#####################################################
# quarter_wave_transformer_RLC.lsf
#
# Quarter-wavelength microstrip transmission line 
# terminated in <RLC> load.
#
# This script calculates the frequency 
# response and compare the reflection coefficient 
# and SWR percent bandwidth to transmission line
# theory.
#
# Copyright 2016 Lumerical Solutions Inc
#####################################################

# Get S11 and freqeuncy vector result from port
Port1=getresult("FDTD::ports::port 1","S");
S11_sim=Port1.S;
freq=Port1.f;

# Transmission-line theory to calculate reflection 
# coefficient. Assumes a TEM mode. 
Zfeed=100;ZL=350;
fc=4e9; #center frequency/wavelengt 
Z0=187.1; #c
eps_eff=1.66;
l1=14.55e-3;
lambda0=c/freq;
lambdag=lambda0/sqrt(eps_eff);
beta_l=2*pi*l1/lambdag; #propagation constant * length (assumes TEM mode)
 
Zin=Z0*(ZL+1i*Z0*tan(beta_l))/(Z0+1i*ZL*tan(beta_l)); #input impedance seen by the feeding TL
G_theory=(Zin-Zfeed)/(Zin+Zfeed); #theoretical reflection coefficient
G_sim=S11_sim; #simulated absolute reflection coefficient

# plot
plot(freq/1e9,abs(G_theory),abs(G_sim),"Freq (GHz)","Reflection Coefficient","Quarter-wave Transformer");
legend("TL Theory", "Simulation");

#calculate SWR<=2 bandwidth
SWR_theory=(1+abs(G_theory))/(1-abs(G_theory));
SWR_sim=(1+abs(G_sim))/(1-abs(G_sim));
fBW_t=[freq(min(find(SWR_theory<=2))),freq(max(find(SWR_theory<=2)))];
delta_t=(fBW_t(2)-fBW_t(1))/fc;
fBW_s=[freq(min(find(SWR_sim<=2))),freq(max(find(SWR_sim<=2)))];
delta_s=(fBW_s(2)-fBW_s(1))/fc;
?"SWR<=2 Percent bandwidth from Theory is "+num2str(100*delta_t)+ "%" ;
?"SWR<=2 Percent bandwidth from Simulation is "+num2str(100*delta_s)+ "%" ;