Using MATLAB to Display a Frequency Response

Let’s use MATLAB to display the Bode plot or frequency response plot corresponding to a network function. As an example, consider this network function:

and this MATLAB script:

% Bode.m - plot the Bode plot of a network function

%---------------------------------------------------------------

% Create a list of logarithmically spaced frequencies.

%---------------------------------------------------------------

wmin=1; % starting frequency, rad/s

wmax=10000; % ending frequency, rad/s

w = logspace(log10(wmin),log10(wmax));

%---------------------------------------------------------------

% Enter values of the parameters that describe the

% network function.

%---------------------------------------------------------------

K= 10; % constant

z= 100; % zero

p1=10; p2=1000; % poles

%---------------------------------------------------------------

% Calculate the value of the network function at each frequency.

% Calculate the magnitude and angle of the network function.

%---------------------------------------------------------------

for k=1:length(w)

H(k) = K*(1+j*w(k)/z) / ( (1+j*w(k)/p1) * (1+j*w(k)/p2) );

mag(k) = abs(H(k));

phase(k) = angle(H(k));

end

%---------------------------------------------------------------

% Plot the Bode plot.

%---------------------------------------------------------------

subplot(2,1,1), semilogx(w/(2*pi), 20*log10(mag))

xlabel('Frequency, Hz'), ylabel('Gain, dB')

title('Bode plot')

subplot(2,1,2), semilogx(w/(2*pi), phase)

xlabel('Frequency, Hz'), ylabel('Phase, deg')

Here’s the Bode plot produced by running the MATLAB script:

1