

[soundguruman]

It's really that the plate and grid are run side by side, to increase capacitance between the two.