- H Parameters Definition: H parameters (hybrid parameters) are defined as measurements that describe the relationship between voltage and current in two-port networks using Z and Y parameters.
- Matrix Representation: H parameters can be represented in matrix form, simplifying the analysis of complex circuits.
- Application Example: In cases where Z parameters are impractical, such as with ideal transformers, H parameters provide a viable solution for circuit analysis.
- Short Circuit and Open Circuit Analysis: H parameters include short circuit input impedance, short circuit current gain, reverse voltage gain, and open circuit output admittance for comprehensive network analysis.
- Usage in Transistors: H parameters are crucial for analyzing Bipolar Junction Transistors (BJTs), whereas g parameters are used for Junction Field Effect Transistors (JFETs).
What are H Parameters (Hybrid Parameters?)
H parameters (hybrid parameters) use Z parameters, Y parameters, voltage ratios, and current ratios to show the relationship between voltage and current in a two port network. They are useful for describing input-output characteristics, especially when Z or Y parameters are hard to measure, like in transistors.
H parameters capture all key linear characteristics of a circuit, making them valuable for simulations. The relationship between voltages and currents in h parameters can be shown in matrix form:
This can be represented in matrix form as:
For example, in an ideal transformer where Z parameters can’t be used, h parameters can describe the voltage-current relationships.
An ideal transformer’s voltage can’t be expressed in terms of current, making Z parameters ineffective for analysis. Instead, hybrid parameters (h parameters) solve this problem.
An ideal transformer’s voltage can’t be expressed in terms of current, making Z parameters ineffective for analysis. Instead, hybrid parameters (h parameters) solve this problem.
How to Find H Parameters in Two Port Networks
Let 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 to as the short circuit input impedance. Now, the ratio of the output current to input current at the 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 the output voltage of the network, but voltage gain is defined as the ratio of output voltage to the input voltage of a network.
Now:
It is referred as open circuit output admittance.
h Parameter Equivalent Network of Two Port Network
To 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:
Equation (i) can be represented as a circuit based on Kirchhoff Voltage Law:
Equation (ii) can be represented as a circuit based on Kirchhoff Current Law:
Combining these two parts of the network we get:
Inverse Hybrid Parameters or g Parameters
There is another set of parameters which is closely related to the 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 Network
g parameters can be obtained in a similar way to h parameters. The equivalent circuit of two port network using g parameter can be constructed.
The relations between currents and voltages in g parameter are:
As per equation (iii), we can show:
As per equation (iv) we can show:
Combining these two circuits, we get,
H parameters are used to analyze Bipolar Junction Transistors (BJTs). In contrast, g parameters are used for Junction Field Effect Transistors (JFETs).
