Question

The [y] parameter of a two port network is given by

I had been asked this question in semester exam.

This interesting question is from Two Port Network in section EDC Overview of Electronic Devices & Circuits

Answer 1

The [y] parameter of a two-port network, also known as the admittance parameters, is a matrix that relates the input and output currents to the input and output voltages in the network. It is defined in terms of the following variables:

• V1V_1V1​ and V2V_2V2​ are the input and output voltages, respectively.
• I1I_1I1​ and I2I_2I2​ are the input and output currents, respectively.

The general form of the [y] parameter matrix for a two-port network is:

[I1I2]=[y11y12y21y22][V1V2]\begin{bmatrix} I_1 \\ I_2 \end{bmatrix} = \begin{bmatrix} y_{11} & y_{12} \\ y_{21} & y_{22} \end{bmatrix} \begin{bmatrix} V_1 \\ V_2 \end{bmatrix}[I1​I2​​]=[y11​y21​​y12​y22​​][V1​V2​​]

This equation can be expanded to give the relationships between the currents and voltages as:

I1=y11V1+y12V2I_1 = y_{11} V_1 + y_{12} V_2I1​=y11​V1​+y12​V2​ I2=y21V1+y22V2I_2 = y_{21} V_1 + y_{22} V_2I2​=y21​V1​+y22​V2​

Explanation of Parameters:

• y11y_{11}y11​: Input admittance of the two-port network when the output voltage V2V_2V2​ is zero.
• y12y_{12}y12​: Reverse transfer admittance of the network, showing how I1I_1I1​ depends on V2V_2V2​.
• y21y_{21}y21​: Forward transfer admittance of the network, showing how I2I_2I2​ depends on V1V_1V1​.
• y22y_{22}y22​: Output admittance of the two-port network when the input voltage V1V_1V1​ is zero.

Physical Interpretation:

• The [y] parameters are used primarily in analyzing networks where the admittance (rather than impedance) of the network is of interest. They are particularly useful for high-frequency circuit analysis.
• The input admittance (y11y_{11}y11​) and the output admittance (y22y_{22}y22​) describe how the currents are related to the voltages at the respective ports.
• The off-diagonal terms y12y_{12}y12​ and y21y_{21}y21​ represent how the voltage or current at one port affects the current or voltage at the other port.

Summary:

The [y] parameters of a two-port network describe the relationship between the voltages and currents at the input and output ports using admittances. These parameters are useful for analyzing circuits in terms of how currents are related to voltages in the presence of admittance-based networks.