Lecture 38_39_v2

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

This preview shows pages 1–5. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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....
View Full Document

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).

Page1 / 16

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

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online