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

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

or, in matrix form,

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

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

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

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

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

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