ABCD Matrix for a Multi branched Power Line
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hello everyone, i have to calculate the transfer function for a multi branched powerline (from source to destination). let's say N equidistant branches with loads at ends (with the same impedance zl). D is the cable length. every 2 branches are separated with D/N (meter). the load is L=1m far from the connection node. I wanted to know if what I did is correct because i have a doubt:
T0=Series(zs); //the source ABCD matrix [1 zs;0 1]
d=D/N;
T1=TLL(f,d); //the ABCD matrix for a transmission line of length d :
[cosh(sigma*d) z*sinh(sigma*d); 1/z sinh(sigma*d) cosh(sigma*d) ]
with sigma=propagation_constant(f);
and z=caracteristic impedance(f);
T3=Shunt(zeq); //the shunt ABCD matrix for each branch [0 1; 1/zeq 1]
with zeq= z.*(zl+(z*tanh(sigma*L))) / (z+(zl*tanh(sigma*L)));
the resulting matrix is Mat= T0* (T1*T3)^N *T1;
is that ok? thank you in advance
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