Question

How to find y parameters in two-port network?

Answer 1

In electrical engineering, a two-port network is a mathematical model used to describe the behavior of a network with two pairs of terminals. The y-parameters, or admittance parameters, are one way to characterize the network. They relate the input and output currents and voltages in a specific way. Here's a detailed explanation of how to find the y-parameters for a two-port network:

### Definitions

In a two-port network, you have:

- **Port 1:** with voltage \( V_1 \) and current \( I_1 \)
- **Port 2:** with voltage \( V_2 \) and current \( I_2 \)

The y-parameters are defined as follows:

\[
I_1 = y_{11} V_1 + y_{12} V_2
\]
\[
I_2 = y_{21} V_1 + y_{22} V_2
\]

Where:
- \( y_{11} \): input admittance (current into port 1 per unit voltage at port 1)
- \( y_{12} \): transfer admittance from port 2 to port 1
- \( y_{21} \): transfer admittance from port 1 to port 2
- \( y_{22} \): output admittance (current into port 2 per unit voltage at port 2)

### Steps to Find the Y-Parameters

1. **Set Up the Network:**
   Begin by identifying the two-port network you want to analyze. This can be a circuit consisting of resistors, capacitors, inductors, or a combination of these.

2. **Calculate Y-Parameters:**
   To find the y-parameters, you typically need to conduct a series of tests by applying known voltages and measuring the resulting currents.

   - **Step 1: Determine \( y_{11} \)**
     - Short circuit port 2 (\( V_2 = 0 \)).
     - Apply a known voltage \( V_1 \) at port 1.
     - Measure the resulting current \( I_1 \).
     - Calculate \( y_{11} \):
     \[
     y_{11} = \frac{I_1}{V_1} \text{ (when } V_2 = 0\text{)}
     \]

   - **Step 2: Determine \( y_{12} \)**
     - Set \( V_1 = 0 \) (short circuit port 1).
     - Apply a known voltage \( V_2 \) at port 2.
     - Measure the resulting current \( I_1 \).
     - Calculate \( y_{12} \):
     \[
     y_{12} = \frac{I_1}{V_2} \text{ (when } V_1 = 0\text{)}
     \]

   - **Step 3: Determine \( y_{21} \)**
     - Short circuit port 2 again.
     - Apply a known voltage \( V_1 \) at port 1.
     - Measure the resulting current \( I_2 \).
     - Calculate \( y_{21} \):
     \[
     y_{21} = \frac{I_2}{V_1} \text{ (when } V_2 = 0\text{)}
     \]

   - **Step 4: Determine \( y_{22} \)**
     - Set \( V_1 = 0 \) again.
     - Apply a known voltage \( V_2 \) at port 2.
     - Measure the resulting current \( I_2 \).
     - Calculate \( y_{22} \):
     \[
     y_{22} = \frac{I_2}{V_2} \text{ (when } V_1 = 0\text{)}
     \]

### Summary

Once you've conducted these measurements and calculations, you will have all four y-parameters \( y_{11}, y_{12}, y_{21}, \) and \( y_{22} \). These parameters are particularly useful in analyzing the stability and frequency response of circuits, especially in RF and microwave applications.

### Example

Let’s say you have a two-port network with the following measurements:

- When \( V_1 = 1V \) and \( V_2 = 0V \), \( I_1 = 0.5A \) gives \( y_{11} = 0.5 \, S \).
- When \( V_1 = 0V \) and \( V_2 = 1V \), \( I_1 = 0.1A \) gives \( y_{12} = 0.1 \, S \).
- When \( V_1 = 1V \) and \( V_2 = 0V \), \( I_2 = 0.3A \) gives \( y_{21} = 0.3 \, S \).
- When \( V_1 = 0V \) and \( V_2 = 1V \), \( I_2 = 0.2A \) gives \( y_{22} = 0.2 \, S \).

Thus, the y-parameters for this network would be:
- \( y_{11} = 0.5 \, S \)
- \( y_{12} = 0.1 \, S \)
- \( y_{21} = 0.3 \, S \)
- \( y_{22} = 0.2 \, S \)

This methodology provides a systematic way to analyze two-port networks using y-parameters effectively.

Answer 2

To find the Y parameters (admittance parameters) of a two-port network, you need to determine the relationship between the port voltages and currents. The Y parameters are defined by the following equations:

1. **I1 = Y11 * V1 + Y12 * V2**
2. **I2 = Y21 * V1 + Y22 * V2**

Where:
- \( I1 \) and \( I2 \) are the currents at ports 1 and 2.
- \( V1 \) and \( V2 \) are the voltages at ports 1 and 2.
- \( Y11 \), \( Y12 \), \( Y21 \), and \( Y22 \) are the admittance parameters.

To find these parameters:

1. **Determine \( Y11 \)**: Short circuit port 2 (set \( V2 = 0 \)), and measure the current \( I1 \) as a function of \( V1 \). \( Y11 \) is then \( I1 / V1 \).

2. **Determine \( Y12 \)**: Open circuit port 1 (set \( V1 = 0 \)), and measure the current \( I2 \) as a function of \( V2 \). \( Y12 \) is then \( I2 / V2 \).

3. **Determine \( Y21 \)**: Open circuit port 2 (set \( V2 = 0 \)), and measure the current \( I1 \) as a function of \( V1 \). \( Y21 \) is then \( I1 / V1 \).

4. **Determine \( Y22 \)**: Short circuit port 1 (set \( V1 = 0 \)), and measure the current \( I2 \) as a function of \( V2 \). \( Y22 \) is then \( I2 / V2 \).

By performing these measurements and calculations, you can determine the Y parameters of the two-port network.