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Unformatted text preview: 1 Lecture 16: Bode Diagram Bode Diagram Section 7.8 Online Course Evaluation now open Bode Diagram Another graphical representation of open-loop frequency response Magnitude plot: plot of 20 log | G ( e j ! T )| as a function of ! Phase plot: plot of G ( e j !T ) as a function of log( ! ) Plotted from experimental data or from analytical expression of G ( z ) Compared with the Bode plot of a continuous system G ( s ) Approximation using straight lines 2 Example C ( s ) R ( s ) + 1 e Ts s 1 s ( s +1) G ( z ) = : 368 z +0 : 264 z 2 1 : 368 z +0 : 368 T = 1 G ( e j!T ) = : 368 e j!T +0 : 264 e j 2 !T 1 : 368 e j!T +0 : 368 >> s = tf (s); >> Gz = c2d(1/s/(s+1), 1, zoh ); >> bode(Gz); >> grid on; Matlab code: vs. log ! for 0 < ! < ! s 2 = T Bode diagram in the z-plane: 20log j G ( e j!T ) j and 6 G ( e j!T )-40-20 20 40 60 Magnitude (dB) 10-2 10-1 10 10 1-225-180-135-90 Phase (deg) Bode Diagram Frequency (rad/sec) Bilinear Transformation Between z-Plane and w-Plane w z z = 1+( T= 2) w 1 ( T= 2) w w = 2 T z 1 z +1 The unit circle on the z-plane is transformed to the imaginary axis on the w-plane: z = e j!T 7! w...
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This note was uploaded on 04/15/2011 for the course ECE 483 taught by Professor Evens during the Spring '08 term at Purdue University-West Lafayette.
- Spring '08