Network Analysis and Synthesis. Chapter 5 Two port networks

Transcription

1 Network Anlsis nd Snthesis hpter 5 Two port networks

2 . ntroduction A one port network is completel specified when the voltge current reltionship t the terminls of the port is given. A generl two port on the other hnd hs two pirs of voltge nd current reltionships.

3 The vrile re,,, Two of these re independent vriles, while the rest re dependent vriles. Hence, there re six possile set of equtions tht descrie two port networks. There re vrious ws to write these reltionships Z,, H nd ABD prmeters. We will discuss ech description. 3

4 . Z-prmeters A prticulr set of equtions tht descrie two port networks re Z-prmeter equtions Z Z Z Z n these equtions nd re the dependent vriles, while nd re the independent vriles. 4

5 The individul -prmeters re defined s 0 0 All the -prmeters hve unit of impednce. The individul -prmeters re specified when the current in one of the ports is ero. i.e. open circuit. Hence, sometimes referred s open circuit prmeters

6 Z reltes the voltge nd current in the first port, while Z reltes the voltge nd current in the second port. These re referred s open circuit driving point impednces. Z reltes the voltge on the first port to the current in the second port, while Z reltes the voltge in second port with the current in the first port. These re referred s open circuit trnsfer impednces. 6

7 Exmple Find the open circuit impednces for the following T circuit. Solution: c Z Z Z Z Z Z Z Z Z Z 7

8 Note tht in the previous exmple Z =Z, hence, the circuit is reciprocl. Most pssive time-invrint networks re reciprocl. 8

9 3. -prmeters The -prmeters re defined s The voltges nd t the ports re the independent vriles, where s the currents through the two ports re the dependent vriles. 9

10 The individul -prmeters re specified s All the -prmeters hve unit of dmittnce. The individul -prmeters re specified when the voltge t one of the ports is ero. i.e. short circuit. Hence, sometimes referred s short circuit prmeters. 0 0

11 Exmple Find the -prmeters of the following circuit. Soln.: Using mesh nlsis, we cn write the following equtions s s s s s

12 Solving for nd, we get

13 Exmple 3 Find the -prmeters for the following π circuit. Solution: We short circuit port to find the nd. We short circuit port to find the nd. A B 3

14 4. H prmeters A set of prmeters tht re ver useful in descriing trnsistor circuits re h prmeters. H prmeters re given the following eqution h h h h nd re the independent vriles, wheres nd re dependent vriles. 4

15 The individul h prmeters re descried s h nd h re short circuit prmeters, while h nd h re open circuit prmeters. Note tht h h h =/. 0 0 h h 0 0 h =/ While h nd h re trnsfer prmeters. 5

16 h prmeters re sometimes clled hrid prmeters since the hve oth short circuit prmeters nd open circuit prmeters. 6

17 Exmple 4 For the pi circuit elow, find the h prmeters using open circuit nd short circuit. Solution: Short circuit the second port to find h nd h Open circuit the first port to find h nd h. A A B A A A h h h h

18 5. ABD prmeters or Trnsmission mtrix The ABD prmeters re given in mtrix form s A B D Or in eqution form The mtrix representtion is clled the trnsmission mtrix. The reson we multipl negtive is in most cses the current on the output port is coming out of the port. 8 A B D

19 n these equtions nd re the independent vriles, while nd re the dependent vriles. The individul A, B,, D prmeters re D B A 9

20 Lets descrie the ABD prmeters with - prmeters nd -prmeters. Exercise: prove the ove eqution. 0

21 Exmple 5 Find the ABD prmeters for the pi circuit elow. Solution: A A B B A B D B A

22 6. Reltionship etween two port prmeters Previousl we showed tht some h prmeters cn e given s function of nd prmeters. t turns out tht n prmeter cn e expressed s function of n other prmeter. This is ovious since ll 4 prmeters specif given port network completel.

23 For exmple lets derive the reltionship etween nd prmeters. f we express the nd prmeter equtions using mtrix representtion 3 or, prmeter representtion into the prmeters Sustituting the Hence

24 Tht is, det det The following slide shows the reltionship etween the 4 prmeters. 4

25 5

26 7. nterconnection of two port networks There re three ws two port networks cn e connected scde Prllel Series We will discuss ech 6

27 7. scde connection A cscde connection is when the port of one two port network is connected to port of the second two port network. Note tht = = 7

28 Lets write the ABD (trnsmission) prmeters for the two networks Hence, when two port networks re interconnected in cscde the trnsmission prmeters re multiplied. 8 D B A D B A D B A D B A since nd

29 7. Prllel A prllel connection is when the voltge t port is equl is equl for the two networks nd the voltge t port is equl is equl for the two networks. Note tht = = = + = + 9

30 Lets write the prmeters for the two networks Hence, when two port networks re connected in prllel, the prmeters re dded. 30 nd since nd

31 7.3 Series connection A series connection of two networks is when the current in port of the networks is the sme nd when the current in port of the two networks is the sme. Note tht = = = + = + 3

32 Lets write the prmeters for the two networks Hence, when two port networks re connected in series the prmeters re dded 3 nd since nd

33 8. Trnsfer function using two port prmeters We hve seen how to get trnsfer function using trnsformed network nlsis. Here, we will discuss how to otin trnsfer functions using two port prmeters. There re two rod ctegories: Without lod or source impednce nd With lod nd/or source impednce. 33

34 8. Without lod or source impednce These cn e descried using the prmeters ( or ) lone. For exmple, the open circuit voltge rtio cn e given s We don t del with these most of the time, since our source will hve source impednce nd we mesure our output on lod. 34 or 0

35 8. With lod or source impednce These trnsfer functions re functions of the prmeters (,, h, t) nd the source nd/or lod impednce. To esil find these trnsfer functions we should discuss out circuit representtions of two port prmeters. 35

36 Z prmeter ircuit representtions + Z Z + Z Z - - Z nd Z re controlled voltge sources in series with Z nd Z respectivel.. 36

37 prmeter nd re controlled current sources in prllel with nd respectivel. 37

38 H prmeter + h + h h /h - - h is controlled voltge source while /h is controlled current source. 38

39 The voltge nd current sources relting the vrious dependent vriles with the independent vriles re clled controlled sources. (This is ecuse the re controlled some vrile on the other port). 39

40 Exmple Find the trnsfer mpednce / following network with prmeter. for the Solution: R nserting the second eqution R R 40

41 Exmple Find the trnsfer dmittnce / following network with prmeter. Solution: for the R nserting the second eqution R R R 4

42 Exmple Find the trnsfer function / g for the network terminted t oth ends, shown elow. Solution: g nd R g R R R R R g g R R R 4

43 Exmple Find the input impednce or / following hrid circuit for the 43

44 44