PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

Analog and Digital Filters 601

axis ([-5e4 5e4 0 1.1])

subplot (2,1,2);

plot (w/(2*pi),angle(Hlp)*180/pi);

xlabel (‘frequency in Hrz’);

ylabel (‘phase in degrees’);

title(‘Phase of H(f) vs. frequency’);

figure(2)

db = 20.*log(abs(Hlp));

subplot(2,1,1);

semilogx(w/(2*pi),db);

ylabel(‘mag.in dbs’);

title(‘ magnitude (dbs) vs. freqs.’);

axis([1e3 1e5 -40 5]);grid on;

subplot(2,1,2);

semilogx(w/(2*pi),angle(Hlp)*180/pi);

title(‘phase ang. vs. freqs.’);

ylabel(‘phase in degrees’);

xlabel(‘frequency, in Hrz’);

axis([1e3 1e5 -80 0]);grid on;

figure(3);

bode(num,den,w)

title(‘Bode plots with argument w’);

figure(4);bode(num,den)

title(‘Bode plots with no w’);

figure(5)

% using standard circuit approach (complex algebra)

XC = 1./(w.*C);

Z = sqrt(R^2+XC.^2);

magHele = abs(XC./Z); phaseHele =-atan(R./XC);

subplot(2,2,1)

plot(w./(2*pi),magHele);

title(‘mag.vs. freq.’);

ylabel(‘magnitude’)

axis([-5e4 5e4 0 1.1]); grid on;

subplot(2,2,2)

plot(w./(2*pi),phaseHele*180/pi);

title(‘phase vs. freq.’);

ylabel(‘phase (in degrees)’);grid on;

subplot(2,2,3);

dbele = 20.*log10(magHele);

semilogx(w./(2*pi),dbele);title(‘mag.(in db) vs. freq. ‘)

ylabel(‘magnitude(db)’);

xlabel(‘frequency in Hrz’);

axis([1e3 1e6 -15 1.0]);grid on;

subplot(2,2,4);

semilogx(w./(2*pi),phaseHele*180/pi);title(‘phase vs. freq. ‘)

xlabel(‘frequency in Hrz’);

ylabel(‘phase(degrees)’); grid on;

Back in the command window, the script fi le LP_fi lter_analysis is executed and the

results are as follows (Figures 6.26 through 6.30):

>> LP _ filter _ analysis