- Y Parameters Definition: Y parameters, or admittance parameters, quantify how current and voltage interact in a two-port network under specific conditions.
- Matrix Representation: Representing Y parameters in a matrix helps analyze and calculate the interaction of voltages and currents efficiently.
- Calculation Method: To find y parameters of two port network, one port is typically short-circuited to measure responses at the other, revealing important electrical characteristics.
- Practical Application: These parameters are crucial for designing and understanding circuits, especially in telecommunications and signal processing.
- Comparison with Other Parameters: Understanding Y parameters alongside Z, h, and ABCD parameters offers a complete view of network behavior under various conditions.
What is a Y Parameter?
Y parameters (also known as admittance parameters or short-circuit parameters) are properties used in electrical engineering to describe the electrical behavior of linear electrical networks. These Y-parameters are used in Y-matrixes (admittance matrixes) to calculate the incoming and outgoing voltages and currents of a network.
Y-parameters are also known as “short-circuit impedance parameters”, as they are calculated under open-circuit conditions. That is to say that Ix=∞, where x=1, 2 refers to the input and output currents flowing through the ports of a two port network.
Y parameters are commonly used alongside Z parameters, h parameters, and ABCD parameters to model and analyze transmission lines.
How to Find Y Parameters in Two Port Networks
The below example goes over how to calculate the Y parameters of a two-port network. Note that Y parameters are also known as admittance parameters, and these terms may be used interchangeably in these examples.
In analyzing Z parameters—also called impedance parameters—we express voltage through current using the following equations.
Similarly, we represent current in terms of voltage using the admittance parameters of a two port network, allowing us to define the current-voltage relations as follows.
This relationship can also be succinctly represented in a matrix format, as shown below:
Here, Y11, Y12, Y21, and Y22 are admittance parameters (or Y parameters).
We can determine the values of the parameters of a particular two port network by making a short-circuited output port and input port alternatively as follows.
First, let us apply a current source of I1 at the input port keeping the output port short-circuited as shown below.
In this case, the voltage across the output port will be zero since the terminals of the port are short-circuited.
Now, the ratio of the input current (I1) to the input voltage (V1), with the output voltage (V2) at zero, is calculated as:
This is called short circuit input admittance.
The ratio of output current I2 to input voltage V1 while output voltage V2 = 0, is
This is referred to as the short circuit transfer admittance from the input port to the output port.
Now, let us short circuit the input port of the network and apply current I2 at the output port, as shown below.
In this case,
This is called short circuit output admittance.
This is called short circuit transfer admittance from the input port to the output port.
So finally,
