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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 from 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)') ylabel('Angle (rad)') axis([10 1e5 -3.5 0.5]) % Manual axis adjustment %==============================================

**RLC Circuit Transfer Function Frequency Response:**

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