Open circuit and Short circuit impedance of a two-port network in terms of ABCD parameters   From the generalized ABCD parameter equation V1=AV2 – BI2 I1=CV2 – DI2 Applying Open circuit at port-2; I2=0 we get   V1= AV2;                               I1= CV2 Z1O   =   V1/I1= A/C   ------------------------------(i) Applying the short circuit at port-2; V2=0, we get V1= - BI2 I1=-DI2 Or Z1S = V1/I1 = B/D                --------------------------(ii) Now looking from port and applying: Open circuit port-1, I1=0 0 = CV2 – DI2 CV2= DI2 Z2O = V2/I2 = D/C                               --------------------------(iii) Now short circuiting the port-1, V1=0, we get 0 = AV2 – BI2 AV2  =  BI2 Z2s   =  V2/I2 = B/A             ---------------------------(iv) Ratio of open circuit to short circuit ratio Z1O/ Z1S = (B/D)(C/A)     --------------------------(v) To find ABCD parameters Z2O   -   Z2S = D/C – B/A     = (AD –BC)/CA But for the two network to be reciprocal, the

Interconnection of Networks: With the concept that impedance in series are additive and admittance in parallel are additive, we can easily solve the series and parallel combination of networks in terms of Z and Y parameters respectively. Networks can be connected in: Parallel connection Series Connection Parallel Connection of two-port networks Figure:1 Parallel connection of two networks We know the basic Y parameter equation as: From the figure, it can be seen that V1 =        V1a          =             V1b V2 =        V2a          =             V2b And currents in parallel I1             =             I1a           +             I1b I2             =             I2a           +             I2b The Y parameters in series are the additive I1   =  Y11a V1a +   Y12a V2a = (Y11a + Y11b)V1     +  (Y12a + Y12b)V2 I2   =  Y21a V1a +   Y22a V2a  = (Y21a

Inter-relationship between the two-port Parameters The following steps of operations can be used for the transformation one set of parameters in terms of other set of parameters: Step 1. Write the standard equations for both sets. Step 2. Solve or rearrange the second set of equations and writing them in terms of the independent variables of 1st set of equations. Step 3. Compare the equations obtained in step 2 with those of the first set to obtain the required parameters. Z parameter in terms of Y parameters Step-1: Writing Z and Y parameter equations Z parameter equation Y parameter equation V1= Z11I1  + Z12I2 V2= Z21I1 + Z22I2 I1= Y11V1 + Y12V2 I2= Y21V1 + Y22V2   Step-2: Solve or rearrange the second set of equations and writing them in terms of the independent variables of 1st

Reciprocity Condition in two port Parameters Reciprocity Theorem states that the two networks are said to be reciprocal of each other if the ratio of the source voltage t one port to response (current) in other branch remain unchanged upon interchanging the position of the excitation and the response From Network-1, the Response to Excitation ratio=  I2’/ Vs From Network-2, the Response to Excitation ratio=  I1’/ Vs therefore for the two networks to be reciprocal  :       I2’/ Vs  =  I1’/ Vs Reciprocity in Z Parameter The generalized Z parameters equations are: V1  = Z11I1  + Z12I2 V2  = Z21I1 +  Z22I2 Case-1: Port-2 shorted, V2=0, I2=-I2’; and V1=Vs Case-2:  Port-1 shorted, V1=0, I1=-I1’; and V2=Vs So the equations become: Vs  = Z11I1  - Z12 I2’-------------(1) 0   =  Z21I1 - Z22 I2’  --------------(2) From (2) I1 = (Z22/ Z21) I2’ Putting it

Transmission Parameters: A network is an interconnection of basic electrical elements. A network is called an electric circuit when it has current and voltage sources connected to it. Thus an electric is a closed energized network. Figure below shows an electric network and an electrical circuit. Two-Port Network We can write the equations for the dependent variable in terms of the independent variables (V1,V2) = f(I1,I2) [V] =[Z][I] For a two-port network V1=Z11I1  +  Z12I2 V2=Z21I1  +  Z22I2 Solving When I2 =0, the equation reduces to V1=Z11I1 ; so we get         Z11=  V1/I1 V2=Z21I1 ; so we get         Z21=  V2/I1 When I1 =0, the equation reduces to V1=Z12I2 ; so we get         Z12=  V1/I2 V2=Z22I2 ; so we get         Z22=  V2/I2 Equivalent Circuit of Loop equations We know the two loop equations: V1=Z11I1  +  Z12I2 V2=Z21I1  +