Any linear two-port network is described by the following equations

$$\begin{equation}V_1=z_{11}I_1 + z_{12}I_2\end{equation}$$ $$\begin{equation}V_2=z_{21}I_1 + z_{22}I_2\end{equation}$$

or, in matrix form,

$$\begin{bmatrix}V_1\\V_2\end{bmatrix} = \begin{bmatrix}z_{11} & z_{12}\\z_{21} & z_{22}\end{bmatrix} \begin{bmatrix}I_1\\I_2\end{bmatrix}$$

The 4 parameters are called:

• $z_{11}$ - open-circuit input admittance
• $z_{12}$ - open-circuit transfer impedance
• $z_{21}$ - open-circuit transfer impedance (similar to $z_{12}$)
• $z_{22}$ - open-circuit output impedance

Using the above definition, once can show that the impendance parameters can be computed by using the following equations

$$\begin{equation}z_{11}=\left.{\frac{V_1}{I_1}} \right|_{I_2=0}\end{equation}$$ $$\begin{equation}z_{12}=\left.{\frac{V_1}{I_2}} \right|_{I_1=0}\end{equation}$$ $$\begin{equation}z_{21}=\left.{\frac{V_2}{I_1}} \right|_{I_2=0}\end{equation}$$ $$\begin{equation}z_{22}=\left.{\frac{V_2}{I_2}} \right|_{I_1=0}\end{equation}$$

The above formulas can be used to build the circuit that we need to solve to measure the z-parameters. For instance, if we want to measure the $z_{12}$ parameter, we need to:

• Open-circuit the input terminals (because the constraint requires $I_{1}=0$ A, which is equivalent to an open-circuit)
• We connect a current source of 1 A at the output terminals (because the denominator in the definition of $z_{12}$ contains a current and the subscript is $2$, which denotes the output)
• Compute voltage $V_{1}$ at the input terminals (because the numerator in the definition of $z_{12}$ contains a current and the subscript is $1$, which denotes the input)