echo on
%
%  EEE202BodePlt.m   Keith Holbert   October 2006
%
clear all
% Initialize a frequency vector (Hz) using linspace(a,b,n)
% which generates an n point vector from a to b inclusive.
f = linspace(0.0001,10,100);

% Encode the desired transfer function (Prob. P9-3).
xfer = 2 ./ (1 + j*4* (2*pi.*f));

% We will plot both the magnitude and phase characteristics 
% in various forms using this MATLAB program.

% First Bode plot uses linear frequency and magnitude axes.
subplot(2,1,1); 
plot(f,abs(xfer)); 
title('Transfer Function Magnitude (Linear Data; Linear Freq.)'); 
ylabel('Gain (units)');

subplot(2,1,2); 
% Don't forget to convert the phase angle from radians to degrees.
plot(f,180/pi*angle(xfer));
title('Transfer Function Phase'); 
ylabel('Angle (degrees)');

xlabel('Frequency (Hz)');

% Unfortunately, the linear frequency axis compresses information
% at lower frequencies such that a log frequency axis is needed.

pause
figure;

% The second Bode plot uses a log frequency axis (semilog plot).
% The gain magnitude has units but they were not explicitly
% specified by the textbook, but they are likely volts/amp. 
subplot(2,1,1); 
semilogx(f,abs(xfer)); 
title('Transfer Function Magnitude (Linear Data; Log Freq.)'); 
ylabel('Gain (A/V)');

subplot(2,1,2); 
semilogx(f,180/pi*angle(xfer));
title('Transfer Function Phase'); 
ylabel('Angle (degrees)');

xlabel('Frequency (Hz)');

% Here the lower frequency information is visible; however, the 
% transfer function was computed with a linear-spaced frequency 
% vector such that low frequency resolution is lost.  So, we need 
% to compute the transfer % function at logarithmically spaced 
% intervals.

pause
figure;

% The remaining Bode plots use a log frequency axis, but we
% first re-generate the frequency vector with log spacing using
% logspace(a,b,n) which generates an n-point vector from decades 
% 10^a to 10^b inclusive.
f = logspace(-4,1,100);

% Next, re-create the transfer function.
xfer = 2 ./ (1 + j*4* (2*pi.*f));

subplot(2,1,1); 
semilogx(f,abs(xfer)); 
title('Transfer Function Magnitude (Log Data; Log Freq.)'); 
ylabel('Gain (A/V)');

subplot(2,1,2); 
semilogx(f,180/pi*angle(xfer));
title('Transfer Function Phase'); 
ylabel('Angle (degrees)');

xlabel('Frequency (Hz)');

% This is much better.
pause
figure;

% The fourth plot changes the gain magnitude scale to a log axis.

subplot(2,1,1); 
loglog(f,abs(xfer)); 
title('Transfer Function Magnitude (Log Data; Log Scales)'); 
ylabel('Gain (A/V)');

subplot(2,1,2); 
semilogx(f,180/pi*angle(xfer));
title('Transfer Function Phase'); 
ylabel('Angle (degrees)');

xlabel('Frequency (Hz)');

% This is very similar to a hand-drawn straight-line approximation.

pause
figure;

% The fifth and last plot changes the gain magnitude units into dBs.
subplot(2,1,1); 
% Since the log is taken while the dB gain value of the xfer function 
% is computed, we should not use MATLAB loglog plotting function.
semilogx(f,20*log10(abs(xfer))); 
title('Transfer Function Magnitude (Log Data; dB scale)'); 
ylabel('Gain (dB)');

subplot(2,1,2); 
semilogx(f,180/pi*angle(xfer));
title('Transfer Function Phase'); 
ylabel('Angle (degrees)');

xlabel('Frequency (Hz)');

% It is worthwhile to compare the third and fourth/fifth Bode 
% magnitude plots to one another to appreciate the different views.
% Also, plotting other functions may require an adjustment to
% the selected frequency range over which the function is generated.