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-port
2-port
2-port
2-port
1-port

3. Thevenin’s Equivalent Circuit
Norton’s Equivalent Circuit

4. N NO
For LTI network
In frequency domain
No independent sources

5. Nonlinear
one port

6. Bias point v ( V ) i (mA) t Q I 0.5 D 0.75 0.55 0.6 0.65 0.7 1 1.5 21
1.5 2
2.5 3
3.5 v D ( V ) i
(mA) t
Bias point Q I

7. For small

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

9. Where

11. Slope at Q point = Bias point i (mA) I t Q V v ( V ) t D D D 0.5 D 3.5
2.5
Slope at Q point = 2
Bias point I D
1.5 t Q 1
0.5 V D v ( V )
0.5
0.75 D
0.55
0.6
0.65
0.7 t

12. Example If
find

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

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

15. Determine the output impedance of the circuit in Fig. 3
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. re equivalent model
Hybrid equivalent model

21. Various two-port descriptions
Port current
Port voltage or
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 Yin
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 Zin
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
Fig 16
Determine a) The input impedance and
b) The overall voltage gain
c) Check the matching of the load and output impedance

38. Z parameter analysis of terminated two-port
Solution

39. Z parameter analysis of terminated two-port
0.902
225.6

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 L1=L2=M=1H
Fig. 19
In frequency domain

47. The h-parameter
In matrix form

48. The h-parameter
With L1=L2=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
Hence

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 or
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

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

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