magnitude characteristic of the Bode plot

I want to see a graph of magnitude characteristic of the Bode plot for the transfer function by using mathlab program.

the info of transfer function:

G(jw)=[10(jw+10)(jw+100)]/[jw(-w^2+4jw+102)]

"w" means 2*pi*frequency. "j" means imaginary number.

Answer 1

[AR]

Hi Rance,

We can compute it manually as the denominator contains a ‘−w^2' term, making it non-rational in terms of ‘s=jω’.

Follow the below steps to plot the magnitude characteristic:

1. Define frequency range (rad/s)

w = logspace(-1, 3, 1000);  % from 0.1 to 1000 rad/s

2. Define s as jω

s = 1j * w; 

3. Define the numerator and denominator

num = 10 .* (s + 10) .* (s + 100); 
den = s .* (-w.^2 + 4 .* s + 102); 

4. Compute the transfer function G(jw)

Gjw = num ./ den; 
mag_dB = 20 * log10(abs(Gjw)); 

5. Plot the graph

semilogx(w, mag_dB, 'LineWidth', 2); 
grid on; 
xlabel('Frequency (rad/s)'); 
ylabel('Magnitude (dB)'); 
title('Magnitude Characteristic of Bode Plot');

Hope this is helpful!