digital integrated circuits a design...

EE141

1

EE1411

© Digital Integrated Circuits2nd Combinational Circuits

Designing CombinationalDesigning CombinationalLogic CircuitsLogic Circuits

Digital Integrated CircuitsDigital Integrated CircuitsA Design PerspectiveA Design PerspectiveJan M. Rabaey et al.

Adapted from Chapter 6 of

Copyright 2003 Prentice Hall/Pearson

EE1412


Combinational vs. Sequential LogicCombinational vs. Sequential Logic

Combinational Sequential

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

CombinationalLogicCircuit

OutInCombinational

LogicCircuit

OutIn

State

EE141

2

EE1413


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.

EE1414


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

……

EE141

3

EE1415


NMOS Transistors NMOS Transistors in Series/Parallel Connectionin 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

EE1416


PMOS Transistors PMOS Transistors in Series/Parallel Connectionin 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

EE141

4

EE1417


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

EE1418


Complementary CMOS Logic StyleComplementary CMOS Logic Style

EE141

5

EE1419


Example Gate: NANDExample Gate: NAND

EE14110


Example Gate: NORExample Gate: NOR

EE141

6

EE14111


Complex CMOS GateComplex CMOS Gate

OUT = D + A • (B + C)

DA

B C

D

AB

C

EE14112


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

EE141

7

EE14113


Cell DesignCell Design

Standard CellsGeneral purpose logicCan be synthesizedSame height, varying width

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

EE14114


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

signals

Routingchannel

VDD

GND

EE141

8

EE14115


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

M2

No Routingchannels VDD

GNDM3

VDD

GND

Mirrored Cell

Mirrored Cell

EE14116


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

EE141

9

EE14117



InOut

VDD

GND

In Out

VDD

GND

With silicideddiffusion

With minimaldiffusionrouting

OutIn

VDD

M2

M1

EE14118



A

Out

VDD

GND

B

2-input NAND gate

B

VDD

A

EE141

10

EE14119


Stick DiagramsStick Diagrams

Contains no dimensionsRepresents relative positions of transistors

In

Out

VDD

GND

Inverter

A

Out

VDD

GNDB

NAND2

EE14120


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

EE141

11

EE14121


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

X

CA B A B C

X

VDD

GND

VDD

GND

EE14122


Consistent Euler PathConsistent Euler Path

j

VDDX

X

i

GND

AB

C

A B C

EE141

12

EE14123


OAI22 Logic GraphOAI22 Logic Graph

C

A B

X = (A+B)•(C+D)

B

A

D

VDDX

X

GND

AB

C

PUN

PDN

C

D

D

ABCD

EE14124


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

EE141

13

EE14125


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

Less diffusion capacitance

EE14126


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)

EE141

14

EE14127


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

EE14128


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

EE141

15

EE14129


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

EE14130


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]

81A= 1→0, B=1

80A=1, B=1→0

45A=B=1→0

61A= 0→1, B=1

64A=1, B=0→1

67A=B=0→1

Delay(psec)

Input DataPattern

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

EE141

16

EE14131


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

EE14132


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

EE141

17

EE14133


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.

EE14134


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

EE141

18

EE14135


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

All gates have the same drive current.

tpNAND2

tpINV

Slope is a function of “driving strength”

EE14136


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

EE141

19

EE14137


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

EE14138



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

EE141

20

EE14139


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

F = ABCDEFGH

EE14140



Isolating fan-in from fan-out using buffer insertion

CLCL

EE141

21

EE14141



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 )

EE14142


RatioedRatioed LogicLogic

EE141

22

EE14143


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

EE14144


RatioedRatioed LogicLogicVDD

VSS

PDNIn1In2In3

F

RLLoadResistive

N transistors + Load

• VOH = VDD

• VOL = RPN

RPN + RL

• Assymetrical response

• Static power consumption

•

• tpL= 0.69 RLCL

EE141

23

EE14145


Active LoadsActive LoadsVDD

VSS

In1In2In3

F

VDD

VSS

PDNIn1In2In3

F

VSS

PDN

DepletionLoad

PMOSLoad

depletion load NMOS pseudo-NMOS

VT < 0

EE14146


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!!!

EE141

24

EE14147


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]

Vou

t[V

]

W/Lp = 4

W/Lp = 2

W/Lp = 1

W/Lp = 0.25

W/Lp = 0.5

EE14148


Improved LoadsImproved Loads

A B C D

F

CL

M1M2 M1 >> M2Enable

VDD

Adaptive Load

EE141

25

EE14149


Improved Loads (2)Improved Loads (2)VDD

VSS

PDN1

Out

VDD

VSS

PDN2

Out

AABB

M1 M2

Differential Cascode Voltage Switch Logic (DCVSL)

EE14150


DCVSL ExampleDCVSL Example

B

A A

B B B

Out

Out

XOR-NXOR gate

EE141

26

EE14151


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]

Vol

tage

[V] A B

A B

A,BA,B

EE14152


PassPass--TransistorTransistorLogicLogic

EE141

27

EE14153


PassPass--Transistor LogicTransistor Logic

Inpu

ts Switch

Network

OutOut

A

B

B

B

• N transistors• No static consumption

EE14154


Example: AND GateExample: AND Gate

B

B

A

F = AB

0

EE141

28

EE14155


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]

Vol ta

ge[V

]

xOut

In

EE14156


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)

EE141

29

EE14157


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

M2

M1

Mn

Mr

OutA

B

VDDVDDLevel Restorer

X

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

EE14158


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

tage

[V]

Time [ps]

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

EE141

30

EE14159


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

EE14160


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)

EE141

31

EE14161


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

EE14162


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

EE141

32

EE14163


PassPass--Transistor Based MultiplexerTransistor Based Multiplexer

AM2

M1

B

S

S

S F

VDD

GND

VDD

In1 In2S S

S S

EE14164


Transmission Gate XORTransmission Gate XOR

A

B

F

B

A

B

BM1

M2

M3/M4

EE141

33

EE14165


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)

EE14166


Delay OptimizationDelay Optimization

EE141

34

EE14167


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

EE14168


Dynamic LogicDynamic Logic

EE141

35

EE14169


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

EE14170


Dynamic GateDynamic Gate

In1

In2 PDNIn3

Me

Mp

Clk

ClkOut

CL

Out

Clk

Clk

A

BC

Mp

Me

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

EE141

36

EE14171


Dynamic GateDynamic Gate

In1

In2 PDNIn3

Me

Mp

Clk

ClkOut

CL

Out

Clk

Clk

A

BC

Mp

Me

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

on

off

1off

on

((AB)+C)

EE14172


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

EE141

37

EE14173


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

EE14174


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

EE141

38

EE14175


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

CL

Clk

ClkOut

A

Mp

Me

Leakage sources

CLK

VOut

Precharge

Evaluate

Dominant component is subthreshold current

EE14176


Solution to Charge LeakageSolution to Charge Leakage

CL

Clk

Clk

Me

Mp

A

B

Out

Mkp

Same approach as level restorer for pass-transistor logic

Keeper

EE141

39

EE14177


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

CL

Clk

Clk

CA

CB

B=0

AOut

Mp

Me

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

EE14178


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

EE141

40

EE14179


Charge SharingCharge Sharing

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

or

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

∆Vout VDDCa

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

–=

case 1) if ∆Vout < VTn

case 2) if ∆Vout > VTnB = 0

Clk

X

CL

Ca

Cb

A

Out

Mp

Ma

VDD

Mb

Clk Me

EE14180


Solution to Charge RedistributionSolution to Charge Redistribution

Clk

Clk

Me

Mp

A

B

OutMkp

Clk

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

EE141

41

EE14181


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

EE14182


BackgateBackgate Coupling EffectCoupling Effect

-1

0

1

2

3

0 2 4 6

Vol

tage

Time, ns

Clk

In

Out1

Out2

EE141

42

EE14183


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.

EE14184


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

EE141

43

EE14185


Other EffectsOther Effects

Capacitive couplingSubstrate couplingMinority charge injectionSupply noise (ground bounce)

EE14186


Cascading Dynamic GatesCascading Dynamic Gates

Clk

Clk

Out1In

Mp

Me

Mp

Me

Clk

Clk

Out2

V

t

Clk

In

Out1

Out2 ∆V

VTn

Only 0 → 1 transitions allowed at inputs!

EE141

44

EE14187


Domino LogicDomino Logic

In1

In2 PDNIn3

Me

Mp

Clk

Clk Out1

In4 PDNIn5

Me

Mp

Clk

ClkOut2

Mkp

1 → 11 → 0

0 → 00 → 1

EE14188


Why Domino?Why Domino?

Clk

Clk

Ini PDNInj

IniInj

PDN Ini PDNInj

Ini PDNInj

Like falling dominos!

EE141

45

EE14189


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

EE14190


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!

EE141

46

EE14191


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

EE14192


Differential (Dual Rail) DominoDifferential (Dual Rail) Domino

A

B

Me

Mp

Clk

ClkOut = AB

!A !B

MkpClk

Out = ABMkp Mp

Solves the problem of non-inverting logic

1 0 1 0

onoff

EE141

47

EE14193


npnp--CMOSCMOS

In1

In2 PDNIn3

Me

Mp

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

EE14194


NORA LogicNORA Logic

In1

In2 PDNIn3

Me

Mp

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!

digital integrated circuits a design...

Documents