Chapter 18 Two-port Networks

the four terminals have been paired into ports four-terminal network two-port network KCL At all times, the instantaneous current flowing into one terminal is equal to the instantaneous current flowing out the other. i1 i2 i3 i4 i1 i4 i1=-i2 ; i3=-i4 i1+i2+i3+i4=0(KCL)

The network is linear(without independent sources).

Impedance Parameters Impedance or z parameters are defined by impedance matrix Z                                          Open-circuit input impedance. Open-circuit transfer impedance from port 1 to port 2 Open-circuit transfer impedance from port 2 to port 1 Open-circuit output impedance.

Determining of the z parameters: (a) finding z11 and z21, (b) finding z12 and z22 Examples

(a) T equivalent circuit (for reciprocal case only), (b) general equivalent circuit

Admittance Parameters Admittance or y parameters are defined by admittance matrix Y Short-circuit input admittance. Short-circuit transfer admittance from port 1 to port 2 Short-circuit transfer admittance from port 2 to port 1 Short-circuit output admittance.

Determination of the y parameters: (a) finding y11 and y21, (b) finding y12 and y22.

(a) -equivalent circuit (for reciprocal case only), (b) general equivalent circuit.

Hybrid Parameters Hybrid or h parameters are defined by hybrid matrix Z Short-circuit input impedance. Open-circuit reverse voltage gain Short-circuit forward current gain Open-circuit output admittance.

The h-parameter equivalent network of a two-port network

Inverse hybrid parameters (g parameters) The g-parameter model of a two-port network

Transmission Parameters Transmission or T parameters are defined by Transmission matrix T Open-circuit voltage ratio Negative short-circuit transfer impedance Open-circuit transfer admittance Negative short-circuit current ratio

Inverse transmission parameters

Reciprocal Two-Port Circuits ------------- linear and has no dependent source If a two-port circuit is reciprocal, the following relationships exist among the port parameters:

Symmetric Two-Port Circuit A reciprocal two-port circuit is symmetric if its ports can be interchanged without disturbing the values of the terminal currents and voltages. If a two-port circuit is symmetric, the following relationships exist among the port parameters: (besides those exist in reciprocal)

Question: How many calculations or measurements are needed to determine a set of parameters of a two-port circuit? For a general two-port with sources: 6 For a general linear two-port: 4 For a reciprocal two-port: 3 For a symmetric two-port: 2

Relationships between parameters Example: z parameters y parameters

Interconnection of networks Series connection of two two-port networks

Parallel connection of two two-port networks

Cascade connection of two two-port networks

Transistor amplifier with source and load resistance