 # System Magnitude and Phase Response Plotting

## Question

1. Systems:
1
a) 𝐺(𝑠) = ----------
𝑠(𝑠+2)(𝑠+4)

(𝑠+5)
b) 𝐺(𝑠) = ------------
(𝑠+2)(𝑠+4)

(𝑠+3)(𝑠+5))
c) 𝐺(𝑠) = -----------------
𝑠(𝑠+2)(𝑠+4)
2. For each function above, make a plot of the log-magnitude and the phase, using log frequency in rad/s as the ordinate. Do not use asymptotic approximations.
3. For each function above, make a polar plot of the frequency response.
4. For each function above, sketch the Bode asymptotic magnitude and asymptotic phase plots.

## Solution Preview

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%clearing the screen, closing all open windows and clearing memory
clc;
clear;
close all;
%defining s as the transfer function element
s=tf('s');
%making a logarithmical frequency vector with 500 points between 10^-2 and
%10^2
freq = logspace(-2,2,500);
%defining the system a
Ga = zpk(1/(s*(s+2)*(s+4)));
%getting numerator and denumerator from the transfer function
[numa,dena] = tfdata(Ga,'v');
%getting a frequency response
ha = freqs(numa,dena,freq);
%getting magnitude in decibels
magadb = db(abs(ha));...
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