Solution 10.8.9.2 The MATLAB program w=logspace(-2,3,200);; s=j*w;; K=100 z1 = 1 p1 = 0 p2 = 4 p3 = 4 p4 = 20 mag = 20*log10( abs((K.*( +z1))./((s+p1).*(s+p2).*(s+p3).*(s+p4))));; phase=(angle(s+z1)-angle(s+p1)-angle(s+p2)-angle(s+p3)-angle(s+p4))*180/pi;; M=1.2 c=-M^2/(M^2 - 1) r=abs(M/(M^2-1)) theta = linspace(0,pi,180);; x=c+r*cos(theta);; y=r*sin(theta);; s=x+j*y;; gamma1 = angle(s)*180/pi-360;; rho1 = 20*log10(abs(s)) theta = linspace(-0.0001,-pi+0.001,180);; x=c+r*cos(theta);; y=r*sin(theta);; s=x+j*y;; gamma2 = angle(s)*180/pi;; plot(phase,mag,'k-',gamma1,rho1,'k--',gamma2,rho2,'k--') grid on axis([-360 0 -80 40]) print -deps 10892a.eps draws the log magnitude plot in Figure 1 1 -350 -300 -250 -200 -150 -100 -50 0 -80 -60 -40 -20 0 20 40 Phase in degrees Magnitude in decibels Figure 1: Log magnitude with M-circle 1.2 2