UNIT 4
BASIC CIRCUIT DESIGN
CONCEPTS
(Pucknell p:- 86-110)
• Each of layers have their own characteristics like
capacitance and resistances
• Concepts such as sheet resistance Rs and a
standard unit capacitance □Cg
• Also delay associated with wiring, with inverters
and with other circuitry may be evaluated in
terms of a delay unit τ .
• Consider a uniform slab of conduction material
of resistivity ρ,of width W, thickness t, length
between faces L
• Consider the resistance between two opposite
faces
RAB= ρL/A Ω
• Where area of the slab A=Wt.
RAB= ρL/Wt Ω
• Now, consider the case in witch L=W, that is a
square of resistive material, then
RAB= ρ/t =Rs
• Where
• Rs =ohm per square or sheet resistance
• The table of values for a 5µm technology is listed
below.5µm technology means minimum line
width is 5µm and λ= 2.5µm.
Capacitance
Value in pF*10-4/µm2(relative values in
brackets)
Gate to channel
4 (1.0)
Diffusion
1 (.25)
Poly to sub
0.4 (.1)
M1 to sub
0.3 (0.075)
M2 to sub
0.2 (0.05)
M2 to M1
0.4 (0.1)
M2 to poly
0.3 (0.075)
Relative value = specified value / gate to channel value for that technology
W=3λ
L = 20λ
<-
100 λ
-> I<- 4 λ -> I
3λ
4λ
Metal
1λ
2λ
Diffusion
2λ
Polysilicon
Metal 1
|<-
50 λ
-> I<- 4 λ -> I <-
3λ
50 λ
-> I
4λ
1λ
2λ
Diffusion
2λ
Polysilicon
Td= (1 + Z p.u / Z p.d) τ
Td= (1 + Z p.u / Z p.d) τ
Estimation of CMOS inverter delay
• The inverter either charges or discharges the
load capacitance CL.
• Raise-time and fall-time estimations obtained
by following analysis
• In this condition p-device stays in saturation for
entire charging period of the load capacitance CL
• the p device is in saturation current given by
Idsp=ßp(Vgs-|Vtp|)2 /2
----(1)
• The above current charges the capacitance
and it has a constant value. The output is the
drop across the capacitance, given by
• Vout =Idsp x t /CL
------(2)
• Let t= τr ,Vout=Vdd, Vtp=0.2Vdd and Vgs=Vdd
• We have τr = 3CL /ßpVdd
Fall time estimation
• Similar reasoning can be applied to the discharge
of CL through the n- transistor
• Making similar assumptions we may write for falltime : τf = 3CL /ßnVdd
Summary of CMOS fall time and rise
factors
• Final expression we may deduce that:
τr / τf = ßn / ßp
• Raise time is slower by factor of 2.5 when both
‘n’ and ‘p’ are in same size
• In order to achive symmetrical operation need to
make Wp=2.5 Wn
• The factors which affect rise-time and fall-time as
follows:
1) τr and τf are proportional to 1/Vdd
2) τr and τf are proportional to CL
3) τr =2.5 τf for equal n and p transistor geometries
• The problem of driving large capacitive loads
arises when signals must travel outside the
chip.
• Usually it so happens that the capacitance
outside the chip are higher.
• To reduce the delay these loads must be
driven by low resistance.
•
•
Consider Vin=1
Inverter formed by T1 and T2 is turned on and thus the gate of T3 is pulled down to 0V but T4 is
turned on and the output is pulled down
• Consider Vin=0,then the gate of T3 is allowed to rise quickly to Vdd,T4 is turned
off.
• T3 is made to conduct with Vdd on its gate,i.e twice the average voltage that
applied to gate
• Super buffers are better solution for large capacitance load delay
problems
BiCMOS driver
VDD
R
Vout
1
0
Vin
CL
GND
BiCMOS driver
• High current drive capabilities for small areas
in silicon
• Working of bipolar transistor depends on two
main timing components:
1) Tin the time required to charge the base of
the transistor which is large
2) TL the time take to charge output load
capacitor which is less
Delay T
CMOS
BiCMOS
Tin
CL(crit)
Load Capacitance CL
• Critical value of load capacitance CL(crit) below
which the BiCMOS driver is slower than a
comparable CMOS driver
Cascaded inverters as drivers
• N cascaded inverters, each one of which is larger
than the preceding by a width factor f .
• Now both f and N can be complementary. If f for
each stage is large the number of stages N
reduces but delay per stage increases. Therefore
it becomes essential to optimize.
4: f
4: f2
4:1
1:1
CL
1: f
1: f2
GND
• Fix N and find the minimum value of f.
• For nMOS inverters
• Delay per stage = fτ for ↑Vin
•
or = 4fτ for ↓Vin
• The delay for a nMOS pair is 5 fτ
• For N=even
• Td=2.5 Neτ for nmos,
• Td=3.5 Neτ for cmos
• For N=odd
nMOS
CMOS
Transition from 0
to 1
Td=[2.5(N-1)+1] eτ
Td=[3.59N-1)+2]eτ
Transition from1 to
0
Td=[2.5(N-1)+4]eτ
Td=[3.5(N-1)+5]eτ
Propagation delay
• Cascaded pass transistors: delay introduced when the
logic signals have to pass through a chain of pass
transistors
• The transistors could pose a RC product delay
• Ex: the response at node V2 is given by
C dV2/dt =(I1-I2)= [(V1-V2)(V2-V3)]/R
• Lump all the R and C we have
Rtotal=nrRs
….eq-1
Ctotal=ncﾛCg
….eq-2
Where r=relative resistance/section in terms of Rs
c=relative capacitance/section in terms ofﾛCg
• Overall delay τd for n sections is given by
τd = n2rc
Long wires may be a problem with slowly rising signals
wiring capacitances
• Fringing field: is due to parallel fine metal lines
running across the chip for power connection.
Total wire capacitance Cw=Carea+Cff
• Interlayer capacitance: is due to different layers
cross silicon area
• Peripheral capacitance: is due to junction of two
devices (regions)
Total diffusion capacitance Ctotal = Carea + Cperi
Choice of layer
1) Vdd and Vss lines must be distributed on metal lines
due to low Rs value
2) Long lengths of poly must be avoided because they
have large Rs
3) The resistance effects of the transistors are much
larger, hence wiring effects due to voltage divider
effects b/w wiring and transistor resistances
4) Diffusion areas must be carefully handled because
they have larger capacitance to substrate.