Lecture 38_39_v2 - Spring 2011 ECE 2100, Cornell Univ,...

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Unformatted text preview: Spring 2011 ECE 2100, Cornell Univ, Prof. Molnar 1 Lecture 38+39 More Bode plots Phase, complex conjugate poles Some filter design Spring 2011 ECE 2100, Cornell Univ, Prof. Molnar 2 Bode plots, phase Phasor transform of each pole/zero gives angle as exp. Same idea: can describe total phase as sum of phases from poles/zeros Single pole: As <<p, H(j )~ 0 As >>p, H(j )~-90 At =p, H(j )~ -45 Plot vs on a log scale Can approximate as flat for <<p/10, >>10p Straight line, -45/decade Provided pole is real Single zero: As <<z, H(j )~ 0 As >>z, H(j )~ 90 At =z, H(j )~ 45 Otherwise same idea. ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 = + = + = - = + = + =-- z j j z j H s z s H p j j p j H s p s H z p 1 1 tan tan 1 1 ( 29 ( 29 ( 29 ( 29( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 2 1 2 1 2 1 2 1 2 2 1 1 2 2 1 1 2 1 2 1 exp exp exp exp exp p p z z p p z z p p p p z z z z j m m m m G j m j m j m j m G j p j p j z j z G j H -- + = = + + + + = Bode phase one pole-90-75-60-45-30-15 0.001 0.01 0.1 1 10 100 1000 w /p degrees Spring 2011 ECE 2100, Cornell Univ, Prof. Molnar 3 Bode phase: multi-pole/zero For more complex, magnitude curves just add curves for single poles/zeros For example: ( 29 ( 29 ( 29( 29 ( 29 ( 29 ( 29 ( 29 2 2 1 1 2 1 2 1 2 1 2 1 z p p z j p j p j z j z j p j p j z j z H < < < + - + - + + + = + + + + = z 1 p 1 p 2 z 2 z 1 p 1 p 2 z 2 Actual curve: z1=.03, p1=1,p2=30, z2=1000,G=1 Spring 2011 ECE 2100, Cornell Univ, Prof. Molnar 4 Simple example: RC circuit H(s): 1/(RC(s+1/RC)) 1 Pole at s=-1/RC Low pass filter So Bode is simple....
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This note was uploaded on 06/10/2011 for the course ECE 2100 taught by Professor Kelley/seyler during the Spring '05 term at Cornell University (Engineering School).

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Lecture 38_39_v2 - Spring 2011 ECE 2100, Cornell Univ,...

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