#########################################################
# cross_talk.lsf
#
# Uses FDTD to calculate the scattering parameters of the 
# test bench crosstalk example. Compares the simulated and
# theoretical NEXT (S31) and FEXT (S41), in which the 
# effective parameters used in the theory is found using 
# MODE. The theory follows Ref. Hill, David A., et al.
# "Crosstalk between microstrip transmission lines." 
# IEEE Transactions on electromagnetic compatibilit vol. 4,
# pp. 314-321, 1994.
#
# Copyright 2016 Lumerical Solutions Inc
##########################################################

clear;
#Theoretical characteristic impedance and effective index of the microstrip
# lines even (Zev, eps_ev) and odd (Zodd, eps_odd) mode, and the isolated
# microstrip line (eps_eff), and coaxial waveguide (Z0).
Zev=39.7;Zodd=37.8;Z0=42;eps_ev=1.406^2;eps_odd=1.364^2;eps_eff=1.37^2; #Values read from cross_talk_z0.lsf for the coarse mesh 

#Extract Port Data and Generate scattering parameters
S11=getresult("::model::FDTD::ports::port 1","S");
f=S11.f;S11=S11.S;
S21=getresult("::model::FDTD::ports::port 2","S");S21=S21.S;
S31=getresult("::model::FDTD::ports::port 3","S");S31=S31.S;
S41=getresult("::model::FDTD::ports::port 4","S");S41=S41.S;
omega=2*pi*f;

#Calculate theoretical NEXT and FEXT
dZ=(Zev-Zodd)/2;
gev=1i*omega*eps_ev^0.5/c;
godd=1i*omega*eps_odd^0.5/c;
g0=1i*omega*eps_eff^0.5/c;
dk=(gev-godd)/(2i);
l=19.6e-2;
S31t=dZ/(2*Z0)*(1-exp(-2*g0*l)*(cos(2*dk*l)+dZ/Z0*sin(2*dk*l)));
S41t=-1i*exp(-g0*l)*sin(dk*l);

#Plot theory and simulation
holdoff;plot(f/1e9,20*log10(abs(S31t)));holdon;plot(f/1e9,20*log10(abs(S31)));
setplot("x label","Frequency (GHz)");setplot("y label", "(dB)");
legend("Theory","Simulation");setplot("title","NEXT");

holdoff;plot(f/1e9,20*log10(abs(S41t)));holdon;plot(f/1e9,20*log10(abs(S41)));
setplot("x label","Frequency (GHz)");setplot("y label", "(dB)");
legend("Theory","Simulation");setplot("title","FEXT");