What are poles and zeros ?

[rakarlin]

I did a Google search on Poles Zeros, to see what was out there. It popped on the search. I joined up as a member of electro-tech-online because it looked interesting. I typed an answer just to learn how to post a reply. I was surprised that it was not locked. The original post is truly very old, but from the action still of much interest. Hopefully at least some of this interest is in the technical question. I would hate to think all these people have nothing better to do than read the dates on posts. The fact that Google popped it and that I could post to the thread says it is on-line and open. I cannot tell you why. I don't get to vote on on-line/offline or open/closed.
My regards, Richard

 

[rakarlin]

What you need are Bode plots. You need a plot of loop gain versus frequency and one of loop phase shift versus frequency. It is also possible to combine these two things into a single plot: a Bode stability plot. This plot has real gain to the left, imaginary gain to the right, and frequency is degrees from the real axis. (A cylindrical graph.) You want it to be heart shaped, with the dip to the right. Phase shift at zero degrees and loop gain at 1.000 must lie outside the heart. Loop gain at 0.2 or less when loop phase shift is zero degrees is excellent. You cannot get there by just pushing poles around. A lot of the poles are fixed by device characteristics (like transistor gain-bandwidth rolloff), or by parasitic elements, like collector-base capacitance. Usually, the first amplifier stage will have most of the gain (speaking of audio amplifiers now). This usually insures that it will have the first rolloff. We add capacitance to make this the dominant rolloff and establish its position. The first stage has most of the gain for reasons of noise, voltage slewing, and power. It is first, so it will set the noise limit. If it is followed by additional gain, it has reduced slew demand, which is compatible with high gain parameters, and the less the power demand, the more gain can be obtained. If other rolloffs are too near and phase shift is excessive, we have three ways to fix this: reduce the loop gain; lower the dominant rolloff; raise the other rolloffs. Roffoffs can be raised by lowering the R or lowering the C, or applying local feedback. For example, add an emitter resistor to a stage to get degeneration in that stage. Now you can use poles and zeros manipulation. Bypass the degeneration resistor and you get a frequency boost and a phase shift reduction, but beware. When the gain boost runs out, you go down and shift at twice the rate. I hope this all is some help. Remember, everything walks around with device tolerances, temperature, voltage, age, etc.