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

$$\begin{equation}V_1=A V_2 - B I_2\end{equation}$$ $$\begin{equation}I_1=C V_2 - D I_2\end{equation}$$

or, in matrix form,

$$\begin{bmatrix}V_1\\I_1\end{bmatrix} = \begin{bmatrix}A & B\\C & B\end{bmatrix} \begin{bmatrix}V_2\\-I_2\end{bmatrix}$$

The 4 parameters are called:

• $A$ - open-circuit voltage ratio
• $B$ - negative short-circuit transfer impedance
• $C$ - open-circuit transfer admittance
• $D$ - negative short-circuit current ratio

Sometimes, the transmission parameter are denoted by $t_{ij}$ and $$\begin{bmatrix}A & B\\C &D\end{bmatrix} = \begin{bmatrix}t_{11} & t_{12}\\t_{21} & t_{22}\end{bmatrix}$$

Using the above definitiion, once can show that the admittance parameters can be computed by using the following equations

$$\begin{equation}A=\left.{\frac{V_1}{V_2}} \right|_{I_2=0}\end{equation}$$ $$\begin{equation}B=-\left.{\frac{V_1}{I_2}} \right|_{V_2=0}\end{equation}$$ $$\begin{equation}C=\left.{\frac{I_1}{V_2}} \right|_{I_2=0}\end{equation}$$ $$\begin{equation}D=-\left.{\frac{I_1}{I_2}} \right|_{V_2=0}\end{equation}$$

The above formulas can be used to build the circuit that we need to solve to measure the transmission parameters. For instance, if we want to measure the $A$ parameter, we need to:

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

If we want to compute the $B$ parameter, we need to:

• Short-circuit the output terminals (because the constraint requires $V_{2}=0$ V, which is equivalent to a short-circuit)
• Since we short-circuited the output terminals, we can connect a voltage source of 1 A at the input terminals (because the numerator in the definition of $B$ contains a voltage and the subscript is $1$, which denotes the input), and
• Compute current $I_{2}$ at the output terminals (because the numerator in the definition of $B$ contains a current and the subscript is $2$, which denotes the output)