conversion of parameters, H and T and interconnection

H AND T PARAMETERS ,
CONVERSION OF PARAMETERS AND INTERCONNECTION OF TWO PORT NETWORKS

1. Network Theory H AND T PARAMETERS , CONVERSION OF PARAMETERS AND INTERCONNECTION OF TWO PORT NETWORKS

2. What are Two port networks?

3. TWO PORT NETWORK A two-port network (a kind of four-terminal network or quadripole ) is an electrical network (circuit) or device with two pairs of terminals to connect to external circuits

4. TWO PORT NETWORK A two-port network is regarded as a "black box" with its properties specified by a matrix of numbers . This allows the response of the network to signals applied to the ports to be calculated easily, without solving for all the internal voltages and currents in the network

5. EXAMPLES OF TWO PORT NETWORKS Examples of circuits filters, matching networks, transmission lines, transformers, small-signal models for transistors (such as the hybrid-pi model)…

6. TWO PORT NETWORK PARAMETERS: Impedance parameters Admittance parameters Hybrid parameters Inverse-hybrid parameters Transmission parameters Scattering parameters Scattering transfer parameters

7. HYBRID PARAMETERS

8. HYBRID(H)PARAMETERS Hybrid parameters are also referred as h parameters. These are referred as hybrid because, here Z parameters, Y parameters, voltage ratio, current ratio, all are used to represent the relation between voltage and current in a two port network

9. H PARAMETERS Hybrid parameters or h parameters are very much useful in analysing electronics circuit where, transistors like elements are connected. In those circuits, sometimes it is difficult to measure Z parameters and Y parameters but Hybrid parameters can be measured in much easier way

10. H PARAMETERS Even in case of an ideal transformer, Z parameter can not be used Since, the relations between voltages and current in that ideal transformer would be It is impossible to analyse a transformer with Z parameters because a transformer does not have Z parameters

11. INDIVIDUAL VALUES h 11 is Short circuit input Impedance h 12 is Open circuit reverse voltage gain h 21 is Short circuit forward current gain h 22 is Open circuit output Admittance

12. CALCULATION For h 11 and h21 , the condition is that V 2 = 0 Which means that the right side of the two port network is Short circuited. For h 12 and h 22 , the condition is I 1 = 0 which means that the left side of the two port network is Open circuited.

13. H PARAMETER EQUIVALENT CIRCUIT

14. Inverse Hybrid(G) Parameters There is another set of parameters which is closely related to set of  h parameters . The relations between currents and voltages with  g parameters  are represented as,

15. ABCD (T) PARAMETERS

16. T PARAMETERS A major section of power system engineering deals in the transmission of electrical power from one particular place (e.g. generating station) to another like substations or distribution units with maximum efficiency. Thus the entire transmission system can be simplified to a two port network for the sake of easier calculations

17. T PARAMETERS Transmission Parameters relate the variables at the Input port and the variables at the Output port of a two port network.

18. INDIDVIDUAL VALUES A is Open circuit Voltage ratio B is Negative short circuit transfer Impedance C is Open circuit transfer Admittance D is Negative short circuit current ratio

19. Parameter Specification Unit A = V S  / V R Voltage ratio Unit less B = V S  / I R Short circuit resistance Ω C = I S  / V R Open circuit conductance mho D = I S  / I R Current ratio Unit less

20. OTHER

21. SUMS IN H AND T PARAMETER H PARAMETERS T PARAMETERS

22. CONVERSION OF PARAMETERS

23. INTERCONNECTION OF TWO PORT NETWORKS

24. Types Series connection Parallel connection Series - parallel connection Parallel - Series connection Cascade connection

25. CONDITIONS FOR INTERCONNECTION The combination rules need to be applied with care. Some connections (when dissimilar potentials are joined) result in the port condition being invalidated and the combination rule will no longer apply. A Brune test can be used to check the permissibility of the combination

26. BRUNE’S TEST It is used to check the permissibility of the combination of two or more two-port networks (or quadrupoles) in electrical circuit analysis. Tests whether the network still meets the port condition after the two-ports have been combined. Otto Walter Heinrich Oscar Brune

27. SERIES – SERIES CONNECTION When two-ports are connected in a series-series configuration, the best choice of two-port parameter is the z-parameters. The z-parameters of the combined network are found by matrix addition of the two individual z-parameter matrices.

28. SERIES – SERIES CONNECTION

29. SERIES – SERIES CONNECTION

30. BRUNE’S TEST FOR SERIES – SERIES CONNECTION Voltage is applied to the input and the open-circuit voltage is measured/calculated between the output terminals to be connected. If there is a voltage drop, the two-port networks cannot be combined in series. The same test is repeated from the output side of the two-port networks Only if there is no voltage drop in both cases, a combination of the two-ports networks is permissible.

31. BRUNE’S TEST FOR SUCCESFUL SERIES – SERIES CONNECTION

32. BRUNE’S TEST FOR SERIES – SERIES CONNECTION FAILURE

33. PARALLEL-PARALLEL CONECTION When two-ports are connected in a parallel-parallel configuration, the best choice of two-port parameter is the  y -parameters. The  y -parameters of the combined network are found by matrix addition of the two individual  y -parameter matrices.

34. PARALLEL OF TWO PORT NETWORKS

35. PARALLEL OF TWO PORT NETWORKS

36. BRUNE’S TEST FOR PARALLEL-PARALLEL CONNECTION Voltage is applied to the input and the open-circuit voltage is measured/calculated between the outputs that are short-circuited each. If there is a voltage drop, the two-port networks cannot be combined in parallel. The same test is repeated from the output side of the two-port networks. Only if there is no voltage drop in both cases, a combination of the two-ports networks is permissible.

37. BRUNE’S TEST FOR SUCCESSFUL PARALLEL-PARALLEL CONNECTION

38. SERIES-PARALLEL CONECTION Two two-port networks with input ports connected in series and output ports connected in parallel The  h -parameters of the combined network are found by matrix addition of the two individual  h -parameter matrices

39. SERIES-PARALLEL CONECTION

40. PARALLEL-SERIES CONECTION Two two-port networks with input ports connected in parallel and output ports connected in series The g-parameters of the combined network are found by matrix addition of the two individual g-parameter matrices.

41. PARALLEL-SERIES CONNECTION

42. BRUNE’S TEST FOR SUCCESSFULL SERIES-PARALLEL CONNECTION

43. CASCADING OF TWO PORT NETWORKS Two two-port networks with the first's output port connected to the second's input port. the best choice of two-port parameter is the ABCD-parameters.

44. CASCADING OF TWO PORT NETWORKS The  a -parameters of the combined network are found by matrix multiplication of the two individual  a -parameter matrices, To combine a cascade of  b -parameter matrices, they are again multiplied, but the multiplication must be carried out in reverse order, so that A chain of n two-ports may be combined by matrix multiplication of the n matrices

45. CASCADING OF TWO PORT NETWORKS

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