% RLC2		MATLAB script file which generates the advanced solution to 
%		Lesson 5 of the 6.003 MATLAB "Pico"-Course.  This script calls
%		on functions   residue.m     and    step.m   for each of the 
%		three cases, and includes the necessary plot commands.

% Case (i)  : R = 1 Ohm, C = 1 Farad, L = 6 Henrys, T = 20 sec
% Case (ii) : R = 1 Ohm, C = 1 Farad, L = 1 Henry , T = 20 sec
% Case (iii): R = 1 Ohm, C = 1 Farad, L = 4 Henrys, T = 20 sec

% Define component values
T = 20;
R = 1;
C = 1;
L = [6; 1; 4];
words = ['poles real,distinct'; ...
         'poles complex conj.'; ...
         'poles real,equal   '];

t = linspace(0,T,201);
% Cycle through the cases, generating all three plots on the same figure
for case = 1:3
  Hnum = [1/C 0];			%Define system function
  Hden = [1 1/(R*C) 1/(L(case,1)*C)];
  			%To continue lesson, type:    return
  keyboard		%Use    printsys   to verify system function

  [K,P] = residue(Hnum,Hden)	%Determine Partial Fraction Expansion

  v(case,:) = step(Hnum,Hden,t)';	%function call
  subplot(3,1,case), hold on
  plot( t, v(case,:), 'rx');
  xlabel('t    (sec)');
  ylabel('v(t)');
  text(10,0.4,words(case,:));
end

subplot(3,1,1)
title('Parallel RLC Circuit: Step Response for Three Cases');