Contents

RC Frequency Domain Demo

/home/dimarzio/Documents/working/12229/lectures/rcfreq.m Sun Oct 29 13:07:12 2017 Chuck DiMarzio, Northeastern University See Lecture notes for week 9, EECE2150

f=10.^[0:0.01:6];
omega=2*pi*f;
R=10e3;C=10e-6;
Zc=1./(1j*omega*C);
Av=Zc./(R+Zc);

Plot and Check: Did I do my math right?

Acheck=(1-1j*omega*R*C)./(1+(omega*R*C).^2);
f1=figure;semilogx(f,abs(Av));grid on;
xlabel('f, Frequency, Hz');ylabel('Gain Magnitude');
figure;semilogx(f,angle(Av)*180/pi);grid on;
xlabel('f, Frequency, Hz');ylabel('Gain Phase, Deg.');
figure;semilogx(f,abs(Av-Acheck));grid on;
xlabel('f, Frequency, Hz');ylabel('Gain Error');
% Yup.  The math was right

Locate the cutoff frequency and the frequency at Av=0.1

f707=1.59;A707=(1-1j*2*pi*f707*R*C)./(1+(2*pi*f707*R*C).^2);
f10=15.8;A10=(1-1j*2*pi*f10*R*C)./(1+(2*pi*f10*R*C).^2);
figure(f1);hold on;
semilogx(f707,abs(A707),'o');
semilogx(f10,abs(A10),'+');
hold off;

Do it in dB (Note 20 dB per decade)

figure;semilogx(f,20*log10(abs(Av)));grid on;
xlabel('f, Frequency, Hz');ylabel('Gain, dB');

Add 600 ohm load and do it again

RL=600;
AvL=(1./(1./Zc+1/RL))./(R+1./(1./Zc+1/RL));

figure;semilogx(f,abs(Av),f,abs(AvL));grid on;
xlabel('f, Frequency, Hz');ylabel('Gain Magnitude');

figure;semilogx(f,20*log10(abs(Av)),f,20*log10(abs(AvL)));grid on;
xlabel('f, Frequency, Hz');ylabel('Gain, dB');

% That's really bad!

Bandpass filters with Op-Amps

f=10.^[0:0.01:6];
omega=2*pi*f;

low-frequency audio bandpass

R1=10e3;C1=1e-6;R2=20e3;C2=0.02e-6;
Zc1=1./(1j*omega*C1);
Zc2=1./(1j*omega*C2);

Z1=R1+Zc1;
Z2=1./(1./R2+1./Zc2);
Av=-Z2./Z1;
figure;semilogx(f,20*log10(abs(Av)));grid on;
xlabel('f, Frequency, Hz');ylabel('Gain, dB');
% Note Midband gain determined by resistors

Another filter for the next part of the spectrum

C1=C1/60;C2=C2/5;
Zc1=1./(1j*omega*C1);
Zc2=1./(1j*omega*C2);

Z1=R1+Zc1;
Z2=1./(1./R2+1./Zc2);
Av2=-Z2./Z1;
figure;semilogx(f,20*log10(abs(Av)),f,20*log10(abs(Av2)));grid on;
xlabel('f, Frequency, Hz');ylabel('Gain, dB');
% Note we fall short of the desired midband gain

Published with MATLAB® R2017a