1. © Digital Integrated Circuits 2nd Inverter EE5900 Advanced Algorithms for Robust VLSI CAD The Inverter Dr. Shiyan Hu Office: EERC 731 shiyan@mtu.edu Adapted and modified from Digital Integrated Circuits: A Design Perspective by Jan M. Rabaey, Anantha Chandrakasan, and Borivoje Nikolic.

2. © Digital Integrated Circuits 2nd Inverter Circuit Symbols

3. © Digital Integrated Circuits 2nd Inverter The CMOS Inverter: A First Glance Vin=Vdd,Vout=0 Vin=0,Vout=Vdd V in V out C L V DD S D D S

4. © Digital Integrated Circuits 2nd Inverter CMOS Inverter - First-Order DC Analysis V DD V V in V DD V in 0 V out V R n R p

5. © Digital Integrated Circuits 2nd Inverter CMOS Inverter: Transient Response V out V R n R p V DD V V in V DD V in 0 (a) Low-to-high(b) High-to-low C L C L Delay=0.69RC

6. © Digital Integrated Circuits 2nd Inverter NMOS In Inverter For NMOS 1.Vin=0, Vgsn=0<Vtn, Vdsn=Vout=Vdd, NMOS is in cut-off region, X1. 2.PMOS is on. Vout=Vdd. 3.Vin=Vdd, instantaneously, Vgsn=Vdd>Vtn,Vdsn=Vout=Vdd, Vgsn- Vtn=Vdd-Vtn<Vdd, NMOS is in saturation region, X2 4.Instantaneously, Vgsp=0>Vtp. PMOS cut-off 5.NMOS is on so Vdsn->0. The operating point follows the arrow to the origin. Vout=0 at X3. V in V out C L V DD S D D S

7. © Digital Integrated Circuits 2nd Inverter Propagation Delay

8. © Digital Integrated Circuits 2nd Inverter Rising delay and Falling delay  Rising delay tr=time for the signal to change from 10% to 90% of Vdd  Falling delay tf=time for the signal to change from 90% to 10% of Vdd  Delay=time from input signal transition (50% Vdd) to output signal transition (50% Vdd).

9. © Digital Integrated Circuits 2nd Inverter Delay

10. © Digital Integrated Circuits 2nd Inverter Inverter falling-time

11. © Digital Integrated Circuits 2nd Inverter NMOS falling time For NMOS 1.Vin=0, Vgsn=0<Vt, Vdsn=Vout=Vdd, NMOS is in cut-off region, X1 2.Vin=Vdd, instantaneously, Vgsn=Vdd>Vt,Vdsn=Vout=Vdd, Vgsn- Vtn=Vdd-Vtn<Vdd, NMOS is in saturation region, X2 3.The operating point follows the arrow to the origin. So Vout=0 at X3. V in V out C L V DD S D D S

12. © Digital Integrated Circuits 2nd Inverter NMOS falling time  When Vin=Vdd, instantaneously, Vgsn=Vdd  tf=tf1+tf2  tf1: time for C L to switch from 0.9Vdd to Vgsn-Vtn=Vdd-Vtn  tf2: time for C L to switch from Vdd-Vtn to 0.1Vdd tf1 tf2

13. © Digital Integrated Circuits 2nd Inverter NMOS falling time  For tf1:  Integrate Vout from 0.9Vdd to Vdd-Vt  For tf2, we have Vgsn=Vdd Vdsn=Vout

14. © Digital Integrated Circuits 2nd Inverter NMOS falling time  tf=tf1+tf2  Assume Vt=0.2Vdd

15. © Digital Integrated Circuits 2nd Inverter Rising time  Assume |Vtp|=0.2Vdd

16. © Digital Integrated Circuits 2nd Inverter Falling and Rising time  Assume Vtn=-Vtp, then we can show that  Thus, for equal rising and falling time, set  That is, Wp=2Wn since up=un/2

17. © Digital Integrated Circuits 2nd Inverter Power Dissipation

18. © Digital Integrated Circuits 2nd Inverter Where Does Power Go in CMOS?

19. © Digital Integrated Circuits 2nd Inverter Dynamic Power Dissipation Power = C L * V dd 2 * f Need to reduce C L, V dd, andf to reduce power. VinVout C L Vdd Not a function of transistor sizes

20. © Digital Integrated Circuits 2nd Inverter Dynamic Power Dynamic power is due to charging/discharging load capacitor C L In charging, C L is loaded with a charge C L Vdd which requires the energy of QVdd= C L Vdd 2, and all the energy will be dissipated when discharging is done. Total power = C L Vdd 2 If this is performed with frequency f, clearly, total power = C L Vdd 2 f

21. © Digital Integrated Circuits 2nd Inverter Dynamic Power- II  If the waveform is not periodic, denote by P the probability of switching for the signal  The dynamic power is the most important power source  It is quadratically dependant on Vdd  It is proportional to the number of switching. We can slow down the clock not on the timing critical path to save power.  It is independent of transistor size since it only depends on the load of the transistor.

22. © Digital Integrated Circuits 2nd Inverter Short Circuit Currents Happens when both transistors are on. If every switching is instantaneous, then no short circuits. Longer delay -> larger short circuit power

23. © Digital Integrated Circuits 2nd Inverter Short-Circuit Currents

24. © Digital Integrated Circuits 2nd Inverter Leakage Sub-threshold current one of most compelling issues in low-energy circuit design.

25. © Digital Integrated Circuits 2nd Inverter Subthreshold Leakage Component

26. © Digital Integrated Circuits 2nd Inverter Principles for Power Reduction  Prime choice: Reduce voltage  Recent years have seen an acceleration in supply voltage reduction  Design at very low voltages still open question (0.5V)  Reduce switching activity  Reduce physical capacitance

27. © Digital Integrated Circuits 2nd Inverter Impact of Technology Scaling

28. © Digital Integrated Circuits 2nd Inverter Goals of Technology Scaling  Make things cheaper:  Want to sell more functions (transistors) per chip for the same money  Build same products cheaper, sell the same part for less money  Price of a transistor has to be reduced  But also want to be faster, smaller, lower power

29. © Digital Integrated Circuits 2nd Inverter Scaling  Goals of scaling the dimensions by 30%:  Reduce gate delay by 30%  Double transistor density  Die size used to increase by 14% per generation  Technology generation spans 2-3 years

30. © Digital Integrated Circuits 2nd Inverter Technology Scaling  Devices scale to smaller dimensions with advancing technology.  A scaling factor S describes the ratio of dimension between the old technology and the new technology. In practice, S=1.2-1.5.

31. © Digital Integrated Circuits 2nd Inverter Technology Scaling - II  In practice, it is not feasible to scale voltage since different ICs in the system may have different Vdd. This may require extremely complex additional circuits. We can only allow very few different levels of Vdd.  In technology scaling, we often have fixed voltage scaling model.  W,L,tox scales down by 1/S  Vdd, Vt unchanged  Area scales down by 1/S 2  Cox scales up by S due to tox  Gate capacitance = CoxWL scales down by 1/S  scales up by S  Linear and saturation region current scales up by S  Current density scales up by S 3  P=Vdd*I, power density scales up by S 3  Power consumption is a major design issue

32. © Digital Integrated Circuits 2nd Inverter Summary  Inverter  Inverter delay  Power  Dynamic  Leakage  Short-circuit  Technology scaling