Unit 4 twoportnetwork
Download as PPT, PDF16 likes14,264 views
The document provides a comprehensive overview of two-port network parameters, including z, y, abcd, and h-parameters, covering definitions, equations, conditions for symmetry and reciprocity, and their implications in various electrical systems. It highlights the significance of these parameters in simplifying complex network analyses by treating them as black boxes within larger circuits. Additionally, the document includes examples that demonstrate how to compute these parameters and assess the symmetry and reciprocity of different circuits.
Unit 4 twoportnetwork
- 1. PREPARED BY D V S RAMANJANEYULU ASST.PROF ACE ENGINEERING COLLEGE 1 UNIT-4 TWO PORT NETWORKS
- 2. Syllabus …… 2 Z,Y, ABCD and h- Parameters Conversion of one parameter to other Condition for Reciprocity and symmetry Two port networks connected in series, parallel and cascaded configurations Problem solving
- 3. 3
- 4. Port : A port is pair of terminals connecting an electrical network or circuit to an external circuit i.e it is a point of entry or exit for electrical energy Two Port network : A two port network is an electrical network having two pair of terminals to connect to an external circuit, with one pair at the input called input port and other at out put called theoutput port . 4
- 5. Knowing the parameters of a two port network enables us to treat it as a black box when embedded with in a larger network, thus making analysis of network (large circuitsin particular) very easy . Thistechniqueiswell applied in areasof Communication Electronics Control system Power system 5
- 6. 6 APPROACH TO TWO PORT PARAMETERS There are four variables �1, �2 , �1 and �2 associated with a two port network . Two of these variables can be expressed in terms of other two variables. Thus there will be two dependent variables and two independent variables. The number of possible combinations generated by four variables taken two at a time is six i.e there are 6 possible sets of equations describing a two-port network 6
- 7. 7
- 8. Z- PARAMETERS (OPEN CIRCUIT PARAMETERS) TheZ-parametersof atwo port network may bedefined by expressing two port voltages�1 𝑎𝑛𝑑 �2 in termsof two port currents�1 and �2 Matrix Form Open circuit input impedance Open circuit reverse transfer impedance Open circuit forward transfer impedance Open circuit output impedance 8
- 9. CONDITION FOR SYMMETRY AND RECIPROCITY OF Z PARAMETERS Symmetry : For the network to be symmetrical, the voltage-to- current ratio at oneport should bethesameasthevoltage-to-current ratio at theother port with oneof theport short circuited. Condition for symmetry 9
- 10. Reciprocity : 10 A network issaid to bereciprocal if thetheratio of excitation at oneport to responseat other port issame if excitation and responsesareinterchanged Condition for Reciprocity
- 11. Y- PARAMETERS (SHORTCIRCUIT PARAMETERS) TheY-parametersof atwo port network may bedefined by expressing two port currents�1 and �2 in termsof two port voltages�1 𝑎𝑛𝑑 �2 Matrix Form Short circuit input admittance short circuit reverse transfer admittance short circuit forward transfer admittance short circuit output admittance 11
- 12. CONDITION FOR SYMMETRY AND RECIPROCITY OF Y PARAMETERS Symmetry : For the network to be symmetrical, the voltage-to- current ratio at oneport should bethesameasthevoltage-to-current ratio at theother port with oneof theport short circuited. Condition for symmetry 12
- 13. A network issaid to bereciprocal if thetheratio of excitation at one port to responseat other port issameif excitation and responsesare interchanged Condition for Reciprocity 13
- 14. ABCD - PARAMETERS (TRANSMISSION LINE PARAMETERS) The ABCD-parameters of a two port network serve to relate the voltage and currentsof input port (�1 𝑎𝑛𝑑 �1) to voltageand currentsof output port (�2and �2) Matrix Form 14
- 15. CONDITION FOR SYMMETRY AND RECIPROCITY OF Y PARAMETERS Symmetry : For the network to be symmetrical, the voltage-to- current ratio at oneport should bethesameasthevoltage-to-current ratio at theother port with oneof theport short circuited. Condition for symmetry 15
- 16. Reciprocity : 16 A network issaid to bereciprocal if thetheratio of excitation at oneport to responseat other port issame if excitation and responsesareinterchanged Condition for Reciprocity
- 17. h – PARAMETERS (Hybrid PARAMETERS) The h -parameters of a two port network serve to relate the voltage of input port (�1) 𝑎𝑛𝑑 current of output port ( �2) in terms of currents of input port (�1) and voltageof output port (�2) Matrix Form 17
- 18. CONDITION FOR SYMMETRY AND RECIPROCITY OF h PARAMETERS Condition for symmetry 18
- 19. Reciprocity : 19 A network issaid to bereciprocal if thetheratio of excitation at oneport to responseat other port issame if excitation and responsesareinterchanged Condition for Reciprocity
- 20. SYNOPSIS OF ALL PARAMETERS 20
- 21. EQUIVALENT CIRCUITS OF ALL PARAMETERS Transmission line parameters NOT POSSIBLE v 21
- 22. Example 1 : Find Z-parametersfor thecircuit shown below and comment on symmetry and reciprocity of circuit Ans : � 𝟏𝟏 = � 𝟏 +�� � 𝟏� = �� ��𝟏 = �� ��� = �� +�� RECIPROCAL SYMMETRICAL IF � 𝟏 = �� 22
- 23. 23
- 24. 24
- 25. Ans : � 𝟏𝟏= 11/5 � 𝟏� = 4/5 ��𝟏 = 4/5 ��� = 6/5 Example 2 : Find Z-parametersfor thecircuit shown below and comment on symmetry and reciprocity of circuit 25
- 26. 26
- 27. Example 3 : Find open circuit parametersfor thecircuit shown ANS 27
- 28. 28
- 29. Example 4 : 29
- 30. Example 1 : Find Y-parametersfor thecircuit shown below and comment on symmetry and reciprocity of circuit Ans : � 𝟏𝟏 = 5/11 � 𝟏� = -2/11 ��𝟏 = -2/11 ��� = 3/11 Circuit is reciprocal (since � 𝟏� = ��𝟏 ) Non symmetrical (since � 𝟏𝟏 ≠ ��� ) 30
- 31. 31
- 32. Example 2 : Find Y-parametersfor thecircuit shown below and comment on symmetry and reciprocity of circuit Ans : � 𝟏𝟏 = 1/2 � 𝟏� = -1/4 ��𝟏 = -1/4 ��� = 5/8 Circuit is reciprocal (since � 𝟏� = ��𝟏 ) Not symmetrical (since � 𝟏𝟏 ≠ ��� ) 32
- 33. 33
- 34. Example 3 : Find Y-parametersfor thecircuit shown below and comment on symmetry and reciprocity of circuit ANS 34
- 35. 35
- 36. Example 1 : Find transmission parametersfor thecircuit shown below and comment on symmetry and reciprocity of circuit Ans : A= 6/5 B= 17/5 C= 1/5 D= 7/5 Circuit is NOT reciprocal (since AD-BC ≠ 1) Not symmetrical (since A ≠ D) 36
- 37. 37
- 38. 38
- 39. Example 2 : Find ABCD parametersfor thecircuit shown below and comment on symmetry and reciprocity of circuit Ans : A= 11/4 B= 5/2 C= 5/4 D= 3/2 Circuit is NOT reciprocal (since AD-BC ≠ 1) Not symmetrical (since A ≠ D) 39
- 40. 40
- 41. Example 3 : Find ABCD parametersfor thecircuit shown below Ans : 41
- 42. 42
- 43. Example 1: 43
- 44. Example 2 : Find hybrid parametersfor thecircuit shown below and comment on symmetry and reciprocity of circuit Ans : � 𝟏𝟏 = 2 � 𝟏𝟐 = 1/2 � 𝟐𝟏 = -1/2 � 𝟐𝟐 = 1/2 Circuit is reciprocal (since � 𝟏𝟐 = − � 𝟐𝟏 ) Non symmetrical (since � 𝟏𝟏 � 𝟐𝟐 − � 𝟐𝟏 � 𝟏𝟐 ≠1) 44
- 45. 45
- 46. 46
- 47. INTER-RELATIONSHIPS BETWEEN PARAMETERS Objective :When it is required to find out two or more parameters of a particular network then finding each parameter will be tedious. But if we find a particular parameter then the other parameters can be found if the inter-relation ship between them in known. 47
- 48. Wher ∆ 𝒁 = 𝒁 𝟏𝟏 𝒁 𝟐𝟐− 𝒁 𝟏𝟐 𝒁 𝟐𝟏 , ∆ 𝒚 = � 𝟏𝟏 � 𝟐𝟐- � 𝟏𝟐 � 𝟐𝟏 , ∆ 𝑯 = � 𝟏𝟏 � 𝟐𝟐− � 𝟏𝟐 � 𝟐𝟏 , ∆�=AD-BC Z-Parameters Y-Parameters T-Parameters H-Parameters 48
- 49. 1. Z-Parameters in terms of Y-Parameters 49
- 50. 2. Z-Parameters in terms of ABCD -Parameters 50
- 51. 3. Z-Parameters in terms of H-Parameters 51
- 52. 1. Y-Parameters in terms of z-Parameters 52
- 53. 2. Y-Parameters in terms of T-Parameters 53
- 54. 3. Y-Parameters in terms of H -Parameters 54
- 55. 1. ABCD -Parameters in terms of z-Parameters 55
- 56. 2. ABCD -Parameters in terms of Y-Parameters 56
- 57. 3. ABCD -Parameters in terms of H-Parameters 57
- 58. 1. H -Parameters in terms of z-Parameters 58
- 59. 2. H -Parameters in terms of Y-Parameters 59
- 60. 3. H -Parameters in terms of ABCD -Parameters 60
- 61. Example 1 : TheZ-Parametersof 2 port network are�11= 20ohm, �12= �21= 10ohm, �22= 30 ohm. Find Y and ABCD Parameters.61
- 62. 62
- 63. Example 2 : Currents�1 and �2 entering at port1 and port2 respectively of a2 port network isgiven by following equation Find Y , Z and ABCD Parametersof network. 63
- 64. 64
- 65. 65
- 66. Example 1 : Two identical sectionsof thenetwork shown in figureare connected in series.Obtain Z parametersof over all network 66
- 67. 67
- 68. Example 2 : Obtain Z parametersof following network. 68
- 69. 69
- 70. Example 3 : Obtain Y parametersof following network. 70
- 71. 71
- 72. 72
- 73. Example 4: Two identical sections of the network shown are connected in cascade. Obtain the transmission parameters of over all network 73
- 74. 74