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

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

or, in matrix form,

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

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

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

The above formulas can be used to build the circuit that we need to solve to measure the g-parameters. For instance, if we want to measure the $g_{22}$ parameter, we need to:

• Short-circuit the input terminals (because the constraint requires $V_{1}=0$ V, which is equivalent to a short-circuit)
• We connect a current source of 1 A at the output terminals (because the denominator in the definition of $g_{22}$ contains a current and the subscript is $2$, which denotes the output)
• Compute voltage $V_{2}$ at the output terminals (because the numerator in the definition of $g_{22}$ contains a current and the subscript is $2$, which denotes the output)