Question 19.10: Find [z] and [g] of a two-port network if [T] = [10 1.5 S 2 ...

If A = 10, B = 1.5, C = 2, D = 4, the determinant of the matrix is

∆_T = \pmb{AD − BC} = 40 − 3 = 37

From Table 19.1,

\pmb{z _{11}}=\pmb{\frac{ A }{ C }}=\frac{10}{2}=5, \quad \pmb{z _{12}}=\frac{\Delta_T}{ \pmb{C} }=\frac{37}{2}=18.5 \\ \space \\ \pmb{z _{21}}=\frac{1}{ \pmb{C} }=\frac{1}{2}=0.5, \quad \pmb{z _{22}}=\pmb{\frac{ D }{ C }}=\frac{4}{2}=2 \\ \space \\ \pmb{g _{11}}= \pmb{\frac{ C }{ A }}=\frac{2}{10}=0.2, \quad \pmb{g _{12}}=-\frac{\Delta_T}{ \pmb{A} }=-\frac{37}{10}=-3.7 \\ \space \\\pmb{g _{21}}=\frac{1}{ \pmb{A} }=\frac{1}{10}=0.1, \quad \pmb{g _{22}}=\pmb{\frac{ B }{ A }}=\frac{1.5}{10}=0.15

TABLE 19.1
Conversion of two-port parameters.

Thus,

[ \pmb{z} ]=\left[\begin{array}{cc}5 & 18.5 \\ 0.5 & 2 \end{array}\right]  \Omega, \quad[ \pmb{g} ]=\left[\begin{array}{cc} 0.2  S & -3.7 \\ 0.1 & 0.15  \Omega \end{array}\right]