%% Time delay model for transmission line reflections
%% C.R. Paul, Electromagnetics for Engineers, Ch 6
%% Ramo, Whinnery & VanDuzer, Fields and Waves in Communication Electronics
%% E.W. Hansen, Engs 23 04F, 7.28.04
%% Revised 10.3.04 to allow finite rise time for input

%% Time is normalized, t' = t / T, T=L/v
%% Space is normalized, x' = x/L
%% Line parameters are summarized by reflection coefficients at source and
%% load, gS and gL.  This model does not take into account the frequency response of the
%% transmission line -- edge shape is preserved
%% Input is either a unit step or a unit-height rectangular pulse of
%% variable width.  
%% To explore transition to lumped behavior, let Tr->6 (Tr > 6 is lumped)

%% User can change these parameters
Zo = 53.5;       % Characteristic impedance
Rs = 50;       % Source resistance
RL = Inf;       % Load resistance (termination)

InputType = 'step';        % 'pulse' or 'step'
Tr = 2;        % Risetime of pulse (as a fraction of single pass delay T)
Tp = 2*Tr;        % Length of pulse input (as a fraction of single pass delay T)

N = max(6, Tp+Tr);          % Number of round trips in the simulation

%%------------------------------------------------------------------------
%% Don't change anything after this unless you know what you're doing

Nr = 10;          % Number of samples per pulse rise (from 0 to 1).
Nt = round(Nr/Tr);      % Number of time samples per pass (2 passes per round trip)

%% Calculate reflection and transmission coefficients
if Rs == inf,
    gS = 1;
else
    gS = (Rs-Zo)/(Rs+Zo);
end

if RL == inf,
    gL = 1;
else
    gL = (RL-Zo)/(RL+Zo);
end    

%% Inputs
Vstep = ones(1,2*N*Nt);                     % Step input
Vstep(1:Nr) = (1-cos(pi*linspace(0, 1, Nr)))/2;     % Put the finite rise in (raised cosine)

if strcmp(InputType, 'step')==1,            % Pick an input
    Vs = Vstep;        
else
    shift = round(Nt*Tp);                   % Pulse is step - shifted step
    Vs = Vstep - [zeros(1, shift), Vstep(1 : end-shift)];
end

%% Propagate the input down the line and back, multiple times
V0 = (1-gS)/2 * Vs;             % Initialize the construction
VL = (1-gS)/2 * (1+gL) * [zeros(1, Nt), Vs];    % One-pass offset   

for n=1:N,                  % Construct V0 & VL by adding successive bounces
    x0 = (1-gS)/2 * (1+gS)*gL*(gL*gS)^(n-1) * Vs;
    xL = (1-gS)/2 * (1+gL) * (gL*gS)^n * Vs;
    
%   Extend the wave to make room for adding the new reflection
    V0 = [V0, V0(end)*ones(1, 2*n*Nt+length(x0)-length(V0))];
    VL = [VL, VL(end)*ones(1, (2*n+1)*Nt+length(xL)-length(VL))];
%   Add the reflection
    V0(2*n*Nt+1 : end) = V0(2*n*Nt+1 : end) + x0;
    VL((2*n+1)*Nt+1 : end) = VL((2*n+1)*Nt+1 : end) + xL;

%   Display the results at the end of each pass
    plot((0:length(V0)-1)/Nt, V0, 'r', (0:length(VL)-1)/Nt, VL, 'b',...
         (0:length(Vs)-1)/Nt, Vs, 'k')
    hold off
    set(gca, 'xlim', [0, (2*N+1)])
    set(gca, 'ylim', [-2.1, 2.1])
    set(gca, 'fontsize', 12)
    xlabel('t / T', 'fontsize', 14)
    ylabel('V(x,t) / Vo', 'fontsize', 14)
    legend('V(0,t)', 'V(L,t)', 'V_{in}(t)')
    title(['LINE REFLECTIONS: \Gamma_S=',num2str(gS),', \Gamma_L=', num2str(gL)], 'fontsize', 14)
%    pause(1)
end