Poles_and_Zeroes

Poles_and_Zeroes - A Fool-Proof (Maybe) Method for...

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Unformatted text preview: A Fool-Proof (Maybe) Method for Determining FL(s), Fu(s), and Amid (1) You must first determine the "low-frequency" poles and zeroes, and the "high-frequency" poles and zeroes. This can only reliably be done by sketching the Bode magnitude response. It is not important to have the level correct yet, since the breakpoints are determined solely by the poles and zeroes. (2) In order for there to be a flat ("midband") region, there must be an equal number of "low-frequency" poles and zeroes. From the original transfer function, group the factors corresponding to low-frequency poles and zeroes together. You must make this group of factors limit to 1 as s goes to infinity. Steal from the transfer function's constant value (in other words, multiply and divide by the appropriate number) to make this so. The resulting collection of factors and the normalizing number give you FL(s). (3) The factors corresponding to the remaining high-frequency poles and zeroes are grouped together. This group of factors lTIUStlimit to 1 as s goes to zero. Again, multiply and divide by the appropriate number in order to make this so. The resulting collection of factors and the normalizing number give you Fu(s). (4) The original transfer function constant has likely been modified as the result of steps (2) and (3). Having separated out FL(s) and FH(S), what is left is Amid. In the transfer function example below, the low-frequency zero is at 0, and the low-frequency pole is at 103 rad/s. ~~---------------------- -------- - ._- ~-r.:J LL\ L'.i W u.; 'L :eXT U)' (J) (/) :':' l(: :-- o C) C :.f) 0 c.> , ::._~ '- AcrroaCG ;tl - O(l2-W 6b?tt pl"r ~ T(;,) = T- 0' ~-:'" '& '<:.:t ".: ..--- -r~~" ITty) ( NN (,~ C,'; ("'1 ("'.j ...
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This note was uploaded on 10/23/2009 for the course EE 482 taught by Professor Bowman during the Spring '07 term at RIT.

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Poles_and_Zeroes - A Fool-Proof (Maybe) Method for...

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