%Problem 1.26 Power Electronics %Rob Garrone 9_13_14 %initial pulse train visualization pulsewidth = 1/100000; % pulse width ydutycycle = .75; %75 percent duty cycle t = 0 : 1/10e6 : 11*pulsewidth; %1Mhz sample rate t2 = 0: 1/10e6: 50*pulsewidth; d = 0 : pulsewidth : 10*pulsewidth; %100kHz pulse train for 10 cycles V_A = 10*pulstran(t,d,@rectpuls,(pulsewidth*ydutycycle)); %7.5us pulse, a 75% duty cycle as described figure(); plot(t,V_A); hold on; V_OUT = 10*ydutycycle; plot(t,V_OUT,'r'); axis([0 10*pulsewidth -0.5 11]); title('Relationship of Input and Output Voltage over 10 cycles') %Title xlabel('Seconds'); % x-axis label ylabel('Voltage'); % y-axis label legend('V_A','V_O'); %Legend %Transfer function of RLC filter circuit: R = .5; % Resistor C = 100e-6; %Capacitor L = 5e-6; %Inductor w = linspace(1000,130000,1000); %1000 points between 1kHz and 130kHz figure(); H = tf([(R^2)*C -R] , [(R^2)*L*(C^2) 0 (R^2)*C-L -R]); bodeplot(H,w); title('RLC Frequency Response Bode Plot') %Title figure(); %fourier series expansion of our signal w_0 = 2*pi/(10e-6); % omega zero term a_0 = 7.5; % fourier series a_0 term %fourier series a_n terms a_1 = (10/(1*pi))*(sin(.75*1*pi)-sin(-.75*1*pi)); a_2 = (10/(2*pi))*(sin(.75*2*pi)-sin(-.75*2*pi)); a_3 = (10/(3*pi))*(sin(.75*3*pi)-sin(-.75*3*pi)); a_4 = (10/(4*pi))*(sin(.75*4*pi)-sin(-.75*4*pi)); a_5 = (10/(5*pi))*(sin(.75*5*pi)-sin(-.75*5*pi)); %fourier series b_n terms b_1 = (-10/(1*pi))*(cos(.75*1*pi)-cos(-.75*1*pi)); b_2 = (-10/(2*pi))*(cos(.75*2*pi)-cos(-.75*2*pi)); b_3 = (-10/(3*pi))*(cos(.75*3*pi)-cos(-.75*3*pi)); b_4 = (-10/(4*pi))*(cos(.75*4*pi)-cos(-.75*4*pi)); b_5 = (-10/(5*pi))*(cos(.75*5*pi)-cos(-.75*5*pi)); a_array = [a_1*cos(1*w_0), a_2*cos(2*w_0), a_3*cos(3*w_0), a_4*cos(4*w_0), a_5*cos(5*w_0)]; b_array = [b_1*sin(1*w_0), b_2*sin(2*w_0), b_3*sin(3*w_0), b_4*sin(4*w_0), b_5*sin(5*w_0)]; C_array = sqrt(a_array.^2 + b_array.^2); theta_array = atan2(-b_array,a_array); n= [1:5]; subplot(2,1,1); stem(n,C_array); title('Amplitude Spectra of the Harmonics'); ylabel('C_n'); xlabel('nth harmonic'); subplot(2,1,2); stem(n,theta_array); title('Phase Spectra of the Harmonics'); ylabel('\theta_n'); xlabel('nth harmonic'); figure(); a_n_component = a_1*cos(1*w_0*t) + a_2*cos(2*w_0*t) + a_3*cos(3*w_0*t) + a_4*cos(4*w_0*t) + a_5*cos(5*w_0*t); b_n_component = b_1*sin(1*w_0*t) + b_2*sin(2*w_0*t) + b_3*sin(3*w_0*t) + b_4*sin(4*w_0*t) + b_5*sin(5*w_0*t); F = a_0 + a_n_component + b_n_component; plot(t,F); title('Fourier Series Expansion of V_A using 5 terms'); ylabel('Amplitude'); xlabel('time');