How to I plot Laplace transfer function characteristics using the symbolic toolbox?

Hi there,

I'd like to be able to use the symbolic toolbox for plotting the amplitude and phase response of a transfer function in the Laplace domain. Reason is because I find symbolic functions to keep my work neat and easily readable.

I've tried plotting the transfer functions' amp and phase characteristics using the following piece of code. Transfer function H describes a simple passive RC low pass filter where R*C = 0.001 in Vx = Vy + R*C*Vy*s.

syms s;
H = 1/(0.001*s+1);
figure; fplot(abs(H), [0 100000]);
figure; fplot(angle(H), [0 100000]);

I would expect the phase shift between Vy and Vx to go from 0 to -pi/2 (or -90 deg), as in the bode plot below:

bode([0 1], [0.001 1]);

However, when plotting the angle with fplot I see no phase shift:

fplot(angle(H), [0 100000]);

I'd be glad if anyone could explain to me why bode and fplot give different results.

Thanks in advance!

Answer 1

[Star Strider]

Here, ‘s’ needs to be complex:

syms s;
H = 1/(0.001*1j*s+1);
figure; fplot(20*log10(abs(H)), [0 100000]);
% set(gca, 'XScale','log')
figure; fplot(angle(H), [0 100000]);
% set(gca, 'XScale','log')

For some reason, setting the 'XScale' to 'log' (so that it matches the bode plot) fails for fplot plots. I will experiment with that and post back if I can figure out a way to get it to work.

[Rogier Reerink]

Thank you! I find the need to convert 's' to a complex number a bit strange, since the Symbolic Toolbox states that sym variables are complex by default. But it did solve the problem.

I found a post that answers how to fplot logarithmically by starting the plot at a value (slightly) greater than 0 and setting the XScale to log as your answer suggests.

[Star Strider]

As always, my pleasure!

Symbolic variables are ‘complex’ by definition, however by defaault the imaginary parts are equal to 0, making them real. I set ‘s’ to be purely imaginary in my code.

I also had no problems creating logarithmic x-axis (and y-axis) scaling, however I could not get it to work correctly when I converted ‘H’ to decibels and plotted the y-axis linearly after the transformation to dB, with logarithmic x-axis scaling. That is what I wanted to do, and could not.

[Andrew Krill]

Oh man, this entire thread was really helpful.

Thing I noticed,

figure; fplot(20*log10(abs(H)), [0 100000]);

Doesn't work, because log(0) is undefined.

figure; fplot(20*log10(abs(H)), [1 100000]);

Worked just fine.