The transmission parameters or chain parameters orABCD parameters serve to relate the voltage & current at input port to voltage & current at the output port. In equation form

$\therefore{}\left(V_1,I_1\right)=f\left(V_2,-I_2\right) $

$V_1=AV_2-BI_2 $

$I_1=CV_2-DI_2 $

In matrix form

$\left[\begin{array}{ cc} V_1 \\ I_1 \end{array}\right]=\left[\begin{array}{ cc} A & B \\ C & D \end{array}\right]\left[\begin{array}{ cc} V_2 \\ -I_2 \end{array}\right]\ \ \ where\ \left[\begin{array}{ cc} A & B \\ C & D \end{array}\right]=transmision\ matrix$

Condition of symmetry

(a) When the output port is open circuit i.e. $I_2=0$

$V_1=Vs $

$\therefore{}Vs=AV_2 $

$I_1=CV_2 $

$\therefore{}\dfrac{Vs}{I_1}=\dfrac{A}{C} $

(b) When the input port is open circuited $=i.e.\ I_1=0$

$V_2=Vs $

$CVs=DI_2 $

$\therefore{}\dfrac{Vs}{I_2}=\dfrac{D}{C} $

For network to be symmetrical

$\dfrac{Vs}{I_1}=\dfrac{Vs}{I_2} $

i.e. A=D