DC Characteristics of a CMOS Inverter

1. A complementary CMOS inverter consists of a p-type and an n-type device connected in series. The DC transfer characteristics of the inverter are a function of the output voltage (Vout) with respect to the input voltage (Vin). The MOS device first order Shockley equations describing the transistors in cut-off, linear and saturation modes can be used to generate the transfer characteristics of a CMOS inverter. Plotting these equations for both the n- and p-type devices produces voltage-current characteristics shown below. DC Characteristics of a CMOS Inverter

2. IV Curves for nMOS

3. PMOS IV Curves

4. 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, we that Idsn = |Idsp| • We could solve equations • But graphical solution gives more insight

5. Transistor Operation • Current depends on region of transistor behavior • For what Vin and Vout are nMOS and pMOS in • Cutoff? • Linear? • Saturation?

6. nMOS Operation

7. nMOS Operation

8. nMOS Operation Vgsn = Vin Vdsn = Vout

9. nMOS Operation Vgsn = Vin Vdsn = Vout

10. pMOS Operation

11. pMOS Operation

12. pMOS Operation Vgsp = Vin - VDD Vdsp = Vout - VDD Vtp < 0

13. pMOS Operation Vgsp = Vin - VDD Vdsp = Vout - VDD Vtp < 0

14. I-V Characteristics • Make pMOS wider than nMOS such that bn = bp

15. Current vs. Vout, Vin

16. Load Line Analysis • For a given Vin: • Plot Idsn, Idsp vs. Vout • Vout must be where |currents| are equal.

17. Load Line Analysis • Vin = 0

18. Load Line Analysis • Vin = 0.2VDD

19. Load Line Analysis • Vin = 0.4VDD

20. Load Line Analysis • Vin = 0.6VDD

21. Load Line Analysis • Vin = 0.8VDD

22. Load Line Analysis • Vin = VDD

23. Load Line Summary

24. DC Transfer Curve • Transcribe points onto Vin vs. Vout plot

25. Operating Regions • Revisit transistor operating regions

26. Operating Regions • Revisit transistor operating regions

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

28. The DC transfer characteristic curve is determined by plotting the common points of Vgs intersection after taking the absolute value of the p-device IV curves, reflecting them about the x-axis and superimposing them on the n-device IV curves. We basically solve for Vin(n-type) = Vin(p-type) and Ids(n-type)=Ids(p-type) The desired switching point must be designed to be 50 % of magnitude of the supply voltage i.e. VDD/2. Analysis of the superimposed n-type and p-type IV curves results in five regions in which the inverter operates. Region A occurs when 0 leqVin leq Vt(n-type). The n-device is in cut-off (Idsn =0). p-device is in linear region, Idsn = 0 therefore -Idsp = 0 Vdsp = Vout – VDD, but Vdsp =0 leading to an output of Vout = VDD. Region B occurs when the condition Vtn leq Vin le VDD/2 is met. Here p-device is in its non-saturated region Vds neq 0. n-device is in saturation Saturation current Idsn is obtained by setting Vgs = Vin resulting in the equation: DC Characteristics of a CMOS Inveter

29. CMOS Inverter DC Characteristics

30. In region B Idsp is governed by voltages Vgs and Vds described by: Region C has that both n- and p-devices are in saturation. Saturation currents for the two devices are: Region D is defined by the inequality p-device is in saturation while n-device is in its non-saturation region. Equating the drain currents allows us to solve for Vout. (See supplemental notes for algebraic manipulations). CMOS Inverter Transfer Characteristics

31. In Region E the input condition satisfies: The p-type device is in cut-off: Idsp=0 The n-type device is in linear mode Vgsp = Vin –VDD and this is a more positive value compared to Vtp. Vout = 0 nMOS & pMOS Operating points CMOS Inverter Static Charateristics Vout =Vin-Vtp A VDD B Vout =Vin-Vtn Both in sat C nMOS in sat Output Voltage pMOS in sat D E 0 VDD/2 VDD+Vtp VDD Vtp Vtn