Consider a transmission line with Z0=R+jXL and Y0=G+jXC. The propagation constant and the characteristic impedance are:
γ=Sqrt(Z0Y0)
ZC=Sqrt(Z0\Y0)
Considering the transmission line is symmetric, we regard the two-port as a T-network with Z0/2 on both sides. Then the ABCD parameters are:
A=D=1+(Z0Y0)/2
B=Z0(1+Z0Y0/4)
C=Y0
For a reciprocal two-port Z0 and γ are:
Z0=Sqrt(B/C)=Sqrt(Z0\Y0*(1+Z0Y0))
γ=ln(Sqrt(BC)+Sqrt(AD))=ln(Z0Y0(1+Z0Y0)+1+Z0Y0/2)
But here comes the problem. If ZC=Sqrt(Z0\Y0) then Z0Y0=0 and this means that γ=0. Something is wrong and i don't understand what.
Nothing wrong, you are applying relation obtained for medium line(T or Pai) "APPROXIMATION", would true and y would not be zero for long line A,B,C and D calculation.....
Hi Boris
just follow microwave engineering written by D M Pozar. Its clearly stated
Hi Boris!
Elements ABCD matrix transmission line are of the form: a11=a22=cos(γ*l), a12=j*ZC*sin(γ*l), a21=j*sin(γ*l)/ZC. Z0 and Y0 resistance and conductance of the line per unit length. l is the length of the line.
Best wishes.
Sameer, that's a good book, though it doesn't present things different than most books do.
Яков, I suppose you mean sinh and cosh. Anyway i suppose i had the wrong approach.
The reason i started this question is because in all books they simply say something like:
"Then we obtain d2V(z)/dz2-γ2V(z)=0 where γ=Sqrt(Z0Y0) is the propagation constant".
And then i ask myself right away "Why?". I mean the propagation constant has already been introduced during the two-ports theory as one of the characteristic parameters (I know that in some countries/universities the theory of two-ports doesn't include characteristic parameters but here it does). I like to keep a logical sequence between everything i teach so there's no point in introducing this constant twice. A more logical approach would be to prove that for a transmission line the propagation constant should be γ=Sqrt(Z0Y0)
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