Hybrid Parameters or h Parameters
Hybrid parameters are also referred as h parameters. These are referred as hybrid because, here Z parameters, Y parameters, voltage ratio, current ratio, all are used to represent the relation between voltage and current in a two port network. The relations of voltages and current in hybrid parameters are represented as, This can be represented in matrix form as,
Hybrid parameters or h parameters are very much useful in analyzing electronics circuit where, transistors like elements are connected. In those circuits, sometimes it is difficult to measure Z parameters and Y parameters but h parameters can be measured in much easier way. Even in case of an ideal transformer, Z parameter can not be used Since, the relations between voltages and current in that ideal transformer would be,
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Since, in an ideal transformer voltages can not be expressed in terms of current, it is impossible to analyze a transformer with Z parameters because a transformer does not have Z parameters. The problem can be solved by using hybrid parameters.
Determining h ParametersLet us short circuit the output port of a two port network as shown below,
Now, ratio of input voltage to input current, at short circuited output port, is This is referred as short circuit input impedance. Now, the ratio of the output current to input current at short circuited output port, is
This is called short circuit current gain of the network. Now, let us open circuit the port 1. At that condition, there will be no input current (I1=0) but open circuit voltage V1 appears across the port 1, as shown below, Now, This is referred as reverse voltage gain because, this is the ratio of input voltage to output voltage of the network, but voltage gain is defined as ratio of output voltage to input voltage of a network. Now, It is referred as open circuit output admittance.
h Parameter Equivalent Network of Two Port NetworkTo draw h parameter equivalent network of a two port network, first we have to write the equation of voltages and currents using h parameters. These are, Clearly, the equation (i) can be represented as circuit based on Kirchhoff Voltage Law. Clearly, the equation (ii) can be represented as circuit based on Kirchhoff Current Law. Combining these two parts of the network, we get,
Inverse Hybrid Parameters or g ParametersThere is another set of parameters which is closely related to set of h parameters. These parameters are called inverse hybrid parameters or g parameters. The relations between currents and voltages with g parameters are represented as, In matrix form, where,
g Parameter Equivalent Network of Two Port NetworkIn the same way as explained, in the previous section of h parameter. The equivalent circuit of two port network using g parameter can be drawn,
The relations between currents and voltages in g parameter are, As per equation (iii) we can draw, As per equation (iv) we can draw, Combining these two circuits, we get, The h parameters are used to analyzing Bipolar Junction Transistor or BJT. Whereas, g parameter are used to analyzing Junction Field Effect Transistor or JFET.