2. Two – Port Network

2.1. Impedance parameters

A linear two port network represented by black box is considered, having I1 and I2 as independent variables and V1 and V2 as dependent variables.

                            V1 = f1 ( I1, I2 )

                                             V2 = f2 ( I1, I2 )                                                  ------ (2.1)

            The changes in the dependent variables may be given by:

                                                                    ∂V                  ∂V

                                                 dV 1dI 1dI 2 ∂I         ∂I

                                       dV 2

=

dI 1 +

dI 2 ------ (2.2)

 The partial derivatives in these equations become constant with operation over linear region of the device curve with constant slope.

            The equations may, therefore, be written as: 

                                            V 1 = Z 11 I 1 + Z 12 I 2

                                           V 2 = Z 21 I 1 + Z 22 I 2               ------      (2.3)

            In the matrix form it is given by:

                                                       V1    Z 11      Z 12 I 1

=

                                                                            ------ (2.4)

                                                      V 2    Z 21      Z 22 I 2

                 Where Z’s are the impedance (resistance for d. c.) parameters, which may be defined as:

                                                         Z 11 =, is the input impedance when output is open

I 2 = 0

circuited or open- circuit input impedance.

                                                            Z 12 = , is the reverse transfer impedance when

I 1 = 0

input is open circuited or open circuit reverse transfer impedance.

                                                            Z 21 =, is the forward transfer impedance when

I 2 = 0

output is open circuited or open circuit forward transfer impedance. and                            Z 22 =, is the output impedance when input is open

I 1 = 0

circuited or open circuit output impedance.

 These Z parameters also known as open circuit parameters, since in these parameters either input or output is open circuited. The equivalent circuit of the network using Z- parameters may be drawn as given below: