hwsln-421-s06-11

hwsln-421-s06-11 - ECE 421, Spring 2006 Solutions to HW...

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ECE 421, Spring 2006 Solutions to HW Assignment #11 Problem #B-8-5 The Bode magnitude and phase plots are shown in Fig. 1. The transfer function has one poles at the origin ( N =1) , so at low frequencies the magnitude plot has a slope of 20 db/decade and the phase plot has a value of 90 . There are n =3 poles and m =2 zeros, so n m =1 making the magnitude plot have as lopeo f 20 db/decade and the phase plot have a value of 90 at high frequencies. The peaks in the magnitude curve and rapid changes in the phase curve are due to the small damping ratios of the complex conjugate poles and zeros. The damping ratio and natural frequency of the zeros are 0.2 and 1 rad/sec, and for the poles they are 0.1333 and 3 rad/sec, respectively. The small damping ratio of the zeros causes the negative peak in the magnitude and the sharp rise in the phase curve. The e f ects of the poles are in the opposite directions. 10 -2 10 -1 10 0 10 1 10 2 10 3 -100 -80 -60 -40 -20 0 20 40 60 Frequency (r/s) M a g n i t u d e ( b ) & P h s Bode Plots for Prob. B-8-5 Figure 1: Bode plots for Problem B-8-5. 1
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Problem #B-8-7 The Bode magnitude and phase plots are shown in Fig. 2. The transfer function has no poles at the origin ( N =0) , so at low frequencies the magnitude plot has a slope of 0 db/decade and the phase plot has a value of 0 . There are n =3 poles and m =1 zeros, so n m =2 mak ingthemagn itudep lothaveas lope of 40 db/decade at high frequencies. If all the poles and zeros were in the left-half plane, then the phase plot would have a value of
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hwsln-421-s06-11 - ECE 421, Spring 2006 Solutions to HW...

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