TwoPort Networks1 30 2021 30 TwoPort Network1 1

Two-Port Networks-1 30������� 2021 30������� Two-Port Network-1 1

To be Discussed l Multi-Port Networks. l Two-Port Network. l Six Possibilities of Characterization. l open-circuit, impedance, or z-paramters. Circuit Using z-parameters. l Conditions for Reciprocity and Symmetry. l Equivalent l Short-circuit, admittance, or y-paramters. Circuit Using y-Parameters. l Conditions for Reciprocity and Symmetry. l Equivalent 30������� 2021 30������� Two-Port Network-1 2

Port l. A port of a network consists of two terminals — one for the entry of current and other for its exit. l The currents in the two terminals of a port are equal. l ‘Porte’ in French means ‘door’. 30������� 2021 30������� Two-Port Network-1 3

Multi-Terminal Network 30������� 2021 30������� Two-Port Network-1 4

Multi-Port Networks (a) 3 -Port Network 30������� 2021 30������� (b) 5 -Port Grounded Network Two-Port Network-1 5

Two-Port Network The port variables are port currents I 1 and I 2 and the port voltages V 1 and V 2. Note the reference directions of currents and voltages. 30������� 2021 30������� Two-Port Network-1 6

l Assume linear time-invariant elements. l May contain dependent sources but not independent sources. l We need two linear equations in portvariables to characterize such a two-port network. l Two can be taken as the independent variables and the remaining two as the dependent variables. l The choice is just a matter of convenience for a given applications. 30������� 2021 30������� Two-Port Network-1 7

Six Possibilities impedance, or z-parameters. l Short-circuit, admittance, or y-parameters. l Hybrid, or h-parameters. l Inverse hybrid, or g-parameters. l Transmission, or ABCD-parameters. l Inverse transmission, or abcd-parameters l Open-circuit, 30������� 2021 30������� Two-Port Network-1 8

30������� 2021 30������� Two-Port Network-1 9

OPEN-CIRCUIT, IMPEDANCE, OR z-PARAMTERS Impedance Matrix 30������� 2021 30������� Two-Port Network-1 10

1. Input driving point impedance, 2. Reverse transfer impedance, 30������� 2021 30������� Two-Port Network-1 11

3. Forward transfer impedance, 4. Output driving point impedance, 30������� 2021 30������� Two-Port Network-1 12

Equivalent Circuit Using z-parameters It is just a picturization of the defining equations. 30������� 2021 30������� Two-Port Network-1 13

Alternate way of drawing the equivalent circuit. 30������� 2021 30������� Two-Port Network-1 14

Conditions for Reciprocity A network is said to be reciprocal, if 30������� 2021 30������� Two-Port Network-1 15

Condition for Symmetry A two-port network is said to be symmetrical if its ports can be interchanged without changing the port voltages and currents. 30������� 2021 30������� Two-Port Network-1 16

SHORT-CIRCUIT, ADMITTANCE, OR y-PARAMTERS Admittance Matrix 30������� 2021 30������� Two-Port Network-1 17

1. Input driving point admittance, 2. Reverse transfer admittance , 30������� 2021 30������� Two-Port Network-1 18

3. Forward transfer admittance 4. Output driving point admittance 30������� 2021 30������� Two-Port Network-1 19

Equivalent Circuit Using y-Parameters Picturizing the defining equations, 30������� 2021 30������� Two-Port Network-1 20

Alternatively, 30������� 2021 30������� Two-Port Network-1 21

Conditions for Reciprocity and Symmetry 30������� 2021 30������� Two-Port Network-1 22

Review l Multi-Port Networks. l Two-Port Network. l Six Possibilities of Characterization. l open-circuit, impedance, or z-paramters. Circuit Using z-parameters. l Conditions for Reciprocity and Symmetry. l Equivalent l Short-circuit, admittance, or y-paramters. Circuit Using y-Parameters. l Conditions for Reciprocity and Symmetry. l Equivalent 30������� 2021 30������� Two-Port Network-1 23