Question

1. Draw a simple circuit diagram of half wave specific with sinusoidal input signal define on V_in (t) = A*cos(wt^2*pi*f) with peak voltage of 10 V and frequency of 60 Hz.

2. Design the output voltage in terms of fourier transform.

3. Use matlab to plot the frequency spectrum of the rectified signal for magnitude and phase use load resistance as 1 kilo-ohm and cutoff frequency as 10 Hz.

4. Design a second order butterworth filter of a specific cosine peak viltage of 10V and frequency 60 Hz; sine linke to generate square wave signal.

Answer 1

A simple circuit diagram for the above question is as below,

A zoomed view of the above waveform is as below

Also find the Matlab code which generated the above figure

%% Time specifications:
Fs = 100000; % samples per second
dt = 1/Fs; % seconds per sample
StopTime = 0.25; % seconds
t = (0:dt:StopTime-dt)'; % seconds
%% Sine wave:
Fc = 60; % hertz
x = cos(2*pi.^2*Fc.^2*t.^2);
% Plot the signal versus time:
figure;
plot(t,x);
xlabel('time (in seconds)');
title('Signal versus Time');
zoom xon;

Note from the figure that the signal in the given question is not periodic with 60Hz sine wave. Therefore, the signal when rectified will not be a periodic rectified signal with 60Hz frequency.