Two-Port Network Parameters: Z, Y, h, g, and ABCD

This page delves into the world of two-port network parameters, explaining the ins and outs of impedance (Z) parameters, admittance (Y) parameters, h-parameters, g-parameters, and ABCD parameters.

As depicted in the figure above, a two-port network represents a specific instance of a multi-port network, characterized by each port comprising two terminals. Let’s explore each parameter in detail.

Z-Parameters (Open-Circuit Impedance Parameters)

The Z-parameters relate the voltages at the ports to the currents entering them. They are defined by the following equations:

$V_1 = Z_{11}I_1 + Z_{12}I_2$ $V_2 = Z_{21}I_1 + Z_{22}I_2$

These are also known as open-circuit impedance parameters because each Z-parameter can be found by opening one of the ports (setting its current to zero).

Y-Parameters (Short-Circuit Admittance Parameters)

The Y-parameters, on the other hand, relate the currents at the ports to the voltages applied. They are defined by:

$I_1 = Y_{11}V_1 + Y_{12}V_2$ $I_2 = Y_{21}V_1 + Y_{22}V_2$

These are called short-circuit admittance parameters because each Y-parameter can be found by shorting one of the ports (setting its voltage to zero).

h-Parameters (Hybrid Parameters)

The h-parameters are a hybrid set, relating the input voltage and output current to the input current and output voltage:

$V_1 = h_{11}I_1 + h_{12}V_2$ $I_2 = h_{21}I_1 + h_{22}V_2$

Hybrid parameters are commonly employed in creating models for transistors. They provide a convenient way to characterize the behavior of these devices.

g-Parameters (Inverse Hybrid Parameters)

Similar to h-parameters, g-parameters are another hybrid set, expressing the input current and output voltage in terms of the input voltage and output current:

$I_1 = g_{11}V_1 + g_{12}I_2$ $V_2 = g_{21}V_1 + g_{22}I_2$

ABCD-Parameters (Transmission Parameters or T-Parameters)

The ABCD-parameters, also known as transmission parameters, relate the voltage and current at the input port to the voltage and current at the output port:

$V_1 = AV_2 + BI_2$ $I_1 = CV_2 + DI_2$

These parameters are particularly useful for analyzing cascaded networks.

Symmetry and Reciprocity Conditions

The following table summarizes the conditions for a network to be symmetrical and reciprocal, based on its two-port parameters:

| Parameter | Reciprocal | Symmetrical | | --------------- | ------------------ | ----------------- | --- | ---------------------------------- | | Z-parameters | $Z_{12} = Z_{21}$ | $Z_{11} = Z_{22}$ | | Y-parameters | $Y_{12} = Y_{21}$ | $Y_{11} = Y_{22}$ | | ABCD-parameters | $AD - BC = 1$ | $A = D$ | | h-parameters | $h_{12} = -h_{21}$ | $| h | = h*{11}h*{22} - h*{12}h*{21} = 1$ | | g-parameters | $g_{12} = -g_{21}$ | $| g | = g*{11}g*{22} - g*{12}g*{21} = 1$ |