Jan M. Rabaey Anantha Chandrakasan Borivoje NikolićLogic levels not dependent upon the relative device sizes; ratioless Always a path to Vdd or Gnd in steady state; low output impedance

EE1411

© Digital Integrated Circuits2nd Combinational Circuits

Digital Integrated Digital Integrated CircuitsCircuitsA Design PerspectiveA Design Perspective

Designing CombinationalDesigning CombinationalLogic CircuitsLogic Circuits

Jan M. RabaeyAnantha ChandrakasanBorivoje Nikolić

November 2002.

EE1412


Views / Abstractions / HierarchiesViews / Abstractions / Hierarchies

D.Gajski, Silicon Compilation, Addison Wesley, 1988

ArchitecturalLogic

Circuit

BehavioralStructural

Physical

device Today’s view

EE1413


Design TechnologiesDesign Technologies

EE1414


OverviewOverview

Static CMOS

Conventional Static CMOS Logic

Ratioed Logic

Pass Transistor/Transmission Gate Logic

Dynamic CMOS Logic

Domino

np-CMOS

EE1415


Combinational vs. Sequential LogicCombinational vs. Sequential Logic

Combinational Sequential

Output = f(In) Output = f(In, Previous In)

CombinationalLogicCircuit

OutInCombinational

LogicCircuit

OutIn

State

EE1416


The Basic IdeaThe Basic Idea……

Voltage on the Gate controls the current through the source/drain path

N-Channel - N-Switches are ON when the Gate is HIGH and OFF when the Gate is LOW

P-Channel - P-Switches are OFF when the Gate is HIGH and ON when the Gate is LOW

(ON == Circuit between Source and Drain)

EE1417


Transistors as SwitchesTransistors as Switches

GS

D

GS

D

N Switch

P Switch

0

1

1

0

Passes “good zeros”

Passes “good ones”

EE1418


…….The Rest of the Story....The Rest of the Story...

Put them in series - both must be on to complete the circuitPut them in parallel - either can be on to complete the circuit Generate all sorts of Switching Functions NOT the same as Boolean Functions.... Its RELAY logic - pin ball machines

EE1419


Series Parallel StructuresSeries Parallel Structures

N Channel: on=closed when gate is high

1

1

1 1

GS

D

GS

D G GS S

D D

EE14110


NMOS Transistors in Series/Parallel ConnectionNMOS Transistors in Series/Parallel Connection

Transistors can be thought as a switch controlled by its gate signal

NMOS switch closes when switch control input is high

X Y

A B

Y = X if A and B

X Y

A

B Y = X if A OR B

NMOS Transistors pass a “strong” 0 but a “weak” 1

Digital Integrated Circuits © Prentice Hall 1995IntroductionIntroduction

EE14111


Series Parallel Structures(2)Series Parallel Structures(2)

P Channel: on=closed when gate is low

0

0

0 0

GS

D

GS

D G GS S

D D

EE14112


PMOS Transistors in Series/Parallel ConnectionPMOS Transistors in Series/Parallel Connection

X Y

A B

Y = X if A AND B = A + B

X Y

A

B Y = X if A OR B = AB

PMOS Transistors pass a “strong” 1 but a “weak” 0

PMOS switch closes when switch control input is low


EE14113


……ThatThat’’s it!s it!

This is Non-Trivial: it defines the basis for the logic abstraction which is essential for all Boolean functions.

Provide a path to VDD for 1 Provide a path to GND for 0 For complex functions - provide complex paths

EE14114


From Switches to Boolean From Switches to Boolean Functions... Functions...

Use the Switching Functions to provide paths to Vdd or GND

Vdd is the source of all Truth (Vdd = = 1)GND is the source of all Falsehood (GND == 0)

P-channel N-channel

0

0

1

1

EE14115


The Inverter The Inverter

True to False / False to True Converter

1/0 0/1

EE14116


Static CMOS CircuitStatic CMOS Circuit

At every point in time (except during the switching transients) each gate output is connected to eitherVDD or Vss via a low-resistive path.

The outputs of the gates assume at all times the value of the Boolean function, implemented by the circuit (ignoring, once again, the transient effects during switching periods).

This is in contrast to the dynamic circuit class, which relies on temporary storage of signal values on the capacitance of high impedance circuit nodes.

EE14117


The ExceptionsThe Exceptions

Many interesting and useful circuits which are not fully complementary CMOS

Pass Gates (Transmission Gates)Level shifters, etc.

Even more interesting and useless circuits!

New circuit styles keep being invented

EE14118


Threshold DropsThreshold DropsVDD

VDD → 0PDN

0 → VDD

CL

CL

PUN

VDD

0 → VDD - VTn

CL

VDD

VDD

VDD → |VTp|

CL

S

D S

D

VGS

S

SD

D

VGS

EE14119


Series Parallel Structures (3)Series Parallel Structures (3)

GS D

GSD

N Switch

P Switch

0

1

1

0

Passes “good zeros”

Passes “good ones”

Bi-directional SwitchOpen Circuit, High Z

S

S’

EE14120


Static Complementary CMOSStatic Complementary CMOSVDD

F(In1,In2,…InN)

In1In2

InN

In1In2InN

PUN

PDN

……

PMOS only

NMOS only

PUN and PDN are dual logic networks

EE14121


Complementary CMOS Logic StyleComplementary CMOS Logic Style

EE14122


Example Gate: NANDExample Gate: NAND

EE14123


Physical Layout in MAXPhysical Layout in MAXof 2of 2--input NAND Gateinput NAND Gate

Vdd!

A B

Cout

EE14124


44--input NAND Gateinput NAND Gate

In3

In1

In2

In4

In1 In2 In3 In4

VDD

Out

In1 In2 In3 In4

Vdd

GND

Out


EE14125


Example Gate: NORExample Gate: NOR

EE14126


Physical Layout in MAXPhysical Layout in MAXof 2of 2--input NOR Gateinput NOR Gate

EE14127


Constructing a Complex GateConstructing a Complex Gate

C

(a) pull-down network

SN1 SN4

SN2

SN3D

FF

A

DB

C

D

F

A

B

C

(b) Deriving the pull-up networkhierarchically by identifyingsub-nets

D

A

A

B

C

VDD VDD

B

(c) complete gate

EE14128


Complex CMOS GateComplex CMOS Gate

OUT = D + A • (B + C)

DA

B C

D

AB

C

EE14129


Cell DesignCell Design

Standard CellsGeneral purpose logicCan be synthesizedSame height, varying width

Structured Array CellsTiling structure with multiplicative parametersProgrammed with vias

Datapath CellsFor regular, structured designs (arithmetic)Includes some wiring in the cellFixed height and width

EE14130


Standard Cell Layout Methodology Standard Cell Layout Methodology ––1980s1980s

signals

Routingchannel

VDD

GND

EE14131


Standard Cell Layout Methodology Standard Cell Layout Methodology ––1990s1990s

M2

No Routingchannels VDD

GNDM3

VDD

GND

Mirrored Cell

Mirrored Cell

EE14132


Inside out Inside out NandNand / Nor Gates / Nor Gates

Which is which ?

EE14133


Standard Cell Layout MethodologyStandard Cell Layout Methodology

VDD

VSS

Well

signalsRouting Channel

metal1

polysilicon


EE14134


Standard CellsStandard Cells

Cell boundary

N WellCell height 12 metal tracksMetal track is approx. 3λ + 3λPitch = repetitive distance between objects

Cell height is “12 pitch”

2λ

Rails ~10λ

InOut

VDD

GND

EE14135



InOut

VDD

GND

In Out

VDD

GND

With silicideddiffusion

With minimaldiffusionrouting

OutIn

VDD

M2

M1

EE14136



A

Out

VDD

GND

B

2-input NAND gate

B

VDD

A

Note: well and substrate Contactsprevent external routing in poly

EE14137


MultiMulti--Fingered TransistorsFingered TransistorsOne finger Two fingers (folded)

Less diffusion capacitance

EE14138


Stick DiagramsStick Diagrams

Contains no dimensionsRepresents relative positions of transistors

In

Out

VDD

GND

Inverter

A

Out

VDD

GNDB

NAND2

EE14139


Stick DiagramsStick Diagrams

C

A B

X = C • (A + B)

B

AC

i

j

j

VDDX

X

i

GND

AB

C

PUN

PDNABC

Logic Graph

EE14140


Two Versions of C Two Versions of C •• (A + B)(A + B)

X

CA B A B C

X

VDD

GND

VDD

GND

EE14141


Consistent Euler PathConsistent Euler Path

j

VDDX

X

i

AB

C

GND A B C

EE14142


OAI22 Logic GraphOAI22 Logic Graph

C

A B

X = (A+B)•(C+D)

B

A

D

VDDX

X

AB

GND

C

PUN

PDN

C

D

D

ABCD

EE14143


Example: x = Example: x = ab+cdab+cd

GND

x

a

b c

d

VDDx

GND

x

a

b c

d

VDDx

(a) Logic graphs for (ab+cd) (b) Euler Paths {a b c d}

a c d

x

VDD

GND

(c) stick diagram for ordering {a b c d}b

EE14144


CMOS PropertiesCMOS PropertiesFull rail-to-rail swing; high noise marginsLogic levels not dependent upon the relative device sizes; ratiolessAlways a path to Vdd or Gnd in steady state; low output impedanceExtremely high input resistance; nearly zero steady-state input currentNo direct path steady state between power and ground; no static power dissipationPropagation delay function of load capacitance and resistance of transistors

EE14145


Complex Gate StructuresComplex Gate Structures

A

C

B

A

B

Vdd

Gnd

Out

C

Out = A+(B*C) ...

ABC

And-Or-Invert (AOI)

How to add terms?

EE14146


OAI/AOI DualityOAI/AOI Duality

A

C

B

A

B C

Vdd

Gnd

Out

Out = A*(B+C) ...

ABC

Out = A+(B*C) ...

Or-And-Invert (OAI)

Switch from:

To:

Demorgan’s Law in Action

EE14147


DemorganDemorgan’’ss Law in ActionLaw in Action

Out = A*(B+C) ...

ABC

Or-And-Invert (OAI)

A

C

B

A

B

C

Vdd

Gnd

Out

EE14148



Out = A*(B+C) ...

ABC

Or-And-Invert (OAI)

A

C B A

BC

Vd dG

n d

Ou t

EE14149



Out = A*(B+C) ...

ABC

Or-And-Invert (OAI)

A

C

B

A

B

C

Vdd

Gnd

Out

EE14150



Out = A*(B+C) ...

ABC

Or-And-Invert (OAI)

A

C

B

A

BC

Vdd

Gnd

Out

EE14151



Out = A*(B+C) ...

ABC

Or-And-Invert (OAI)

A

Vdd

Gnd

Out

C

B

A

BC

What is the Magic command to do this?

EE14152


Complex (AOI/OAI) GatesComplex (AOI/OAI) Gates

EE14153


Schematic Representation in SUESchematic Representation in SUEof AOI (andof AOI (and--oror--invert) Gateinvert) Gate

Notice 6 transistors

EE14154


Physical Layout in MAX of AOI GatePhysical Layout in MAX of AOI Gate

A

OUT

Vdd!

A

B

BC

C

B

A

C

OUT

EE14155


Schematic Representation in SUESchematic Representation in SUEof OAI (orof OAI (or--andand--invert)invert)

EE14156


Physical Layout in MAX of OAI GatePhysical Layout in MAX of OAI Gate

A

OUT

Vdd!

A

B

B

C

C

A

B

C

OUT

EE14157


QuizQuiz

EE14158


Step by Step Layout of XNOR Gate Step by Step Layout of XNOR Gate

– The equation for XNOR is: f = (a * b) + (a' * b')

– using DeMorgan's law on each of the two terms gives:f = (a'+ b')' + (a + b)'

– using DeMorgan's law on the two terms together gives:

f = ((a'+ b') * (a + b))'

– This could be directly implemented with a single complementary CMOS gate: the equation is in a simple negated product of sums form. This form can be implemented with the standard Or-And-Invert (OAI) style gate.

EE14159


NonNon--Inverted InputsInverted Inputs

– However, using DeMorgan's law one more time on the left term gives:

f = ((a * b)' * (a + b))’

– This form uses no inverted inputs and can be implemented with two gates a NAND gate and an OAI gate.

ab f

EE14160


Now lets lay it outNow lets lay it out

Start with Vdd! and GND! power buses. Without any more information, about the use of this cell, make the power and ground lines in metal 1sized 3 and 3 apart. Use poly as inputs A B and guess that C might be used.

EE14161


XOR from NOR/AOIXOR from NOR/AOI

EE14162


EE14163


XOR GateXOR Gate

EE14164


IrsimIrsim

EE14165


XOR GATEXOR GATE

EE14166


3.5um x 10um3.5um x 10um

EE14167


.35um x 1um.35um x 1um

EE14168


Lab 2: Full AdderLab 2: Full Adder

Sum = A xor B xor CCout = AB + AC + BC

expand sumSum = ABC+AB’C’+A’BC’+A’B’C

(exactly 1 or 3 inputs true)use Cout to help generate Sum

Sum = ABC + Cout’(A+B+Cin)

EE14169


Full Adder (4 gates)Full Adder (4 gates)

EE14170


Full Adder (4 gates)Full Adder (4 gates)

EE14171


EE14172


EE14173


EE14174


One Solution (125x136)One Solution (125x136)

EE14175


Is this standard cell design?

EE14176


Lab 3: 8 Bit Ripple Carry AdderLab 3: 8 Bit Ripple Carry Adder

EE14177


XX--pandedpanded

EE14178


MS Flip FlopMS Flip Flop

•Is this “edge triggered”? Is any flip flop?

•I could do this with three (3) CMOS gates! (could you?)

EE14179


MS Register BitMS Register BitHow many metals? How are they used? Why?

EE14180


irsimirsim SimulationSimulation

EE14181


H Spice SimulationH Spice Simulation

EE14182


EE14183


EE14184


8 x 8 Register File8 x 8 Register File

EE14185


Register file simulation Register file simulation

EE14186


Properties of Complementary CMOS Gates Properties of Complementary CMOS Gates SnapshotSnapshot

High noise margins: VOH and VOL are at VDD and GND, respectively.

No static power consumption:There never exists a direct path between VDD and VSS (GND) in steady-state mode.

Comparable rise and fall times:(under appropriate sizing conditions)

EE14187


Switch Delay ModelSwitch Delay Model

A

Req

A

Rp

A

Rp

A

Rn CL

A

CL

B

Rn

A

Rp

B

Rp

A

Rn Cint

B

Rp

A

Rp

A

Rn

B

Rn CL

Cint

NAND2 INV NOR2

EE14188


Input Pattern Effects on DelayInput Pattern Effects on Delay

Delay is dependent on the pattern of inputsLow to high transition

both inputs go low– delay is 0.69 Rp/2 CL

one input goes low– delay is 0.69 Rp CL

High to low transitionboth inputs go high

– delay is 0.69 2Rn CL

CL

B

Rn

ARp

BRp

A

Rn Cint

EE14189


Delay Dependence on Input PatternsDelay Dependence on Input Patterns

-0.5

0

0.5

1

1.5

2

2.5

3

0 100 200 300 400

A=B=1→0

A=1, B=1→0

A=1 →0, B=1

time [ps]

Vol

tage

[V]

Input DataPattern

Delay(psec)

A=B=0→1 67

A=1, B=0→1 64

A= 0→1, B=1 61

A=B=1→0 45

A=1, B=1→0 80

A= 1→0, B=1 81

NMOS = 0.5μm/0.25 μmPMOS = 0.75μm/0.25 μmCL = 100 fF

EE14190


Transistor SizingTransistor Sizing

CL

B

Rn

A

Rp

B

Rp

A

Rn Cint

B

Rp

A

Rp

A

Rn

B

Rn CL

Cint

2

2

2 2

11

4

4

EE14191


Transistor Sizing a Complex Transistor Sizing a Complex CMOS GateCMOS Gate

OUT = D + A • (B + C)

DA

B C

D

AB

C

1

2

2 2

4

48

8

6

36

6

EE14192


FanFan--In ConsiderationsIn Considerations

DCBA

D

C

B

A CL

C3

C2

C1

Distributed RC model(Elmore delay)

tpHL = 0.69 Reqn(C1+2C2+3C3+4CL)

Propagation delay deteriorates rapidly as a function of fan-in –quadratically in the worst case.

EE14193


ttpp as a Function of Fanas a Function of Fan--InIn

tpLH

t p(p

sec)

fan-in

Gates with a fan-in greater than 4 should be avoided.

0

250

500

750

1000

1250

2 4 6 8 10 12 14 16

tpHL

quadratic

linear

tp

EE14194


ttpp as a Function of Fanas a Function of Fan--OutOut

2 4 6 8 10 12 14 16

tpNOR2

t p(p

sec)

eff. fan-out

tpNAND2

tpINV

All gates have the same drive current.

Slope is a function of “driving strength”

EE14195


ttpp as a Function of Fanas a Function of Fan--In and FanIn and Fan--OutOut

Fan-in: quadratic due to increasing resistance and capacitanceFan-out: each additional fan-out gate adds two gate capacitances to CL

tp = a1FI + a2FI2 + a3FO

EE14196


Fast Complex Gates:Fast Complex Gates:Design Technique 1Design Technique 1

Transistor sizingas long as fan-out capacitance dominates

Progressive sizing

InN CL

C3

C2

C1In1

In2

In3

M1

M2

M3

MNDistributed RC line

M1 > M2 > M3 > … > MN(the fet closest to theoutput is the smallest)

Can reduce delay by more than 20%; decreasing gains as technology shrinks

EE14197



Transistor ordering

C2

C1In1

In2

In3

M1

M2

M3 CL

C2

C1In3

In2

In1

M1

M2

M3 CL

critical path critical path

charged1

0→1charged

charged1

delay determined by time to discharge CL, C1 and C2

delay determined by time to discharge CL

1

1

0→1 charged

discharged

discharged

EE14198


Fast Complex Gates:Fast Complex Gates:Design Technique 3Design Technique 3Alternative logic structures

F = ABCDEFGH

EE14199



Isolating fan-in from fan-out using buffer insertion

CLCL

EE141100



Reducing the voltage swing

linear reduction in delayalso reduces power consumption

But the following gate is much slower!Or requires use of “sense amplifiers” on the receiving end to restore the signal level (memory design)

tpHL = 0.69 (3/4 (CL VDD)/ IDSATn )

= 0.69 (3/4 (CL Vswing)/ IDSATn )

EE141101


Sizing Logic Paths for SpeedSizing Logic Paths for Speed

Frequently, input capacitance of a logic path is constrainedLogic also has to drive some capacitanceExample: ALU load in an Intel’s microprocessor is 0.5pFHow do we size the ALU datapath to achieve maximum speed?We have already solved this for the inverter chain – can we generalize it for any type of logic?

EE141102


Buffer ExampleBuffer Example

( )∑=

⋅+=N

iiii fgpDelay

1

Out

For given N: Ci+1/Ci = Ci/Ci-1To find N: Ci+1/Ci ~ 4How to generalize this to any logic path?

CL

In

1 2 N

(in units of τinv)

EE141103


Logical EffortLogical Effort

( )fgpCCCRkDelay

in

Lunitunit

⋅+=

⎟⎟⎠

⎞⎜⎜⎝

⎛+⋅=

τγ

1

p – intrinsic delay (3kRunitCunitγ) - gate parameter ≠ f(W)g – logical effort (kRunitCunit) – gate parameter ≠ f(W)f – effective fanout

Normalize everything to an inverter:ginv =1, pinv = 1

Divide everything by τinv(everything is measured in unit delays τinv)Assume γ = 1.

EE141104


Delay in a Logic GateDelay in a Logic Gate

Gate delay:d = h + p

effort delay intrinsic delay

Effort delay:

h = g f

effective fanout = Cout/Cin

logical effort

Logical effort is a function of topology, independent of sizingEffective fanout (electrical effort) is a function of load/gate size

EE141105



Inverter has the smallest logical effort and intrinsic delay of all static CMOS gatesLogical effort of a gate presents the ratio of its input capacitance to the inverter capacitance when sized to deliver the same currentLogical effort increases with the gate complexity

EE141106


Logical EffortLogical EffortLogical effort is the ratio of input capacitance of a gate to the inputcapacitance of an inverter with the same output current

B

A

A B

g = 1 g = 4/3 g = 5/3

F

VDDVDD

A B

A

B

F

VDD

A

A

F

1

2 2 2

2

21 1

4

4

Inverter 2-input NAND 2-input NOR

EE141107


Logical Effort of GatesLogical Effort of Gates

Fan-out (h)

t

Nor

mal

ized

del

ay (d

)

1 2 3 4 5 6 7

pINVt pNAND

F(Fan-in)

g =p =d =

g =p =d =

EE141108



Fan-out (h)

t

Nor

mal

ized

del

ay (d

)

1 2 3 4 5 6 7

pINVt pNAND

F(Fan-in)

g = 1p = 1d = h+1

g = 4/3p = 2d = (4/3)h+2

EE141109



Intrinsic�Delay

EffortDelay

1 2 3 4 5Fanout f

1

2

3

4

5

Inverter:

g = 1; p = 12-i

nput

NAND: g = 4/

3;p =

2

Nor

mal

ized

Del

ay

EE141110


Add Branching EffortAdd Branching Effort

Branching effort:

pathon

pathoffpathonC

CCb

−

−− +=

EE141111


Multistage NetworksMultistage Networks

Stage effort: hi = gifiPath electrical effort: F = Cout/Cin

Path logical effort: G = g1g2…gN

Branching effort: B = b1b2…bN

Path effort: H = GFB

Path delay D = Σdi = Σpi + Σhi

( )∑=

⋅+=N

iiii fgpDelay

1

EE141112


Optimum Effort per StageOptimum Effort per Stage

HhN =

When each stage bears the same effort:

N Hh =

( ) PNHpfgD Niii +=+= ∑ /1ˆ

Minimum path delay

Effective fanout of each stage: ii ghf =

Stage efforts: g1f1 = g2f2 = … = gNfN

EE141113


Optimal Number of StagesOptimal Number of StagesFor a given load, and given input capacitance of the first gateFind optimal number of stages and optimal sizing

invN NpNHD += /1

( ) 0ln /1/1/1 =++−=∂∂

invNNN pHHH

ND

NHh ˆ/1=Substitute ‘best stage effort’

EE141114



From Sutherland, Sproull

EE141115


Example: Optimize PathExample: Optimize Path

Effective fanout, F =G = H =h =a =b =

1a

b c

5

g = 1f = a

g = 5/3f = b/a

g = 5/3f = c/b

g = 1f = 5/c

EE141116


Example: Optimize PathExample: Optimize Path1

ab c

5

g = 1f = a

g = 5/3f = b/a

g = 5/3f = c/b

g = 1f = 5/c

Effective fanout, F = 5G = 25/9H = 125/9 = 13.9h = 1.93a = 1.93b = ha/g2 = 2.23c = hb/g3 = 5g4/f = 2.59

EE141117


Example: Optimize PathExample: Optimize Path

1 a

b c 5

Effective fanout, H = 5G = 25/9F = 125/9 = 13.9f = 1.93a = 1.93b = fa/g2 = 2.23c = fb/g3 = 5g4/f = 2.59

g1 = 1 g2 = 5/3 g3 = 5/3 g4 = 1

EE141118


Example Example –– 88--input ANDinput AND

EE141119


Method of Logical EffortMethod of Logical Effort

Compute the path effort: F = GBHFind the best number of stages N ~ log4FCompute the stage effort f = F1/N

Sketch the path with this number of stagesWork either from either end, find sizes: Cin = Cout*g/f

Reference: Sutherland, Sproull, Harris, “Logical Effort, Morgan-Kaufmann 1999.

EE141120


SummarySummary

Sutherland,SproullHarris

EE141121


RatioedRatioed LogicLogic

EE141122


RatioedRatioed LogicLogic

VDD

VSS

PDNIn1In2In3

F

RLLoad

VDD

VSS

In1In2In3

F

VDD

VSS

PDNIn1In2In3

FVSS

PDN

Resistive DepletionLoad

PMOSLoad

(a) resistive load (b) depletion load NMOS (c) pseudo-NMOS

VT < 0

Goal: to reduce the number of devices over complementary CMOS

EE141123


RatioedRatioed LogicLogicVDD

VSS

PDNIn1In2In3

F

RLLoadResistive

N transistors + Load

• VOH = VDD

• VOL = RPN

RPN + RL

• Assymetrical response

• Static power consumption

•

• tpL= 0.69 RLCL

EE141124


Active LoadsActive LoadsVDD

VSS

In1In2In3

F

VDD

VSS

PDNIn1In2In3

F

VSS

PDN

DepletionLoad

PMOSLoad

depletion load NMOS pseudo-NMOS

VT < 0

EE141125


PseudoPseudo--NMOSNMOS

VDD

A B C D

FCL

VOH = VDD (similar to complementary CMOS)

kn VDD VTn–( )VOLVOL

2

2-------------–

⎝ ⎠⎜ ⎟⎛ ⎞ kp

2------ VDD VTp–( )

2=

VOL VDD VT–( ) 1 1kpkn------–– (assuming that VT VTn VTp )= = =

SMALLER AREA & LOAD BUT STATIC POWER DISSIPATION!!!

EE141126


PseudoPseudo--NMOS VTCNMOS VTC

0.0 0.5 1.0 1.5 2.0 2.50.0

0.5

1.0

1.5

2.0

2.5

3.0

Vin [V]

W/Lp = 4

W/Lp = 2

W/Lp = 1

W/Lp = 0.25

Vou

t[V

]

W/Lp = 0.5

EE141127


Improved LoadsImproved Loads

A B C D

F

CL

M1M2 M1 >> M2Enable

VDD

Adaptive Load

EE141128


Improved Loads (2)Improved Loads (2)VDD

VSS

PDN1

Out

VDD

VSS

PDN2

Out

AABB

M1 M2

Differential Cascode Voltage Switch Logic (DCVSL)

EE141129


DCVSL ExampleDCVSL Example

B

A A

B B B

Out

Out

XOR-NXOR gate

EE141130


DCVSL Transient ResponseDCVSL Transient Response

0 0.2 0.4 0.6 0.8 1.0-0.5

0.5

1.5

2.5

Time [ns]

A B

Vol

tag e

[V]

A B

A,BA,B

EE141131


PassPass--TransistorTransistorLogicLogic

EE141132


PassPass--Transistor LogicTransistor LogicIn

puts Switch

Network

OutOut

A

B

B

B

• N transistors• No static consumption

EE141133


Example: AND GateExample: AND Gate

B

B

A

F = AB

0

EE141134


NMOSNMOS--Only LogicOnly Logic

VDD

In

Outx

0.5μm/0.25μm0.5μm/0.25μm

1.5μm/0.25μm

0 0.5 1 1.5 20.0

1.0

2.0

3.0

Time [ns]

xOut

In

Volt a

ge[V

]

EE141135


NMOSNMOS--only Switchonly Switch

A = 2.5 V

B

C = 2.5V

CL

A = 2.5 V

C = 2.5 V

BM2

M1

Mn

Threshold voltage loss causesstatic power consumption

VB does not pull up to 2.5V, but 2.5V -VTN

NMOS has higher threshold than PMOS (body effect)

EE141136


NMOS Only Logic: NMOS Only Logic: Level Restoring TransistorLevel Restoring Transistor

M2

M1

Mn

Mr

A Out

B

VDDVDDLevel Restorer

X

• Advantage: Full Swing• Restorer adds capacitance, takes away pull down current at X• Ratio problem

EE141137


Restorer SizingRestorer Sizing

0 100 200 300 400 5000.0

1.0

2.0

W/Lr =1.0/0.25 W/Lr =1.25/0.25

W/Lr =1.50/0.25

W/Lr =1.75/0.25

Vol

t ag e

[V]

Time [ps]

3.0•Upper limit on restorer size•Pass-transistor pull-downcan have several transistors in stack

EE141138


Solution 2: Single Transistor Pass Gate with Solution 2: Single Transistor Pass Gate with VVTT=0=0

Out

VDD

VDD

2.5V

VDD

0V 2.5V

0V

WATCH OUT FOR LEAKAGE CURRENTS

EE141139


Complementary Pass Transistor LogicComplementary Pass Transistor Logic

A

B

A

B

B B B B

A

B

A

B

F=AB

F=AB

F=A+B

F=A+B

B B

A

A

A

A

F=A⊕ΒÝ

F=A⊕ΒÝ

OR/NOR EXOR/NEXORAND/NAND

F

F

Pass-TransistorNetwork

Pass-TransistorNetwork

AABB

AABB

Inverse

(a)

(b)

EE141140


Solution 3: Transmission GateSolution 3: Transmission Gate

A B

C

C

A B

C

C

BCL

C = 0 V

A = 2.5 V

C = 2.5 V

EE141141


Resistance of Transmission GateResistance of Transmission Gate

Vout

0 V

2.5 V

2.5 VRn

Rp

0.0 1.0 2.00

10

20

30

Vout, V

Res

ista

nce,

ohm

s

Rn

Rp

Rn || Rp

EE141142


PassPass--Transistor Based MultiplexerTransistor Based Multiplexer

AM2

M1

B

S

S

S F

VDD

GND

VDD

In1 In2S S

S S

EE141143


Transmission Gate XORTransmission Gate XOR

A

B

F

B

A

B

BM1

M2

M3/M4

EE141144


Delay in Transmission Gate NetworksDelay in Transmission Gate Networks

V1 Vi-1

C

2.5 2.5

0 0

Vi Vi+1

CC

2.5

0

Vn-1 Vn

CC

2.5

0

In

V1 Vi Vi+1

C

Vn-1 Vn

CC

InReqReq Req Req

CC

(a)

(b)

C

Req Req

C C

Req

C C

Req Req

C C

Req

CIn

m

(c)

EE141145


Delay OptimizationDelay Optimization

EE141146


Transmission Gate Full AdderTransmission Gate Full Adder

A

B

P

Ci

VDDA

A A

VDD

Ci

A

P

AB

VDD

VDD

Ci

Ci

Co

S

Ci

P

P

P

P

P

Sum Generation

Carry Generation

Setup

Similar delays for sum and carry

EE141147


Dynamic LogicDynamic Logic

EE141148


Dynamic CMOSDynamic CMOS

In static circuits at every point in time (except when switching) the output is connected to either GND or VDD via a low resistance path.

fan-in of n requires 2n (n N-type + n P-type) devices

Dynamic circuits rely on the temporary storage of signal values on the capacitance of high impedance nodes.

requires on n + 2 (n+1 N-type + 1 P-type) transistors

EE141149


Dynamic GateDynamic Gate

In1

In2 PDN

Me

Mp

In3

Clk

ClkOut

CL

Out

Clk

Clk

A

BC

Mp

Me

on

off

1off

on

((AB)+C)

Two phase operationPrecharge (Clk = 0)Evaluate (Clk = 1)

EE141150


Conditions on OutputConditions on Output

Once the output of a dynamic gate is discharged, it cannot be charged again until the next precharge operation.Inputs to the gate can make at most one transition during evaluation.

Output can be in the high impedance state during and after evaluation (PDN off), state is stored on CL

EE141151


Properties of Dynamic GatesProperties of Dynamic GatesLogic function is implemented by the PDN only

number of transistors is N + 2 (versus 2N for static complementary CMOS)

Full swing outputs (VOL = GND and VOH = VDD)Non-ratioed - sizing of the devices does not affect the logic levelsFaster switching speeds

reduced load capacitance due to lower input capacitance (Cin)reduced load capacitance due to smaller output loading (Cout)no Isc, so all the current provided by PDN goes into discharging CL

EE141152


Properties of Dynamic GatesProperties of Dynamic GatesOverall power dissipation usually higher than static CMOS

no static current path ever exists between VDD and GND (including Psc)no glitchinghigher transition probabilitiesextra load on Clk

PDN starts to work as soon as the input signals exceed VTn, so VM, VIH and VIL equal to VTn

low noise margin (NML)Needs a precharge/evaluate clock

EE141153


Issues in Dynamic Design 1: Issues in Dynamic Design 1: Charge LeakageCharge Leakage

CL

Clk

ClkOut

Mp

Me

A

Leakage sources

CLK

VOut

Precharge

Evaluate

Dominant component is subthreshold current

EE141154


Solution to Charge LeakageSolution to Charge Leakage

CL

Clk

Clk

Me

Mp

Out

Mkp

Keeper

A

B

Same approach as level restorer for pass-transistor logic

EE141155


Issues in Dynamic Design 2: Issues in Dynamic Design 2: Charge SharingCharge Sharing

CL

Clk

Clk

CA

CB

A

B=0

OutMp

Me

Charge stored originally on CL is redistributed (shared) over CL and CA leading to reduced robustness

EE141156


Charge Sharing ExampleCharge Sharing Example

CL=50fF

Clk

Clk

A A

B B B !B

CC

Out

Ca=15fF

Cc=15fF

Cb=15fF

Cd=10fF

EE141157


Charge SharingCharge Sharing

CLVDD CLVout t( ) Ca VDD VTn VX( )–( )+=

or

ΔVout Vout t( ) VDD–CaCL-------- VDD VTn VX( )–( )–= =

ΔVout VDDCa

Ca CL+----------------------

⎝ ⎠⎜ ⎟⎛ ⎞

–=

case 1) if ΔVout < VTn

case 2) if ΔVout > VTn

X

CL

Ca

Cb

Out

B = 0

Clk

A

Mp

Ma

VDD

Mb

Clk Me

EE141158


Solution to Charge RedistributionSolution to Charge Redistribution

Clk

Clk

Me

Mp

OutMkp

A

B

Clk

Precharge internal nodes using a clock-driven transistor (at the cost of increased area and power)

EE141159


Issues in Dynamic Design 3: Issues in Dynamic Design 3: BackgateBackgate CouplingCoupling

CL1

Clk

Clk

B=0

A=0

Out1Mp

Me

Out2

CL2In

Dynamic NAND Static NAND

=1 =0

EE141160


BackgateBackgate Coupling EffectCoupling Effect

-1

0

1

2

3

0 2 4 6

Vol

tage

Time, ns

Clk

In

Out1

Out2

EE141161


Issues in Dynamic Design 4: Clock Issues in Dynamic Design 4: Clock FeedthroughFeedthrough

CL

Clk

Clk

B

AOut

Mp

Me

Coupling between Out and Clk input of the prechargedevice due to the gate to drain capacitance. So voltage of Out can rise above VDD. The fast rising (and falling edges) of the clock couple to Out.

EE141162


Clock Clock FeedthroughFeedthrough

-0.5

0.5

1.5

2.5

0 0.5 1

Clk

Clk

In1

In2

In3

In4

Out

In &Clk

Out

Time, ns

Vol

tage

Clock feedthrough

Clock feedthrough

EE141163


Other EffectsOther Effects

Capacitive couplingSubstrate couplingMinority charge injectionSupply noise (ground bounce)

EE141164


Cascading Dynamic GatesCascading Dynamic Gates

Clk

Clk

Out1

Mp

Me

In

Mp

Me

Clk

Clk

Out2

V

t

Clk

In

Out1

Out2 ΔV

VTn

Only 0 → 1 transitions allowed at inputs!

EE141165


Domino LogicDomino Logic

In1

In2 PDN

Me

Mp

In3

Clk

Clk Out1

In4 PDNIn5

Me

Mp

Clk

ClkOut2

Mkp

1 → 11 → 0

0 → 00 → 1

EE141166


Why Domino?Why Domino?

Clk

Clk

Ini PDNInj

IniInj

PDN Ini PDNInj

Ini PDNInj

Like falling dominos!

EE141167


Properties of Domino LogicProperties of Domino Logic

Only non-inverting logic can be implementedVery high speed

static inverter can be skewed, only L-H transitionInput capacitance reduced – smaller logical effort

EE141168


Designing with Domino LogicDesigning with Domino Logic

Mp

Me

VDD

PDN

Clk

In1In2

In3

Out1

Clk

Mp

Me

VDD

PDN

Clk

In4

Clk

Out2

Mr

VDD

Inputs = 0during precharge

Can be eliminated!

EE141169


Footless DominoFootless Domino

The first gate in the chain needs a foot switchPrecharge is rippling – short-circuit currentA solution is to delay the clock for each stage

VDD

Clk Mp

Out1

In1

1 0

VDD

Clk Mp

Out2

In2

VDD

Clk Mp

Outn

InnIn3

1 0

0 1 0 1 0 1

1 0 1 0

EE141170


Differential (Dual Rail) DominoDifferential (Dual Rail) Domino

A

B

Me

MpClk

Clk

Out = AB

!A !B

MkpClk

Out = ABMkp Mp

Solves the problem of non-inverting logic

1 0 1 0

onoff

EE141171


npnp--CMOSCMOS

In1

In2 PDN

Me

Mp

In3

Clk

Clk Out1

In4 PUNIn5

Me

MpClk

Clk

Out2(to PDN)

1 → 11 → 0

0 → 00 → 1

Only 0 → 1 transitions allowed at inputs of PDN Only 1 → 0 transitions allowed at inputs of PUN

EE141172


NORA LogicNORA Logic

In1

In2 PDN

Me

Mp

In3

Clk

Clk Out1

In4 PUNIn5

Me

MpClk

Clk

Out2(to PDN)

1 → 11 → 0

0 → 00 → 1

to otherPDN’s

to otherPUN’s

WARNING: Very sensitive to noise!

Jan M. Rabaey Anantha Chandrakasan Borivoje NikolićLogic levels not dependent upon the relative device sizes; ratioless Always a path to Vdd or Gnd in steady state; low output impedance

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