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Two-port networks Review of one ports Various two-port descriptions Terminated nonlinear two-ports Impedance and admittance matrices of two-ports Other.

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Presentation on theme: "Two-port networks Review of one ports Various two-port descriptions Terminated nonlinear two-ports Impedance and admittance matrices of two-ports Other."— Presentation transcript:

1 Two-port networks Review of one ports Various two-port descriptions Terminated nonlinear two-ports Impedance and admittance matrices of two-ports Other two-port parameter matrices The hybrid matrices The transmission matrices

2 1-port2-port 1-port

3 Thevenin’s Equivalent Circuit Norton’s Equivalent Circuit

4 NNONO For LTI network In frequency domain 0 No independent sources

5 Nonlinear one port

6

7 For small

8 For DC bias For DC bias + small signal From Taylor’s series expansion

9 Where

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11 v D (V) i D (mA) t t Bias point Q V D I D Slope at Q point =

12 Example If find

13 Two-port networks LTI one ports Input impedance Input admittance Fig. 1

14 Two-port networks Example 1 Determine the input impedance of the circuit in Fig. 2 Fig. 2

15 Example 2 Determine the output impedance of the circuit in Fig. 3 Fig. 3

16 Two-port networks Circuits can be considered by theirs terminal variables Voltages and currents are terminal’s variables Complex circuit can be analyzed more easily. There are many kinds of two port parameters. Fig. 4 A two port network

17 Common-Emitter (CE) Fixed-Bias Configuration

18 Removing DC effects of VCC and Capacitors

19 Small signal equivalent circuit

20 Hybrid equivalent model r e equivalent model

21 Various two-port descriptions or Port current Port voltage Or hybrid

22 Two-port networks The Y parameter The admittance or Y parameter of a two port network is defined by or in scalar form

23 The Y parameter The Y parameters can found from These parameters are call short-circuited admittance parameters

24 The Y parameter Example 3 Determine the admittance parameters from the circuit in Fig 5. Fig 5.

25 The Y parameter Example 4 Compute the y-parameter of the circuit in Fig.6 Fig.6

26 Y parameter analysis of terminated two-port Fig. 9 Terminated two-port Y-parameter equations

27 Y parameter analysis of terminated two-port From Crammer’s rules The input admittance Y in and

28 Y parameter analysis of terminated two-port Gain: Fig 10 Terminated two-port Y-parameter model

29 Two-port networks The Z parameter The impedance or Z parameter of a two port network is defined by or in scalar form

30 The Z parameter The Z parameters can be found from These parameters are call open circuit impedance parameters

31 The Z parameter Example 6 Determine the impedance parameters from the circuit in Fig 11 Fig 11. In frequency domain

32 The Y parameter Example 7 Compute the z-parameter of the circuit in Fig.12 Fig.12

33 The Z parameter

34 Z parameter analysis of terminated two-port Fig. 14 Terminated two-port Z-parameter equations

35 Z parameter analysis of terminated two-port From Crammer’s rules The input impedance Z in and

36 Z parameter analysis of terminated two-port Gain: Fig 15 Terminated two-port Z-parameter model

37 Z parameter analysis of terminated two-port Example 9 The circuit in Fig 16 is a two-stage transistor amplifier. The Z-parameters for each stage are Determine a) The input impedance and b) The overall voltage gain c) Check the matching of the load and output impedance Fig 16

38 Z parameter analysis of terminated two-port Solution

39 Z parameter analysis of terminated two-port

40 Z parameter analysis of terminated two-port The overall voltage gain Out put impedance The detail is left to the student to show that

41 Z parameter analysis of terminated two-port Therefore the load is closely matched to the output impedance

42 The h-parameter (Hybrid parameter) H-parameter is the combination of Z and Y parameter defined by or in scalar form H-parameter is commonly used in transistor modeling.

43 The h-parameter The h parameters can found from

44 The h-parameter Fig 17 Hybrid parameter model

45 The h-parameter Example 10 Determine the h-parameter of the two-port circuit shown in Fig. 18 Fig. 18

46 The h-parameter Example 10 Find the h-parameter of the circuit in Fig. 19 assuming L 1 =L 2 =M=1H Fig. 19 In frequency domain

47 The h-parameter In matrix form

48 The h-parameter With L 1 =L 2 =M=1 H

49 The inverse hybrid parameter (g- parameter) g-parameter is defined by or in scalar form g-parameter is an alternative form of hybrid representation.

50 The g parameters can found from

51 Inverse hybrid parameter model

52 Conversion of Two-port parameters Two port parameters can be converted to any form as follows From And and

53 where

54 Conversion of Two-port parameters From y to h

55 Conversion of Two-port parameters Henc e

56 Conversion of Two-port parameters It can be shown that for the terminated two-port with h-parameter the following equations can be derived and

57 Transmission parameter The t-parameter or transmission parameters are used in power system and it is called ABCD parameter. The transmission parameter is defined by This means that the power flows into the input port and flow out to the load from the output port. t-parameter can be calculated from Open or short circuit at the output port or

58 Transmission parameter Example 11 Fig 20 Determine the t-parameter of the circuit shown in Fig 20.

59 Transmission parameter One of the most importance characteristics of the two-port circuit with t-parameter is to determine the overall cascade parameter. Therefore

60

61 Inverse Transmission parameter

62 Interconnection of two-port network Two port networks can be connected in series parallel or cascaded Series and parallel of two-port have 4 configurations  Series input-series output (Z-parameter)  Series input-parallel output (h-parameter)  Parallel in put-series output (g or h -1 -parameter)  Parallel input-parallel output (Y-parameter) With proper choice of parameters the combined parameters can be added together.

63 Interconnection of two-port network

64 Example Bridge-T network

65 N1 // N2

66 For network N2 For network N1

67 Y-parameters of the bridge-t network are

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