I remember that I only got a C+ for the subject of electric circuit II. It faithfully reflected my understanding of the subject. It was unclear to me, but fortunately I passed. Recently I revisited the subject of RLC natural response again because I wanted to analyze the performance of a step up transformer based high voltage generator. For that reasons, I needed to derive RLC characteristic equations, and then solved it numerically in Matlab. After doing the problems for some time, I think now I have a better understanding.

I want to immortalize my notes in this blog. So I can look back to these notes in case I forget how to solve them in the future. Hopefully, you find them useful too 🙂

% Numerically solving RLC natural response using % Ordinary Differential Equation (ode) solver %% -----Rp-------Rs---- % | | | % C L Rl % | | | % -------------------- clear all; C = 100 * 10^(-6); L = 7 * 10^(-3); Rl = 50; Rs = 5; Rp = 2; Vc = 100; a = (Rs+Rp+Rl)*L/(Rs+Rl); %from equation (5) b = (C*Rp*(Rs+Rl)+L)/(C*(Rs+Rl)); %from equation (5) c = 1/C; %from equation (5) tspan = [0 0.05]; init = 0; %i(0+) init2 = ((Rs+Rl)*Vc)/((Rs+Rp+Rl)*L); %di/dt (0+) y0 = [init; init2]; [t, y] = ode45(@(t,y) [y(2); (-c*y(1)-b*y(2))/a], tspan, y0); i3 = y(:,1); i2 = y(:,2)*(L/(Rs+Rl)); %from equation (3) i1 = -(i2+i3); %from equation (1) figure(2) plot(t,i2*Rl) grid on xlabel('time (seconds)') ylabel('V_{RL} (volts)')

Here is the result….

I have verified the result by comparing with a free circuit simulation software LTSPICE IV. Here is the circuit file, if you want to check.