Question

[y] = ?

I had been asked this question in an international level competition.

The question is from Two Port Network in portion EDC Overview of Electronic Devices & Circuits

Answer 1

The [y] matrix, or admittance matrix, for a two-port network is used to relate the input and output currents to the input and output voltages. It is defined as:

[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​​]

Where:

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

Thus, the [y] matrix represents the following set of equations:

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, representing the current at port 1 due to the voltage at port 1, with port 2's voltage held constant.
• y12y_{12}y12​: Reverse transfer admittance, representing the current at port 1 due to the voltage at port 2, with port 1's voltage held constant.
• y21y_{21}y21​: Forward transfer admittance, representing the current at port 2 due to the voltage at port 1, with port 2's voltage held constant.
• y22y_{22}y22​: Output admittance, representing the current at port 2 due to the voltage at port 2, with port 1's voltage held constant.

These parameters are commonly used in high-frequency or microwave circuits, where admittance is more useful than impedance for analysis. The [y] matrix provides a compact way to represent the relationships between voltages and currents at the ports of the two-port network.