Question

Consider a 60 Hz, voltage signal given by v(t) = 17.2 cos (ωt) + 0.15 cos (2ωt) + 2.2 cos (3ωt) + 1.05 cos (7ωt) + 0.75 cos (11ωt) V

(a) Use a CAD tool to plot the signal v(t) over three cycles of the fundamental frequency.

(b) On a separate CAD plot, plot the fundamental and each of the harmonics overlaid on one plot. Please include a legend in this plot indicating each harmonic.

(c) Use a CAD tool plot the harmonic spectrum

(d) Calculate the total harmonic distortion for this signal

Answer 1

% IN FOLLOWING ANSWER MATLAB TOOL IS USED TO PLOT ALL WAVEFORM AND TO CALCULATE THD (TOTAL HARMONIC DISTORTION AND TO PLOT THD

% PROGRAM

clc;
clear all;
f = 60;
w = 2 * pi * f;
T = 1/f;
t = 0: 1/10000: 3*T;
x = 17.2*cos(w*t);
y = 0.15*cos(2*w*t);
z = 2.2*cos(3*w*t);
W = 1.05*cos(7*w*t);
u = 0.75*cos(11*w*t);
v = x+y + z+ W+u ;
% ans (a)
plot (t,v);
title ('V(t)');
xlabel(' t --> ');
ylabel ('V(t)');
legend('Comined signal V(t)');
figure
plot (t,x,y,z,W,u); % you can add different colour by using Linespec
legend('HARMONICS');
figure
sp = fft(v);
plot(sp);
title ('Freequency spectrum');
xlabel(' w --> ');
ylabel ('Amplitude');
legend('Frequency spectrum of V(t)');
% total Harmonic Distortion plot
figure
thd(v,f);

% thd value will be indicated on graph