z- parameter are defined by

$V_1=Z_{11}I_1+Z_2I_2\ \ \ \ -\left(1\right)$

$V_2=Z_{21}I_1+Z_{22}I_2\ \ \ \ -\left(2\right)$

Transmission parameter are defined as

$V_1=AV_2-BI_2$

$I_1=CV_2-DI_2$

Form the equation of z-parameter, substituting

$I_1\ of\ \ ef\left(i\right) \ by\ I_1\ of\ ef \ \left (ii\right)$

$V_1=Z_{11}\left[\dfrac{V_2-Z_{22}I_2}{Z_{21}}\right]+Z_{12}I_2$

$V_1=\dfrac{Z_{11}}{Z_{21}}=V_2-\dfrac{Z_{11}Z_{22}}{Z_{21}}I_2+Z_{12}I_2$

$V_1=\dfrac{Z_{11}}{Z_{21}}\ V_2-\dfrac{\left(Z_{11}Z_{22}-Z_{21}Z_{12}\right)}{Z_{21}}I_2\ -\left(a\right)$

$from\ equation\ \left(a\right),\ A=\dfrac{Z_{11}}{Z_{21}}\ B=\dfrac{\Delta{}Z}{Z_{21}}$

Rearranging equation (ii)

$-Z_{21}I_1=-V_2+Z_{22}I_2$

$I_1=\dfrac{V_2}{Z_{21}}-\dfrac{Z_{22}}{Z_{21}}I_2-\left(b\right)$

$from\ equation\ \left(b\right),\ C=\dfrac{1}{Z_{21}}\ \ D=\dfrac{Z_{22}}{Z_{21}}$