VLSI Design: DC and Transient Response in CMOS Inverters

1. EE466: VLSI Design Lecture 05: DC and transient response – CMOS Inverters 4: DC and Transient Response

2. Outline • DC Response • Logic Levels and Noise Margins • Transient Response • Delay Estimation 4: DC and Transient Response

3. Activity 1)If the width of a transistor increases, the current will  increase decrease not change 2)If the length of a transistor increases, the current will increase decrease not change 3)If the supply voltage of a chip increases, the maximum transistor current will increase decrease not change 4)If the width of a transistor increases, its gate capacitance will increase decrease not change 5)If the length of a transistor increases, its gate capacitance will increase decrease not change 6)If the supply voltage of a chip increases, the gate capacitance of each transistor will increase decrease not change 4: DC and Transient Response

4. Activity 1)If the width of a transistor increases, the current will  increase decrease not change 2)If the length of a transistor increases, the current will increase decrease not change 3)If the supply voltage of a chip increases, the maximum transistor current will increase decrease not change 4)If the width of a transistor increases, its gate capacitance will increase decrease not change 5)If the length of a transistor increases, its gate capacitance will increase decrease not change 6)If the supply voltage of a chip increases, the gate capacitance of each transistor will increase decrease not change 4: DC and Transient Response

5. DC Response • DC Response: Vout vs. Vin for a gate • Ex: Inverter • When Vin = 0 -> Vout = VDD • When Vin = VDD -> Vout = 0 • In between, Vout depends on transistor size and current • By KCL, must settle such that Idsn = |Idsp| • We could solve equations • But graphical solution gives more insight 4: DC and Transient Response

6. Transistor Operation • Current depends on region of transistor behavior • For what Vin and Vout are nMOS and pMOS in • Cutoff? • Linear? • Saturation? 4: DC and Transient Response

7. nMOS Operation 4: DC and Transient Response

8. nMOS Operation 4: DC and Transient Response

9. nMOS Operation Vgsn = Vin Vdsn = Vout 4: DC and Transient Response

10. nMOS Operation Vgsn = Vin Vdsn = Vout 4: DC and Transient Response

11. pMOS Operation 4: DC and Transient Response

12. pMOS Operation 4: DC and Transient Response

13. pMOS Operation Vgsp = Vin - VDD Vdsp = Vout - VDD Vtp < 0 4: DC and Transient Response

14. pMOS Operation Vgsp = Vin - VDD Vdsp = Vout - VDD Vtp < 0 4: DC and Transient Response

15. I-V Characteristics • Make pMOS is wider than nMOS such that bn = bp 4: DC and Transient Response

16. Current vs. Vout, Vin 4: DC and Transient Response

17. Load Line Analysis • For a given Vin: • Plot Idsn, Idsp vs. Vout • Vout must be where |currents| are equal in 4: DC and Transient Response

18. Load Line Analysis • Vin = 0 4: DC and Transient Response

19. Load Line Analysis • Vin = 0.2VDD 4: DC and Transient Response

20. Load Line Analysis • Vin = 0.4VDD 4: DC and Transient Response

21. Load Line Analysis • Vin = 0.6VDD 4: DC and Transient Response

22. Load Line Analysis • Vin = 0.8VDD 4: DC and Transient Response

23. Load Line Analysis • Vin = VDD 4: DC and Transient Response

24. Load Line Summary 4: DC and Transient Response

25. DC Transfer Curve • Transcribe points onto Vin vs. Vout plot 4: DC and Transient Response

26. Operating Regions • Revisit transistor operating regions 4: DC and Transient Response

27. Operating Regions • Revisit transistor operating regions 4: DC and Transient Response

28. Beta Ratio • If bp / bn 1, switching point will move from VDD/2 • Called skewed gate • Other gates: collapse into equivalent inverter 4: DC and Transient Response

29. Noise Margins • How much noise can a gate input see before it does not recognize the input? 4: DC and Transient Response

30. Logic Levels • To maximize noise margins, select logic levels at 4: DC and Transient Response

31. Logic Levels • To maximize noise margins, select logic levels at • unity gain point of DC transfer characteristic 4: DC and Transient Response

32. Transient Response • DC analysis tells us Vout if Vin is constant • Transient analysis tells us Vout(t) if Vin(t) changes • Requires solving differential equations • Input is usually considered to be a step or ramp • From 0 to VDD or vice versa 4: DC and Transient Response

33. Inverter Step Response • Ex: find step response of inverter driving load cap 4: DC and Transient Response

34. Inverter Step Response • Ex: find step response of inverter driving load cap 4: DC and Transient Response

35. Inverter Step Response • Ex: find step response of inverter driving load cap 4: DC and Transient Response

36. Inverter Step Response • Ex: find step response of inverter driving load cap 4: DC and Transient Response

37. Inverter Step Response • Ex: find step response of inverter driving load cap 4: DC and Transient Response

38. Inverter Step Response • Ex: find step response of inverter driving load cap 4: DC and Transient Response

39. Delay Definitions • tpdr: • tpdf: • tpd: • tr: • tf: fall time 4: DC and Transient Response

40. Delay Definitions • tpdr: rising propagation delay • From input to rising output crossing VDD/2 • tpdf: falling propagation delay • From input to falling output crossing VDD/2 • tpd: average propagation delay • tpd = (tpdr + tpdf)/2 • tr: rise time • From output crossing 0.2 VDD to 0.8 VDD • tf: fall time • From output crossing 0.8 VDD to 0.2 VDD 4: DC and Transient Response

41. Delay Definitions • tcdr: rising contamination delay • From input to rising output crossing VDD/2 • tcdf: falling contamination delay • From input to falling output crossing VDD/2 • tcd: average contamination delay • tpd = (tcdr + tcdf)/2 4: DC and Transient Response

42. Simulated Inverter Delay • Solving differential equations by hand is too hard • SPICE simulator solves the equations numerically • Uses more accurate I-V models too! • But simulations take time to write 4: DC and Transient Response

43. Delay Estimation • We would like to be able to easily estimate delay • Not as accurate as simulation • But easier to ask “What if?” • The step response usually looks like a 1st order RC response with a decaying exponential. • Use RC delay models to estimate delay • C = total capacitance on output node • Use effective resistance R • So that tpd = RC • Characterize transistors by finding their effective R • Depends on average current as gate switches 4: DC and Transient Response

44. Effective Resistance • Shockley models have limited value • Not accurate enough for modern transistors • Too complicated for much hand analysis • Simplification: treat transistor as resistor • Replace Ids(Vds, Vgs) with effective resistance R • Ids = Vds/R • R averaged across switching of digital gate • Too inaccurate to predict current at any given time • But good enough to predict RC delay 4: DC and Transient Response

45. RC Delay Model • Use equivalent circuits for MOS transistors • Ideal switch + capacitance and ON resistance • Unit nMOS has resistance R, capacitance C • Unit pMOS has resistance 2R, capacitance C • Capacitance proportional to width • Resistance inversely proportional to width 4: DC and Transient Response

46. RC Values • Capacitance • C = Cg = Cs = Cd = 2 fF/mm of gate width • Values similar across many processes • Resistance • R  6 KW*mm in 0.6um process • Improves with shorter channel lengths • Unit transistors • May refer to minimum contacted device (4/2 l) • Or maybe 1 mm wide device • Doesn’t matter as long as you are consistent 4: DC and Transient Response

47. Inverter Delay Estimate • Estimate the delay of a fanout-of-1 inverter 4: DC and Transient Response

48. Inverter Delay Estimate • Estimate the delay of a fanout-of-1 inverter 4: DC and Transient Response

49. Inverter Delay Estimate • Estimate the delay of a fanout-of-1 inverter 4: DC and Transient Response

50. Inverter Delay Estimate • Estimate the delay of a fanout-of-1 inverter d = 6RC 4: DC and Transient Response