Compensation and NFB
SOME NOTES ON COMPENSATION FOR AN AMPLIFIER WITH NFB APPLIED:
When one speaks of amplifier compensation it means the tailoring of open-loop gain and phase characteristics in order to assure that the amp is stable when the loop is closed. A general principle of compensation is that you make the amplifier more stable only by sacrificing open-loop gain. Keep this in mind.
So why do we need to compensate in the first place? Well, put simply, it’s because the loop gain is still more than 1 (there’s still some amplification going on) by the time the phase shifts approach 180 degrees. Obviously, with that much phase shift, the negative feedback is turned into POSITIVE feedback, and the amp oscillates. With tube amps, a little oscillation isn’t too harmful and usually easy to detect, but try that with a MOSFET output stage and they will destroy themselves in short order–and at a frequency you probably can’t see on your scope!
Compensating the amp, and preventing this oscillation, is to make sure that the closed-loop gain falls below unity before enough phase shift “piles up” and number more than 180 degrees. If you’ve got that, you’ve got stability.
Now, we know that the characteristics of the amp will be determined by both open-loop performance AND the feedback factor. In most cases, doubling the feedback factor will halve the distortion from the stage, and halve the output impedance, and halve the noise, and so on. Remember from above that we make the amplifier more stable only by sacrificing open-loop gain. And if we sacrifice open-loop gain, then we are decreasing the feedback factor. That means more distortion, at least comparatively.
But the feedback factor cannot remain high at all frequencies out to infinity, due to the very fact that we’ve got these damned phase shifts to contend with. Thus compensation is a necessary evil, simply because the amp would be unusable without it.
Note that these phase shifts are not only due to those introduced by the coupling caps in your amplifier. Any amp will begin to roll off at some frequency due to the fact that no source impedance is infinite (there’s no PERFECT voltage source to drive our signal) and all loads (whether they be wires, cathodes, grids, plates, transistor bases, etc) present some capacitive component to the source. We all know that capacitors decrease in reactance with increasing frequency, so as the frequency rises the shunt load on the source (of finite impedance) becomes heavier, and the HF response therefore drops.
At the -3dB frequency (the pole) of the equivalent RC network I’ve just described, the phase shift is -45 degrees. At frequencies lower than this the phase shift approaches 0, and for frequencies higher than this the phase shift approaches -90 degrees. (A good rule a thumb here for single section RC filters is that the phase shift is approx. 6 degrees from its asymptotic value at 1/10th and 10 times the -3dB frequency.) The -3dB frequency is nothing more than 1/2*pi*R*C, which you’ve doubtless seen before as the equation that defines a first order low pass filter. And this IS a low pass filter, with an ultimate slope of 6 dB per octave.
Any multistage amplifier will have a couple of these rolloffs contained within it, which leads one to surmise that the phase shifts will ADD to one another, creating greater phase shifts, and rolling off the HF with greater and greater slope. Indeed that is exactly what happens. The open loop gain begins dropping off at 6 dB/octave at some frequency f1, due to the capacitive loading of the first stage’s output. It continues to drop off with that slope until another stage’s RC comes into play at frequency f2. For frequencies above this point, the rolloff continues at 12 dB/octave, since it is second order. If there are more stages in the amplifier, then this phenomenon continues.
What’s all this mean? Remember the phase characteristics of the RC network which tell us that at the f1 point the phase shift will lag by 45 degrees. Above this frequency it will approach -90 degrees. Now add to that the influence of the f2 point, at which the COMBINED phase shift will be (-90 + -45) or -135 degrees. For frequencies above this point f2 the phase shift will begin to approach -180. According to our rule of thumb, at 10*f2 the phase shift will be about -174 degrees. Alarm bells should be ringing in your head–or maybe you’re hearing the oscillations already. All that is still required to cause that is a gain greater than 1.
Here’s where the actual compensating goes on. The goal, remember, is to keep the open loop phase shift less than 180 at all frequencies with a gain greater than 1. In fact, you’d better keep the phase shift MUCH less than 180 if you expect to have decent stability and freedom from ringing on transients and other impulsive excitation. The easiest way to do this is by “dominant-pole compensation.” This is nothing more than adding enough capacitance (at the stage which first rolls off at 6dB/octave) so that the open loop gain drops to unity or lower around the 3dB frequency of the next RC filter.
When you compensate in this way, the open loop phase shift is held at a constant 90 degrees over most of the passband of the amplifier. As it approaches 180 degrees, the gain is simultaneously approaching unity. Thus, by sacrificing open loop gain, you buy stability. Where did I hear that before?
Now there are other forms of compensation, in fact, some of which are better than the dominant-pole method. One is to use a compensation network that begins rolling off (the “pole”) at some rather low frequency (like the dominant pole method) but then flattens out again (a “zero”) at the frequency of the second natural pole of the amp. By doing this, the amplifier’s second pole is “cancelled out,” giving a smooth 6 dB/octave up to the NEXT pole (if there is one). This is somewhat more involved, since moving the FIRST pole actually causes the SECOND pole to vary in frequency as well, an effect known as “pole splitting.” You can see how this makes the process a good deal more difficult, and no, it’s not a game lumberjacks play.
For those reasons the dominant-pole method is widely used, and to good effect. It is simple and it works.
©1999 Ken Gilbert
