# Verify Y-Parameters of Two-port Network

## Aim

To calculate and verify Y-parameters of two-port network.

## Apparatus

Breadboard, Batteries or DC regulated power supply, Resistors, Digital multimeter, Connecting wires, Alligator clips.

## Theory

Y parameters (also known as admittance parameters or short-circuit parameters) are properties used in electrical engineering to describe the electrical behaviour of linear electrical networks.

For any two-port network, input voltage V1 and output voltage V2 can be expressed in terms of input current I1 and output current I2 respectively.

The Y parameter for a two-port network is defined as

[ I ] = [ Y ] [ V ]

where [ Y ] is the admittance matrix, [ I ] and [ V ] are the current and voltage matrix. From the above matrix form representation of two port network, it is clear that there are four admittance parameters i.e. Y11, Y12, Y21 and Y22.

From the above matrix, we get,

I1 = Y11V1 + Y12V2                …(1)

I2 = Y21V1 + Y22V2                …(2)

• Assuming the output of the two-port network to be short circuited, therefore V2= 0

Now putting V2 = 0 in (1), we get

I1 = Y11V1

Y11 = (I1 / V1)

Similarly putting V2 = 0 in (1), we get

I2 = Y21V1

Y21 = (I2 / V1)

• Again, assuming input port of the two-port network to be short circuited, the input voltage will be zero. i.e. V1= 0

Now putting V1 = 0 in (1), we get

I1 = Y12V2

Y12 = (I1 / V2)

Similarly putting V1 = 0 in (2), we get

I2 = Y22V2

Y22 = (I2 / V2)

Thus, there are four Y parameter for a two port or four terminal network. Their values are tabulated below.

 Y11 (I1 / V1) Condition: Output port of the two-port network is short circuited i.e. V2 = 0 Y21 (I2 / V1) Y12 (I1 / V2) Condition: Input port of the two-port network is short circuited i.e. V1 = 0 Y22 (I2 / V2)

### Significance of Different Y Parameter

• Since Y11is the ratio of input current and voltage when the output port is short circuited, therefore it is known as input driving point admittance.
• Y22is the ratio of output current and voltage when input port is short circuited, therefore it is called output driving point admittance of the network.
• Y12is the ratio of input current and output voltage when input port is short circuited, therefore it is called reverse transfer admittance.
• Y21is the ratio of output current and input voltage when output port is short circuited, therefore it is called forward transfer admittance.

## Circuit Diagram

[Recommended values: R1= 2KΩ, R2= 450Ω, R3= 1kΩ, V1= 10V and V2= 5V OR chose any resistor between 200Ω to 2KΩ and DC supply beween 5V to 12V]

## Procedure

1. Connect the circuit as shown in figure 2.
2. First short the output port (port 2) and supply 10V to input port (port 1). Measure output current and input current using multi-meter.
3. Secondly, short circuit input port and supply 5V to output port. Measure input current and output current using multi-meter.
4. Calculate the values of Y-parameters using respective formulas (Shown in calculation section).
5. Switch ‘OFF’ the supply after taking the readings.

## Precautions

• Before circuit connection working condition of all the components must be checked.
• All the connection should be tight.
• Ammeter must be connected in series while voltmeter must be connected in parallel to the components (resistors).
• The electrical current should not flow the circuit for long time, otherwise its temperature will increase and the result will be affected.

## Observation table

 When output port is short circuited When input port is short circuited V1 I1 I2 V2 I1 I2

## Calculations

For Practical Values:

(a) When output is short circuited i.e. V2 = 0

Y11= I1/V1 = ____S

Y21 = I2/V1 = ____S

(b) When input is short circuited i.e. V1 = 0

Y12 = I1/V2 = ____S

Y22 = I2 /V2 = ____S

For Theoretical Values:

[Use any method to calculate Y-parameters]

Y11 = ____S

Y22 = ____S

Y12 = ____S

Y21 = ____S

## Result

 Parameter→ Y11 Y12 Y21 Y22 Theoretical Practical

## Conclusion

Calculated and practical values of Y-parameters are found to be nearly equal hence Y-parameters are verified.