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https://designers-guide.org/forum/YaBB.pl Design >> Analog Design >> loop stability https://designers-guide.org/forum/YaBB.pl?num=1143075907 Message started by river on Mar 22nd, 2006, 5:05pm |
Title: loop stability Post by river on Mar 22nd, 2006, 5:05pm Consider a loop transfer function which has 3 low-frequency poles and 2 high-frequency zeros. According to bode plot, if loop gain is larger than certain value, the loop will be unstable. but from root locus, the larger the loop gain, the more stable the loop will be. how to explain this paradox? |
Title: Re: loop stability Post by vivkr on Mar 24th, 2006, 1:35am Hi river, A splendid question, and I am afraid the answer is not equally spectacular. It turns out that the Bode plot (or phase and gain margin, so to speak) provides a correct estimate of system stability under some very special assumptions. It so happens that circuit designers often deal with such systems, and hence we are conditioned to treating the Bode plot as sacrosanct. One should always use the Nyquist criteria(if simulating) or a root locus, especially when dealing with complex systems. I have mentioned this in an earlier post somewhere on this forum. For the example you present, the Bode plot fails spectacularly. However, the system is conditionally stable outside a range of gain values. This particular example and other discussions on the merits/risks of using different stability measures are discussed very well in most control systems books, and also in Thomas H Lee's book on "CMOS RF IC Design" where the example quoted by you should also be found. Regards Vivek |
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