Hybrid Parameters

The z and y parameters of a two-port network do not always exist. So there is a need for developing another set of parameters. This third set of parameters is based on making V1 and I2 the dependent variables. Thus, we obtain or in matrix form, The $ \mathbf{h} $ terms are known as the hybrid parameters (or, simply, $ h $ parameters) because they are a hybrid combination of ratios. They are very useful for describing electronic devices such as transistors; it is much easier to measure experimentally the $ h $ parameters of such devices than to measure their $ z $ or $ y $ parameters. In fact, we have seen that the ideal transformer in Fig. (i), described by Eq. (A), does not have $ z $ parameters. The ideal transformer can be described by the hybrid parameters, because Eq. (A) conforms with Eq. (1).
The values of the parameters are determined as It is evident from Eq. (3) that the parameters $ \mathbf{h}_{11}, \mathbf{h}_{12}, \mathbf{h}_{21} $, and $ \mathbf{h}_{22} $ represent an impedance, a voltage gain, a current gain, and an admittance, respectively. This is why they are called the hybrid parameters. To be specific, The procedure for calculating the $ h $ parameters is similar to that used for the $ z $ or $ y $ parameters. We apply a voltage or current source to the appropriate port, short-circuit or open-circuit the other port, depending on the parameter of interest, and perform regular circuit analysis. For reciprocal networks, $ \mathbf{h}_{12}=-\mathbf{h}_{21} $. This can be proved in the same way as we proved that $ \mathbf{z}_{12}=\mathbf{z}_{21} $. Figure $ 1$ shows the hybrid model of a two-port network. A set of parameters closely related to the $ h $ parameters are the $ g $ parameters or inverse hybrid parameters. These are used to describe the terminal currents and voltages as or The values of the $ g $ parameters are determined as Thus, the inverse hybrid parameters are specifically called Figure $ 2 $ shows the inverse hybrid model of a two-port network.