How to Derive the ABCD Matrix for a Transmission Line?

[baby_1]

Hello
I want to obtain ABCD matrix element value.At first I tried to find A element value with boundary conditions but I don't know how can I find relationship between V(1)+ and V(1)- .

Any help appreciate

 

[rude man]

Do you know how to determine the reflection coefficient ρ at position 1? 'Cause that's what V_o1-/V_o1+ is.
A convenient way to find ρ is to put the source at z = 0 and the load at z = L where L is the physical length of the transmission line.

 

[baby_1]

Thank you dear rude man
Before post this thread I think that I can use reflection coefficient too but as you know I don't have any other information before point 1 and my Z0 in this equation is unknown.

 

[rude man]

In post 1 you seem to state that Z₀ was known. Anyway, it has to be known or you can't find the abcd parameters.

 

[baby_1]

Thank you for accompany me
Here is my question we don't have any information before Point 1(Z1) how can define relationship between V+ and V-?

 

[rude man]

I'm having trouble understanding what you say and what you write.
Let me instead suggest:
V₁ = V₂⁺e^jθ + V₂^-e^-jθ
V₂ = V₂⁺ + V₂^-
Γ₂ = V₂^-/V₂⁺ = (Z₂ - Z₀)/(Z₂ + Z₀).
Z₂ = V₂/I₂
You can eliminate the + and - waves using the above.
And there are similar equations for I1, I2+ and I2-.
You wind up with
V₁ = AV₂ + BI₂
I₁ = CE₂ + DI₂
where A, B, C and D contain only θ and Z₀.