EE 330 Lecture 28

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

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

3. Review from Last Lecture Consider now 3 functions, each a function of 3 variables Extending this approach to the two nonlinear functions I2 and I3 where 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 !

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

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

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

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

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

9. Review from Last Lecture SmallSignal Model of MOSFET Large Signal Model 3-terminal device 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

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

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

12. Review from Last Lecture SmallSignal Model of BJT

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

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

15. Recall: Alternative Approach to small-signal analysis of nonlinear networks 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 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 MOSFET BJT Verify the gain expression obtained for the BJT using a small signal analysis

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

18. Example: Determine the small signal voltage gain AV=VOUT/VIN. Assume M1 and M2 are operating in the saturation region and that λ=0

19. Example: Determine the small signal voltage gain AV=VOUT/VIN. Assume M1 and M2 are operating in the saturation region and that λ=0 Small-signal circuit

20. Example: Determine the small signal voltage gain AV=VOUT/VIN. Assume M1 and M2 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 AV=VOUT/VIN. Assume M1 and M2 are operating in the saturation region and that λ=0 Small-signal circuit 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 L1=L2, 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 Device Model (family of curves) VGSQ=-VSS

28. Graphical Analysis and Interpretation Device Model (family of curves) VGSQ=-VSS Saturation region

29. Graphical Analysis and Interpretation Device Model (family of curves) VGSQ=-VSS 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 Device Model (family of curves) VGSQ=-VSS Saturation region Very limited signal swing with non-optimal Q-point location

31. Graphical Analysis and Interpretation Device Model (family of curves) VGSQ=-VSS 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 (VBS< 0 or at least less than 0.3V) for n-channel Shift in threshold voltage with bulk voltage can be substantial Often VBS=0

35. Typical Effects of Bulk on Threshold Voltage for p-channel Device Bulk-Diffusion Generally Reverse Biased (VBS > 0 or at least greater than -0.3V) for n-channel Same functional form as for n-channel devices but VT0 is now negative and the magnitude of VT still increases with the magnitude of the reverse bias

36. Model Extension Summary Model Parameters : {μ,COX,VT0,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 gm If μCOX=100μA/V2 , λ=.01V-1, γ = 0.4V0.5, VEBQ=1V, W/L=1, VBSQ=0V In this example This relationship is common In many circuits, VBS=0 as well

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

42. End of Lecture 28