% 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'])