1. Week 6 – Chapter 3 FET Small-Signal Analysis Mohd Shawal Jadin FKEE UMP © 2009

2. FET Small-Signal Model Transconductance The relationship of V GS (input) to I D (output) is called transconductance. The transconductance is denoted g m. Transfer Curve

3. Graphical Determination of g m

4. Mathematical Definition of g m Using differential calculus

5. FET Impedance Input Impedance Z i : Very large to assume input terminal approximate an open circuit Output Impedance Z o : y os : admittance equivalent circuit parameter listed on FET specification sheets.

6. FET Specification

7. FET AC Equivalent Circuit

8. JFET Fixed-Bias Configuration The input is on the gate and the output is on the drain.

9. JFET Fixed-Bias Configuration Once again: same step as BJT to redraw the network to AC equivalent circuit. Capacitor – short circuit DC batteries V GG and V DD are set to zero volts by a short-circuit equivalent

10. AC Equivalent Circuit

12. Impedances Input Impedance:Output Impedance:

13. Voltage Gain

14. Phase Relationship A CS amplifier configuration has a 180-degree phase shift between input and output.

15. Example Fixed-bias configuration has an operating point defined by V GSQ = -2V and I DQ = 5.625 mA, with I DSS = 10mA and V P = -8V. The value of y os is provided as 40 µS. Determine: a) g m b) Z i c) Z o d) A V e) A V ignoring the effects of r d

16. Solution

17. JFET CS Self-Bias Configuration This is a CS amplifier configuration therefore the input is on the gate and the output is on the drain.

18. AC Equivalent Circuit

19. Impedances Input Impedance: Output Impedance:

20. Voltage Gain

21. Phase Relationship A CS amplifier configuration has a 180-degree phase shift between input and output.

22. JFET CS Self-Bias Configuration – Unbypassed Rs If Cs is removed, it affects the gain of the circuit.

23. AC Equivalent Circuit

24. Impedances Input Impedance: Output Impedance:

25. Impedances

26. Voltage Gain

28. Example

29. Solution

31. JFET CS Voltage-Divider Configuration This is a CS amplifier configuration therefore the input is on the gate and the output is on the drain.

32. AC Equivalent Circuit

33. Impedances Input Impedance:Output Impedance:

34. Voltage Gain

35. JFET Source Follower (Common-Drain) Configuration In a CD amplifier configuration the input is on the gate, but the output is from the source.

36. AC Equivalent Circuit

37. Impedances Input Impedance:Output Impedance:

38. Voltage Gain

39. Phase Relationship A CD amplifier configuration has no phase shift between input and output.

40. JFET Common-Gate Configuration The input is on source and the output is on the drain.

41. AC Equivalent Circuit

42. Impedances Applying Kirchhoff’s voltage law around the output perimeter and Kirchhoff’s current law at node a ::

43. Impedances Input Impedance: Output Impedance:

44. Voltage Gain Applying Kirchhoff’s current law at node b ::

45. Phase Relationship A CG amplifier configuration has no phase shift between input and output.

46. Depletion-Type MOSFETs 1.D-MOSFETs have similar AC equivalent models. 2.The only difference is that V SGQ can be positive for n- channel devices and negative for p-channel devices. 3.This means that g m can be greater than g m0.

47. D-MOSFET AC Equivalent Model

48. Example Find –V GSQ and I DQ –Determine g m and compare to g m0 –r d –Find Z i, Z o, A v

49. Enhancement-Type MOSFETs There are two types of E-MOSFETs: nMOS or n-channel MOSFETs pMOS or p-channel MOSFETs

50. E-MOSFET AC Equivalent Model g m and r d can be found in the specification sheet for the FET. Forward transfer admittance

51. E-MOSFET CS Drain-Feedback Configuration

52. AC Equivalent Circuit

53. Impedances Input Impedance: Output Impedance:

54. The calculation

56. The AC analysis of E-MOSFET Remember that, the biasing arrangement are limited for E-MOSFET

57. Voltage Gain

58. Phase Relationship This is a CS amplifier configuration therefore it has 180-degree phase shift between input and output.

59. Do it Determine input and output and also A V impedance for k=0.3X10 -3

60. E-MOSFET CS Voltage-Divider Configuration

61. AC Equivalent Circuit

62. Impedances Input Impedance: Output Impedance:

63. Voltage Gain

64. Phase Relationship This is a CS amplifier configuration therefore it has 180-degree phase shift between input and output.

65. Solution

66. E-MOSFET CS Voltage-Divider Configuration

67. AC Equivalent Circuit

68. Impedances Input Impedance: [Formula 9.52] Output Impedance:[Formula 9.53] [Formula 9.54]

69. Voltage Gain [Formula 9.55] [Formula 9.56]

70. Summary Table

72. Try yourself Design a self-bias network that have gain of 10. The device should be biased at V GSQ =1/3V P

73. Solution