| Electronics > Beginners |
| Poles and Zeros |
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| npelov:
Hi, I can't grasp the idea of poles and zeros. Can someone explain to me how poles and zeros can be used to tell if a circuit will oscillate or not. For example here: http://www.analog.com/en/analog-dialogue/articles/techniques-to-avoid-instability-capacitive-loading.html poles and zeros are used to calculate the components needed for op amp compensation with capacitive load. What is pole frequency and zero frequency? All the videos in youtube are about mathematics. I can't translate that to electronics. For example "stable" system is one that goes to "0", "unstable" goes to infinity and "marginally stable" goes to a constant value OR oscillates. When I say stable in electronics I imagine constant value and unstable when it's oscillating we look for the two cases of "marginally stable". Maybe I didn't understand correctly. And why unity gain configuration is less stable than gain > 1? Can someone explain and/or give me a link where these are well explained. |
| Benta:
This is basic EE, and if you want to understand it fully you'll need to learn the mathematics (which are normally called Complex Analysis). Simply put, the poles and zeros are the solutions to the transfer function of the circuit. The poles are the complex solutions of the denominator polynomium, the zeros are the complex solutions of the numerator polynomium. In real life, you'll mostly run into second-order polynomiums, which can be solved relatively easily. But you're working in the complex plane, and this is the first concept to get a grab on. |
| Cerebus:
--- Quote from: npelov on June 15, 2018, 04:07:25 pm ---All the videos in youtube are about mathematics. I can't translate that to electronics. --- End quote --- You won't be able to get away from that. Poles and zeroes are fundamentally mathematical in nature as they are components of the mathematical transfer function of a system. The practical mathematics is, contrary to initial appearances, quite simple to use as much of the application can be done in a formulaic fashion but, as with all mathematics, you need to understand what's going on before you start taking a 'fill in the formula' approach. There are rules of thumb for determining stability that don't explicitly involve using poles and zeroes e.g. the Bode plot of the loop gain of a stable amplifier must cross the unity gain axis at a slope of -6dB/octave (-20db/decade). At the end of the day if you want to be able to cope with non-trivial systems then being able to handle the mathematics is almost essential or you get left with only empirical methods to use and that can be limiting. I have struggled to find a good book that teaches control theory (for that is what this is) with a central focus on electronics that is more suitable for the, shall we say, mathematically challenged. I've found that too many texts either assume too much innate mathematical understanding on behalf of the reader, or are OK in that regard but are too focussed on general control systems and make scant mention of electronics applications. If anybody has a book recommendation for a book that doesn't have these weaknesses I'd be very grateful to hear it as I always struggle to find a book to recommend to others (as in this instance). And that's where I stop, as this really is the kind of area that needs you to sit down with a good textbook (or attend a good series of lectures). It isn't something that can be taught via a short series of posts on a forum - you might be able to get a flavour of the territory you're entering, and I suspect some others will make a few posts that might do that, but proper understanding is going to require a reasonable amount of effort studying. |
| Cerebus:
--- Quote from: Benta on June 15, 2018, 04:18:04 pm ---In real life, you'll mostly run into second-order polynomiums, which can be solved relatively easily. --- End quote --- He means polynomials. |
| ferdieCX:
This is a beautiful book to start seriously learning circuit analysis: Hayt and Kemmerly - Engineering Circuit Analysis I suppose, that it is legal to download from archive.org the old 2d edition |
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