Z and Y Parameters

TWO-PORT NETWORK PARAMETERS

NETWORKS AND ELECTRICAL TECHNOLOGY LAB

CIRCUIT DIAGRAM:

Z- Parameters: To find Z11 and Z21:

V1

V2

I1

Z11=V1/I1

Z21=V2/I1

V2

I2

Z12=V1/I2

Z22=V2/I2

To find Z12 and Z22:

V1

NETWORKS AND ELECTRICAL TECHNOLOGY LAB

Y- parameters: To find Y11 and Y21:

V1

I1

I2

Y11=I1/V1

Y21=I2/V1

I1

I2

Y12=I1/V2

Y22=I2/V2

To find Y12 and Y22:

V1

NETWORKS AND ELECTRICAL TECHNOLOGY LAB

AIM: To find the Z & Y parameters of a two port network. APPARATUS: S.No.

Apparatus

Range

Type

Quantity

1

Rheostats

18Ω/8.6A

Wire wound

2

2

Rheostats

100Ω/5A

Wire wound

1

3

Ammeter

(0-2)A

MC

2

4

Voltmeter

(0-15)V

MC

2

THEORY : Two Port Networks : A pair of terminals at which a signal (voltage or current) may enter or leave is called a port.A network having only one such pair of terminals is called a one port network. A two-port network (or four-terminal network, or quadripole) is an electrical circuit or device with two pairs of terminals. Examples include transistors, filters and matching networks. A two-port network basically consists of isolating either a complete circuit or part of it and finding its characteristic parameters. Once this is done, the isolated part of the circuit becomes a "black box" with a set of distinctive properties, enabling us to abstract away its specific physical buildup, thus simplifying analysis. Any circuit can be transformed into a two-port network provided that it does not contain an independent source.

A two-port network is represented by four external variables: voltage and current at the input port, and voltage and current at the output port, so that the two-port network can be treated as a black box modeled by the relationships between the four variables. There exists six different ways to describe the relationships between these variables, depending on which two of the four variables are given, while the other two can always be derived. Z-model : In the Z-model or impedance model, the two currentsI1 and I2 are assumed to be known, and the voltages V1andV2can be found by:

NETWORKS AND ELECTRICAL TECHNOLOGY LAB

where

Y-model : In the Y-model or admittance model, the two voltagesV1 and V2 are assumed to be known, and the currents I1 and I2can be found by:

where

PROCEDURE:Z – Parameters 1. Connect the circuit as shown in figure1. 2. Open circuit port-2 (i.e I2 = 0 ) and measure V1,I2 and V2 and calculate Z11 & Z21 using the formulae V1 V I2 0 Z 21  2 I 2  0 I1 I1 Connect the circuit as shown in figure2. To Measure Z12 and Z22, open circuit port-1 (i.e. I1=0) and measure V1, V2 and I2 and calculate

Z11 

3. 4.

Z12 & Z21 using the formulae Z12 

V1 I1  0 I2

Z 22 

V2 I1  0 I2

Y – Parameters 1. Connect the circuit as shown in figure3. 2. Short circuit port-2 (i.e V2 = 0 ) and measure V1, I1 & I2 and calculate Y11 & Y21 using the formulae Y11 

I1 V2  0 V1

3.Connect the circuit as shown in figure3.

NETWORKS AND ELECTRICAL TECHNOLOGY LAB

Y21 

I2 V2  0 V1

4.To Measure Y12 and Y22, short circuit port-1 (i.e. V1=0) and measure V2, I1 and I2 and calculate Y12 & Y22 using the formulae Y12 

I1 V1  0 V2

Y22 

I2 V1  0 V2

TABULATION S. No. 1.

Parameter Z11

2.

Z12

3.

Z21

4.

Z22

5.

Y11

6.

Y12

7.

Y21

8.

Y22

Theoretical Value

Practical Value

RESULT: Hence Z-parameters and Y-parameters of a given circuit are found and verified with theoretical values.

VIVA VOCE: 1. What is meant by TWO PORT? 2.Name the individual Z parameters. 3. Name the individual Y parameters.

NETWORKS AND ELECTRICAL TECHNOLOGY LAB