Shown below is the output of a TS-500 inverter. (a) Please write the modified si

Question

Shown below is the output of a TS-500 inverter.

(a) Please write the modified sine wave as a summation of its Fourier series components. Only up to but including the 11th harmonic

(b) Plot the harmonic spectrum of the signal in part (a)

(c) Calculate the total harmonic distortion for the signal in part (a)

(d) Write a MATLAB script which produces the modified sine wave signal, plots the harmonic spectrum up to the 50th harmonic, and calculates the total harmonic distortion

Explanation / Answer

% MATLAB script which produces the modified sine wave signal,
% plots the harmonic spectrum up to the 50th (17th in code) harmonic, and
% calculates the total harmonic distortion
clc;
clear all;
f = 50;
w = 2 * pi * f;
T = 1/f;
t = 0: 1/10000: 4*T;
v = 160*sin(w*t);
plot (t,v);

title ('V(t)');
xlabel(' t --> ');
ylabel ('V(t)');
legend('Fundamental V(t)');
%figure
lt = length (t);
%y=zeros(lt);
% for k = 1 : 2 : 11; % t = (0 : L-1)*L;
% S = S + sin(k*t)/k;
% end
% plot (t,S);
y =0;
for k = 1:2:21 % you can change to 50
y = y + 160* sin(k*w*t)/k;
end
hold on
if mod(k,4)==1
display(sprintf('When k = %.0f',k)); % k to string with sprintf
display('then the plot is:');
%cla
plot(t,y)
title({'Truncated Fourier Series';['k_{max} = ',num2str(k)]})
xlabel('t')
ylabel('$$y = sum_{k in odd}^{k_{ m max}} rac{sin(k t)}{k}$$',...
'Interpreter','Latex','Fontsize',14)
end
figure
sp = fft(y); % frequency spectrum
plot(sp);
thd(y,f); % total hormonic distortion
% THD will be shown in Plot
  

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