Question 19.10: Find [z] and [g] of a two-port network if [T] = [ 10 1.5Ω ......
Find [z] and [g] of a two-port network if
[T] = \begin{bmatrix} 10 & 1.5 Ω \\ 2 S & 4 \end{bmatrix}
If A = 10 , B = 1.5 , C = 2 , D = 4 , the determinant of the matrix is
Δ_{T} = AD – BC = 40 – 3 = 37
From Table 19.1,
z_{11} = \frac{A}{C} = \frac{10}{2} = 5 , z_{12} = \frac{Δ_{T}}{C} = \frac{37}{2} = 18.5
z_{21} = \frac{1}{C} = \frac{1}{2} =0. 5 , z_{22} = \frac{D}{C} = \frac{4}{2} = 2
g_{11} = \frac{C}{A} = \frac{2}{10} = 0.2 , g_{12} = – \frac{Δ_{T}}{A} = – \frac{37}{10} = -3.7
g_{21} = \frac{1}{A} = \frac{1}{10} = 0.1 , g_{22} = \frac{B}{A} = \frac{1.5}{10} = 0.15
Thus,
[z] = \begin{bmatrix} 5 & 18.5 \\ 0.5 & 2 \end{bmatrix} Ω , [g] = \begin{bmatrix} 0.2 S & -3.7 \\ 0.1 & 0.15Ω \end{bmatrix}