% This script evaluate integrals symbolically to compute RMS values
% for non sinusoidal waveforms. The integration intervals and terms
% were derived from a power analysis problem for a diode circuit
% presented in the lecture note for Lab 3 in EE462G
%
% written by Kevin D. Donohue (donohue@engr.uky.edu) Sept 2005
%define symbol for equation analysis
syms t
% Compute intersection of sine with the 1.4 voltage amplitude
% to find integration regions
t1 = solve('5*sqrt(2)*sin(2*pi*1e3*t) = 1.4', t)
% define period of signal
tp = 1e-3
% Compute other intersection point of sine with the 1.4 volt level
t2 = tp/2 - t1
% Define expression for source voltage as function of t
v1 = 5*sqrt(2)*sin(2*pi*1e3*t)
% RMS source voltage
v1rms = 5
% Integrate for rms currents
i1rms = sqrt(int(((2*v1-.7)/3e3)^2,t,t1,t2)/tp + int((v1/2e3)^2,t,t2,tp+t1)/tp)
i2rms = sqrt(int(((v1+0.7)/3e3)^2,t,t1,t2)/tp + int((v1/2e3)^2,t,t2,tp+t1)/tp)
i3rms = sqrt(int(((v1-1.4)/3e3)^2,t,t1,t2)/tp)
% Power delivered by source
pavsource = (int(v1*(2*v1-.7)/3e3,t,t1,t2)/tp +int(v1*v1/2e3,t,t2,tp+t1)/tp)% This integral matches the
% voltage and current
% waveforms for correct
% average power
% pavsource = v1rms*i1rms % This is not accurate becuase it does not match the
% the voltage and currents with proper timing
% but it is approximate and corresponds to what
% you measure in the lab.
% Compute powers in all components (all resistors were 1e3 ohms)
pavr1 = i1rms^2*1e3
pavdiode = (.7*int(((v1-1.4)/3e3),t,t1,t2)/tp) % This integral matches the
% voltage and current
% waveforms for correct
% average power
%pavdiode = i3rms*.7 % This is not accurate becuase it does not match the
% the voltage and currents with proper timing
% but it is approximate and corresponds to what
% you measure in the lab.
pavr3 = i3rms^2*1e3
pavr2 = i2rms^2*1e3
% by conservation of power all absorbing components should add up to power
% delivered
pavabsorbed = pavr1+pavr2+pavr3+pavdiode
disp(['Compare power absorbed: ' num2str(double(pavabsorbed)) 'W to power supplied: ' num2str(double(pavsource)) 'W'])