1. EE 330 Lecture 28 Small-Signal Model Extension Applications of the Small-signal Model

2. Nonlinear network characterized by 3 functions each functions of 3 variables Consider 4-terminal network Review from Last Lecture

3. Consider now 3 functions, each a function of 3 variables Extending this approach to the two nonlinear functions I 2 and I 3 This is a small-signal model of a 4-terminal network and it is linear 9 small-signal parameters characterize the linear 4-terminal network Small-signal model parameters dependent upon Q-point ! where Review from Last Lecture

4. A small-signal equivalent circuit of a 4-terminal nonlinear network Equivalent circuit is not unique Equivalent circuit is a three-port network Review from Last Lecture

5. Small-Signal Model 3 Consider 3-terminal network Review from Last Lecture

6. Small-Signal Model A Small Signal Equivalent Circuit Consider 3-terminal network 4 small-signal parameters characterize this 3-terminal (two-port) linear network Small signal parameters dependent upon Q-point Review from Last Lecture

7. Small-Signal Model 2 Consider 2-terminal network Review from Last Lecture

8. Small-Signal Model A Small Signal Equivalent Circuit Consider 2-terminal network Review from Last Lecture

9. Small Signal Model of MOSFET 3-terminal device Large Signal Model MOSFET is usually operated in saturation region in linear applications where a small-signal model is needed so will develop the small-signal model in the saturation region Review from Last Lecture

10. Small Signal Model of MOSFET Alternate equivalent expressions: Review from Last Lecture

11. Small Signal Model of BJT 3-terminal device Usually operated in Forward Active Region when small-signal model is needed Forward Active Model: Review from Last Lecture

12. Small Signal Model of BJT Review from Last Lecture

13. Active Device Model Summary What are the simplified dc equivalent models? Review from Last Lecture

14. Active Device Model Summary What are the simplified dc equivalent models? dc equivalent Review from Last Lecture

15. Recall: 1. Linearize nonlinear devices (have small-signal model for key devices!) 2. Replace all devices with small-signal equivalent 3. Solve linear small-signal network Alternative Approach to small-signal analysis of nonlinear networks Remember that the small-signal model is operating point dependent! Thus need Q-point to obtain values for small signal parameters

16. Comparison of Gains for MOSFET and BJT Circuits BJT MOSFET Verify the gain expression obtained for the BJT using a small signal analysis

17. Note this is identical to what was obtained with the direct nonlinear analysis Neglect λ effects to be consistent with earlier analysis

18. Example: Determine the small signal voltage gain A V = V OUT / V IN. Assume M 1 and M 2 are operating in the saturation region and that λ=0

19. Example: Determine the small signal voltage gain A V = V OUT / V IN. Assume M 1 and M 2 are operating in the saturation region and that λ=0 Small-signal circuit

20. Example: Determine the small signal voltage gain A V = V OUT / V IN. Assume M 1 and M 2 are operating in the saturation region and that λ=0 Small-signal circuit Small-signal MOSFET model for λ=0

21. Example: Determine the small signal voltage gain A V = V OUT / V IN. Assume M 1 and M 2 are operating in the saturation region and that λ=0 Small-signal circuit

22. Example: Small-signal circuit Analysis: By KCL but thus:

23. Example: Small-signal circuit Analysis: Recall:

24. Example: Small-signal circuit Analysis: Recall: If L 1 =L 2, obtain The width and length ratios can be accurately set when designed in a standard CMOS process

25. Graphical Analysis and Interpretation Consider Again

26. Graphical Analysis and Interpretation Device Model (family of curves) Load Line Device Model at Operating Point

27. Graphical Analysis and Interpretation V GSQ =-V SS Device Model (family of curves)

28. Graphical Analysis and Interpretation V GSQ =-V SS Device Model (family of curves) Saturation region

29. Graphical Analysis and Interpretation V GSQ =-V SS Device Model (family of curves) Saturation region Linear signal swing region smaller than saturation region Modest nonlinear distortion provided saturation region operation maintained Symmetric swing about Q-point Signal swing can be maximized by judicious location of Q-point

30. Graphical Analysis and Interpretation V GSQ =-V SS Device Model (family of curves) Saturation region Very limited signal swing with non-optimal Q-point location

31. Graphical Analysis and Interpretation V GSQ =-V SS Device Model (family of curves) Saturation region Signal swing can be maximized by judicious location of Q-point Often selected to be at middle of load line in saturation region

32. Small-Signal MOSFET Model Extension Existing model does not depend upon the bulk voltage ! Observe that changing the bulk voltage will change the electric field in the channel region ! E

33. Further Model Extensions Existing model does not depend upon the bulk voltage ! Observe that changing the bulk voltage will change the electric field in the channel region ! E Changing the bulk voltage will change the thickness of the inversion layer Changing the bulk voltage will change the threshold voltage of the device

34. Typical Effects of Bulk on Threshold Voltage for n-channel Device Bulk-Diffusion Generally Reverse Biased (V BS < 0 or at least less than 0.3V) for n- channel Shift in threshold voltage with bulk voltage can be substantial Often V BS =0

35. Typical Effects of Bulk on Threshold Voltage for p-channel Device Bulk-Diffusion Generally Reverse Biased (V BS > 0 or at least greater than -0.3V) for n-channel Same functional form as for n-channel devices but V T0 is now negative and the magnitude of V T still increases with the magnitude of the reverse bias

36. Model Extension Summary Model Parameters : {μ,C OX,V T0,φ,γ,λ} Design Parameters : {W,L} but only one degree of freedom W/L

37. Small-Signal Model Extension

39. Small Signal Model Summary

40. Relative Magnitude of Small Signal MOS Parameters Consider: 3 alternate equivalent expressions for g m If μC OX =100μA/V 2, λ=.01V -1, γ = 0.4V 0.5, V EBQ =1V, W/L=1, V BSQ =0V In this example This relationship is common In many circuits, V BS =0 as well

41. Large and Small Signal Model Summary Large Signal ModelSmall Signal Model where

42. End of Lecture 28