1. Delay Calculations
Section

2. Load Capacitance Calculation
Cload=Cself+Cwire+Cfanout

3. Fanout Capacitance

4. Fanout Gate Capacitance
Cfanout : fanout capacitance due to the inputs of subsequent gates, CG.
Cfanout=CG1+CG2+CG3….
Assumption: Each fanout is an inverter.

5. Input Capacitance Calculation
COL: overlap capacitance
CGN, CGP: Thin Oxide Capacitance

6. Worst Case Analysis Assumption
The thin-oxide capacitance is voltage dependent.
The worst case analysis uses CoxWL to compute its worst case value.

7. Thin Oxide Capacitance:Cg
CG=WLCox=WL(εox/tox)=WCg
Unit of Cg: fF/μm
[Worst Case Analysis]

8. Cg tox L Cg 110 nm 5 1.61 fF/μm 7.5 nm 0.35 μm 1.65 fF/μm 2.2 nm
Cg is approximately 1.61 fF/μm for the last 25 years.
Exception: the 0.18 μm process, which has a Cg of 1.0 fF/ μm.
[Worst Case Analysis]

9. Thin Oxide Capacitance:Col

10. Components of Col Col=Cf+Cov Cf:fringing capacitance
Cov: overlap capacitance

11. Redefine Cg
For 0.13 μm,
Cg (due to tox alone): 1.6 fF/μm [Hodges, p.72]
Col(due to Cov and Cf): 0.25 fF/ μm [Hodges, p.80]
Redefine Cg [Hodges, p.259] as
Cg=CoxL+2Col
Cg =1.6 fF/μm fF/μm=2 fF/μm
Cg has been constant for over 20 years
Multipy Cg by W to obtain the total capacitance due to tox, Cov and Cf
[Worst Case Analysis]
[Worst Case Analysis]

12. Gate Capacitance of an Inverter
CG=Cg(Wn+Wp)
CG=2fF/μm(Wn+Wp)
[Worst Case Analysis]

13. Input Capacitance of a 3-input NAND Gate2W 2W 2W 3W 3W 3W
CG=Cg(Wn+Wp)=Cg(3W+2W)= Cg(5W)

14. Fanout Gate capacitance of n Inverters
Cfanout=2fF/μm[(Wn+Wp)1+(Wn+Wp)2…(Wn+Wp)n]
For NANDs, NORs, apply the
above equation with appropiate widths.
[Worst Case Analysis]

15. Self-Capacitance Calculation
Eliminate capacitors not connected to the output
Assume the transistors are either on (Saturation) or off (Cutoff).
CGD is negligible in either saturation or cutoff.

16. Calculation of Self-Capacitance of an Inverter
Cself=CDBn+CDBP+2COL+2COL
CDBn=CjnWn
CDBp=CjpWp
COL=ColW
Cself=CjnWn+CjpWp+2Col(Wn+Wp)
Assume Cjn=Cjp
Cself=Ceff(Wn+Wp)
For 0.13: Ceff=1 fF/μm [Hodges, p. 261]

17. Self-Capacitance of a NOR
Condition:
A=0
B=0→1
CDB4, CSB3 do not need to be charged.→NOT THE WORST CASE
CDB3 is charged, while CDB1 and CDB2 are discharged.
To avoid double counting, CDB1 and CDB2 will be called CDB12.

18. Self-Capacitance of NOR
Constant
Voltage at X

19. Self-Capacitance of a NOR
WORST CASE!!
CDB4 and CSB3 need to be charged
CDB3 is charged, while CDB1 and CDB2 are discharged

20. Self-Capacitance of NOR
WORST CASE!!

21. Wire Capacitance
Ignore wire capacitance if the length of a wire is less than a few microns.
Include wires longer than a few microns
Cwire=CintLwire
Cint=0.2 fF/um
For very long wires use distributed model

22. Example 6.4
Capacitance Calculation for Inverter

23. Propagation Delay

24. Conclusion Propagation delay depends on the arrival time of inputs
In a series stack, the delay increases as the late arriving input is further from the output.

25. Sequence:
A: charges X
B: charges Y
C: discharges X, Y, CL
Worst Case

26. Sequence:
C: discharges X, (if any)
B: discharges Y (if any)
A: discharges CL
Improved!

27. Design Strategy 1 Reorder the inputs so that
the earliest signal arrive lower in the stack
The latest signals arrive near the top of the stack

28. Design Strategy 2 To reduce delay: WC>WB>WA Problem:
Device capacitance are increased as the device sizes are increased.

29. Delay Calculation with Input Slope

30. Improve Delay Calculation with Input Slope
iout=iNMOS-iPMOS
Select Vin and Vout
Calculate iNMOS and iPMOS
Calculate iout

31. Inverter Output Current as a function of Vout and Vin

32. Simplified Inverter Output Current as a function of Vout and Vin

33. Example 6.5
Compute the delay (tPHL,step) of a CMOS inverter due to a step input
Compute the delay (tPHL,step) of a CMOS inverter due to an input ramp with a rise time of tr

34. Conclusion from Example 6.5
tramp=Δtramp+tstep tstep=0.7RC Δtramp depends on the tr of the driving circuit. Δtramp=0.7RC/2=0.3RC Assumption: the tr is equal to 2tPLH

35. Inverter Chain Delay for a Ramp Input

36. Example 6.6