Lecture 40,41rev2

# Lecture 40,41rev2 - Lecture 40,41 Bode plots Basic idea...

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Lecture 40,41 Bode plots

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Basic idea: Bode magnitude Want an easy way to plot the frequency response of a circuit with transfer function H(s) – 1 st factor poles, zeros – 2 nd put in j ω form: H(j ω ) Next convert magnitude to decibels (dB): – Power in dB=10log(P) – Voltage in dB = 20log(V) Key point: by taking Log of magnitude, can separate poles/zeros as a sum in decibels Analyze each pole/zero separately ( 29 ( 29 ( 29( 29 ( 29( 29 ( 29 ( 29( 29 ( 29( 29 ( 29 ( 29 ( 29 ( 29( 29 ( 29( 29 ϖ j p j p j z j z j p j p j z j z j H R V R V P j p j p j z j z j H s p s p s z s z s H b s b s a s a s s H + - + - + + + = + + + + = - = = + + + + = + + + + = + + + + = 2 1 2 1 2 1 2 1 2 2 1 2 1 2 1 2 1 2 1 2 2 1 2 log 20 log 20 log 20 log 20 log 20 log 20 log 10 log 20 log 10 log 10
So for a single pole: To generate Bode plot: – Plot 20log|H(j ω )| vs ω – Plot ω on a log scale – Each factor of ten in ω is called a “decade” Can notice certain facts – As ω <<p, |H(j ω )|~1/p – In dB: flat at -20log(p) – As ω >>p, |H(j ω )|~1/ ω – In dB: -20log( ω ): – -20dB/decade: Can draw the asymptotes (black lines) What about when ω =p? – “corner frequency” – |H(j ω )|~1/|j ω +p|=(½) ½ =-3dB – This assume p is real (will do complex shortly) ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ϖ j p j p j H j p j 100 1000 w/p, log scale |H(jw)|, dB

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Lecture 40,41rev2 - Lecture 40,41 Bode plots Basic idea...

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