ENE 104 Electric Circuit Theory

Transcription

1 ENE 4 Electric Circuit Theory Lecture : (ENE) Mon, Apr / (EE) Wed, Apr Week #3 : Dejwoot KHAWPARSUTH

2 ENE 4 Objectives : Ch7 Page Week #3 Objectives include: Learning the distinction between one-port and two-port network Techniques for characterizing networks by y, z, h, and t parameters Transformation methods between y, z, h, and t parameters Performing circuit analysis using network parameters, including cascaded networks

3 ENE 4 ntroduction: Page 3 Week #3 The circuit is linear, and the ability to measure voltages and currents: t is possible to characterize such a network with a set of parameters that allow us to predict how the network will interact with other networks.

4 ENE 4 A multiport Network: Page 4 Week #3 A one-port network. ia must be equal i b A two-port network. ia i b i c i d

5 A multiport Network: Week #3 Page 5 ENE 4 N N NN N N N N N N N N N

6 A multiport Network: Page 6 The circuit determinant: N N ENE N N 3N... N 3... NN Week #3

7 A multiport Network: Week #3 Page 7 ENE 4 The Cramer s rule: minor NN N N N N N N NN N N N N N in

8 ENE 4 Example: Page 8 Week #3 Calculate the input impedance:

9 Example: Week #3 Page 9 ENE 4 By inspection:

10 Example: Week #3 Page ENE 4 By inspection: = 968 Ω 4

11 Example: Week #3 Page ENE 4 By inspection: in Ω

12 ENE 4 Practice: 7. Page Week #3 Find the input impedance of the network shown in Figure below if it is formed into a one-port network by breaking it at terminals: (a) a and a ; (b) b and b ; (c) c and c.

13 ENE 4 Practice: 7. Page 3 Week #3

14 ENE 4 Practice: 7. Page 4 Week #3

15 ENE 4 Practice: 7. Page 5 Week #3

16 ENE 4 Example: Page 6 Week #3 Calculate the input impedance:

17 ENE 4 Example: Page 7 Week #3 and or 4.5 a

18 Example: Week #3 Page 8 ENE Ω

19 ENE 4 Example: Page 9 Week # Ω in Ω

20 ENE 4 Practice: 7. Page Week #3 Write a set of nodal equations for the circuit of figure below, calculate Δ Y, and then find the input admittance seen between: (a) node and the reference node; (b) node and the reference.

21 ENE 4 Practice: 7. Page Week #3

22 ENE 4 Practice: 7. Page Week #3

23 Admittance Parameters: Page 3 A general two-port with terminal voltages and currents specified. The two-port is composed of: - linear elements, no energy stored within the circuits - possibly including dependent sources, - but not containing any independent sources. ENE 4 - all external connections must be made to either the input port or the output port. Week #3

24 ENE 4 Admittance Parameters: Page 4 Week #3 We may begin with the set of equations: y y y y The matrix equation: y y y y

25 ENE 4 Admittance Parameters: Page 5 Week #3 We may begin with the set of equations: y y y y The short-circuit admittance parameters The short-circuit input admittance: y The short-circuit output admittance: y

26 ENE 4 Admittance Parameters: Page 6 Week #3 We may begin with the set of equations: y y y y The short-circuit admittance parameters The short-circuit transfer admittance: y y

27 ENE 4 Example: Page 7 Week #3 Find the short-circuit admittance parameters: y y y y

28 ENE 4 Example: Page 8 Week #3 Find the short-circuit admittance parameters: y S. y 3.5 S.

29 ENE 4 Example: Page 9 Week #3 Find the short-circuit admittance parameters: - When, y. S. - - When, y. S. -

30 ENE 4 Example: Page 3 Week #3 Find the short-circuit admittance parameters: y y y y Write the expressions: y.3...5

31 ENE 4 Practice: 7.3 Page 3 Week #3 By applying the appropriate - sources and short circuits to the circuit shown in figure below, find (a) y ; (b) y ; (c) y ; (d) y

32 ENE 4 Practice: 7.3 Page 3 Week #3

33 ENE 4 Practice: 7.3 Page 33 Week #3

34 ENE 4 The Terminal Equations: Page 34 Week #3 There are six different ways in which to combine the four variables: z z z z a a a a h h h h y y y y b b b b g g g g

35 ENE 4 Admittance parameters: Page 35 Week #3 y y y y y y y y

36 ENE 4 impedance parameters: Page 36 Week #3 z z z z z z z z

37 ENE 4 transmission parameters: Page 37 Week #3 a a a a a a a a S. Note: Hayt s use t instead of a

38 transmission parameters: Week #3 Page 38 ENE 4 b b b b b b S. b b

39 hybrid parameters: Week #3 Page 39 ENE 4 h h h h h S. h h h

40 ENE 4 hybrid parameters: Page 4 Week #3 g g g g g g S. g g

41 Relationships Among : To find the z-parameters as function of y-parameters, y y y y z z z z Page 4 y y y y y y y y y y y y y y y y y y y y y ENE 4 Week #3 y y y y

42 ENE 4 Transformation between : Page 4 Week #3

43 ENE 4 Reciprocal Two-Port Circuits: Page 43 Week #3 The following relationship exist, a b a b z y h g a b a b z y a b h,,,, g,

44 ENE 4 Reciprocal Two-Port Circuits: Page 44 Week #3 A reciprocal two-port circuit: A reciprocal twoport circuit is symmetric if its ports can be interchanged without disturbing the values of the terminal currents and voltages.

45 ENE 4 Some Equivalent Networks: Page 45 Week #3 (a, b) Two-ports which are equivalent to any general linear two-port. The dependent source in part a depends on, and that in part b depends on. (c) An equivalent for a bilateral network.

46 ENE 4 Analysis of the Terminated : Page 46 Week #3 Six characteristics of the terminated two-port circuits define its terminal behavior:

47 ENE 4 Analysis of the Terminated : Page 47 Week #3 Six characteristics of the terminated two-port circuits define its terminal behavior:. The input impedance. the output current 3. the Thevenin voltage and impedance 4. The current gain 5. The voltage gain 6. The voltage gain g

48 ENE 4 Analysis of the Terminated : Page 48 Week #3 Six characteristics in terms of the z-parameters: The input impedance: (the impedance seen looking into port ) z z g L z z g...*...**...***...**** in L z z L z sub in * z

49 ENE 4 Analysis of the Terminated : Page 49 Week #3

50 ENE 4 Example: Page 5 Week #3

51 ENE 4 Example: Page 5 Week #3

52 ENE 4 Example: Page 5 Week #3

53 ENE 4 Example: Page 53 Week #3

54 ENE 4 Example: Page 54 Week #3

55 ENE 4 nterconnected Two-port Circuits: Page 55 Week #3 The five basic interconnections of two-port circuit: (a) Cascade

56 ENE 4 nterconnected Two-port Circuits: Page 56 Week #3 (a) Cascade

57 ENE 4 Example: Page 57 Week #3

58 ENE 4 Example: Page 58 Week #3

59 ENE 4 Example: Page 59 Week #3

60 ENE 4 nterconnected Two-port Circuits: Page 6 Week #3 (b) Series (c) Parallel

61 ENE 4 nterconnected Two-port Circuits: Page 6 Week #3 (d) Series- Parallel (e) Parallel- Series

62 ENE 4 Example: Final /47 Page 6 Week #3

63 ENE 4 Example: Final /47 Page 63 Week #3

64 ENE 4 Example: Final /47 Page 64 Week #3

65 ENE 4 Example: Final /46 Page 65 Week #3

66 ENE 4 Example: Final /46 Page 66 Week #3

67 ENE 4 Example: Final /46 Page 67 Week #3

68 ENE 4 Example: Final /46 Page 68 Week #3

69 ENE 4 Reference: Circuit Analysis and Electrical Engineering Page 69 W.H. Hayt, Jr., J.E. Kemmerly, S.M. Durbin, Engineering Circuit Analysis, Sixth Edition. Copyright McGraw-Hill. All rights reserved. James W. Nilsson, Susan A. Riedel, Electric Circuits Sixth edition, Addison Wesley,