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# RLC Circuit Transfer Function Calculation using Matlab

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Plot the magnitude and the phase response of the voltage transfer function of series RLC circuit for frequencies from 10 Hz to 100kHz.:

Here, we will compute the phase and the magnitude of the voltage transfer function Vo/V1 for frequencies ranging from 10 Hz to 100 kHz. The transfer function can be determined by the following relation:

$H(f)=\frac{{{V}_{o}}}{{{V}_{1}}}=\frac{{{Z}_{C}}}{{{Z}_{C}}+{{Z}_{L}}+R}$

A transfer function is simply a ratio between input and output.

Whereas:

\begin{align} & {{Z}_{C}}=\frac{1}{j\omega C} \\ & {{Z}_{L}}=j\omega L \\\end{align}

Now, let’s compute the transfer function using Matlab:

## Matlab Code RLC Circuit Transfer Function

%Transfer Function Calculation for an AC Circuit
clear all;close all;clc
%% Circuit Parameters
R= 30; % Resistance (30 Ohm)
L= 0.7e-3; % Inductance (0.7 mH)
C= 1.5e-6; % Capacitance (1.5 microfarad)
% Please see "help logspace" in order to understand how does logspace work?
f= logspace(1,5); % Frequency range between 10 Hz and 100 kHz
omega= 2*pi.*f; % Angular Frequency
ZC= 1./(j.*omega.*C); % Capacitive Reactance
ZL= j.*omega.*L; % Inductive Reactance
Hf=ZC./(ZC+ZL+R); % Transfer Function (V0/V1)
%% Plot the phase and the magnitude response of a transfer function
%Magnitude Plot
subplot(211)
%loglog(...) is the same as PLOT(...), except logarithmic scales are used for both the X- and Y- axes.
loglog(f,abs(Hf))
title('Magnitude')
xlabel('Frequency (Hz)')
ylabel('Amplitude')
% Please see "help axis" in order to understand how does axis work.
axis([10 1e5 1e-3 10]) % Manual axis adjustment

%Phase Plot
subplot(212)
%semilogx(...) is the same as PLOT(...), except a logarithmic (base 10) scale is used for the X-axis.
semilogx(f,angle(Hf))
title('Phase')
xlabel('Frequency (Hz)')
axis([10 1e5 -3.5 0.5]) % Manual axis adjustment
%==============================================


RLC Circuit Transfer Function Frequency Response: