EE5900 Advanced
Algorithms for
Robust VLSI CAD
Dr. Shiyan Hu
Office: EERC 731
shiyan@mtu.edu
The Inverter
Adapted and modified from Digital Integrated Circuits: A Design Perspective
by Jan M. Rabaey, Anantha Chandrakasan, and Borivoje Nikolic.
© Digital Integrated Circuits2nd
Inverter
Circuit Symbols
© Digital Integrated Circuits2nd
Inverter
The CMOS Inverter: A First Glance
V DD
S
Vin=Vdd,Vout=0
Vin=0,Vout=Vdd
D
V in
V out
D
CL
S
© Digital Integrated Circuits2nd
Inverter
CMOS Inverter - First-Order DC Analysis
V DD
V DD
Rp
V out
V out
Rn
V in
V DD
© Digital Integrated Circuits2nd
V in
0
Inverter
CMOS Inverter: Transient Response
V DD
V DD
Delay=0.69RC
Rp
V out
V out
CL
CL
Rn
V in
0
(a) Low-to-high
© Digital Integrated Circuits2nd
V in
V DD
(b) High-to-low
Inverter
For NMOS
NMOS In Inverter
VDD
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, VgsnVtn=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.
S
Vin
D
D
Vout
CL
S
© Digital Integrated Circuits2nd
Inverter
Propagation Delay
© Digital Integrated Circuits2nd
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).
© Digital Integrated Circuits2nd
Inverter
Delay
© Digital Integrated Circuits2nd
Inverter
Inverter falling-time
© Digital Integrated Circuits2nd
Inverter
NMOS falling time
For NMOS
VDD
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, VgsnVtn=Vdd-Vtn<Vdd, NMOS is in
saturation region, X2
3.
The operating point follows the arrow
to the origin. So Vout=0 at X3.
S
Vin
D
D
Vout
CL
S
© Digital Integrated Circuits2nd
Inverter
NMOS falling time



tf1

tf2
© Digital Integrated Circuits2nd
When Vin=Vdd,
instantaneously,
Vgsn=Vdd
tf=tf1+tf2
tf1: time for CL to
switch from 0.9Vdd to
Vgsn-Vtn=Vdd-Vtn
tf2: time for CL to
switch from Vdd-Vtn to
0.1Vdd
Inverter
NMOS falling time
 For
 For
Vdsn=Vout
tf1:
 Integrate
Vgsn=Vdd
Vout from 0.9Vdd to Vdd-Vt
tf2, we have
© Digital Integrated Circuits2nd
Inverter
NMOS falling time
 tf=tf1+tf2
 Assume
Vt=0.2Vdd
© Digital Integrated Circuits2nd
Inverter
Rising time
 Assume
|Vtp|=0.2Vdd
© Digital Integrated Circuits2nd
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
© Digital Integrated Circuits2nd
Inverter
Power Dissipation
© Digital Integrated Circuits2nd
Inverter
Where Does Power Go in CMOS?
• Dynamic Power Consumption
Charging and Discharging Capacitors
• Short Circuit Currents
Short Circuit Path between Supply Rails during Switching
• Leakage
Leaking diodes and transistors
© Digital Integrated Circuits2nd
Inverter
Dynamic Power Dissipation
Vdd
Vin
Vout
CL
Power = CL * Vdd2 * f
Not a function of transistor sizes
Need to reduce CL, Vdd, and f to reduce power.
© Digital Integrated Circuits2nd
Inverter
Dynamic Power
Dynamic power is due to charging/discharging
load capacitor CL
In charging, CL is loaded with a charge CL Vdd
which requires the energy of QVdd= CL Vdd2,
and all the energy will be dissipated when
discharging is done. Total power = CL Vdd2
If this is performed with frequency f, clearly,
total power = CL Vdd2 f
© Digital Integrated Circuits2nd
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.
© Digital Integrated Circuits2nd
Inverter
Short Circuit Currents
Vd d
Happens when both
transistors are on.
Vin
Vout
CL
If every switching is
instantaneous, then
no short circuits.
Longer delay ->
larger short circuit
power
IVDD (mA)
0.15
0.10
0.05
0.0
© Digital Integrated Circuits2nd
1.0
2.0
3.0
Vin (V)
4.0
5.0
Inverter
Short-Circuit Currents
© Digital Integrated Circuits2nd
Inverter
Leakage
Vd d
Vout
Drain Junction
Leakage
Sub-Threshold
Current
Sub-threshold current one of most compelling issues
Sub-Threshold
in low-energy
circuitCurrent
design.Dominant Factor
© Digital Integrated Circuits2nd
Inverter
Subthreshold Leakage Component
© Digital Integrated Circuits2nd
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
© Digital Integrated Circuits2nd
Inverter
Impact of
Technology
Scaling
© Digital Integrated Circuits2nd
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
© Digital Integrated Circuits2nd
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
© Digital Integrated Circuits2nd
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.
© Digital Integrated Circuits2nd
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/S2
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 S3
P=Vdd*I, power density scales up by S3
Power consumption is a major design issue
© Digital Integrated Circuits2nd
Inverter
Summary
Inverter
 Inverter delay
 Power

 Dynamic
 Leakage
 Short-circuit

Technology scaling
© Digital Integrated Circuits2nd
Inverter