DESIGNING OF COMBINATIONAL

LOGIC GATES IN CMOS

www.ppttopics.com

COMBINATIONAL VS. SEQUENTIAL LOGIC

CombinationalLogicCircuit

OutInCombinational

LogicCircuit

OutIn

State

Combinational Sequential

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

www.ppttopics.com

STATIC CMOS CIRCUIT

At every point in time (except during the switching

transients) each gate output is connected to either

V DD or V ss via a low-resistive path.

The outputs of the gates assume at all times the value

of the Boolean function, implemented by the circuit

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.

www.ppttopics.com

STATIC COMPLEMENTARY CMOS

F(In1,In2,…InN)

In1

In2

InN

In1

In2

InN

PUN

PDN

PMOS only

NMOS only

PUN and PDN are dual logic networks

www.ppttopics.com

NMOS 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

XY

A

B Y = X if A OR B

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

www.ppttopics.com

PMOS TRANSISTORS

IN SERIES/PARALLEL CONNECTION

X Y

A B

Y = X if A AND B = A + B

XY

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

www.ppttopics.com

THRESHOLD DROPS

VDD 0 PDN

CL VDD CL

S

S D

D

VGS

0 VDD

PUN

0 VDD - VTn

VDD |VTp|

VDD

0 VDD

CL

S

D

CL

VDD

VDD

S

D

VGS

www.ppttopics.com

COMPLEMENTARY CMOS LOGIC STYLE

www.ppttopics.com

www.ppttopics.com

COMPLEX CMOS GATE

D

A

B C

D

A

B

C

OUT = D + A • (B + C)

www.ppttopics.com

CONSTRUCTING 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

www.ppttopics.com

C

A B

X = C • (A + B)

B

A

C

i

j

A B C

Logic Graph

j

VDD X

X

i

GND

A B

C

PUN

PDN

www.ppttopics.com

C

A B

X = (A+B)•(C+D)

B

A

D

VDD X

X

GND

A B

C

PUN

PDN

C

D

D

A B C D

www.ppttopics.com

EXAMPLE: X = AB+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

www.ppttopics.com

PROPERTIES OF COMPLEMENTARY CMOS

GATES:

High noise margins :

V OH and V OL are at V DD and GND , respectively.

No static power consumption :

There never exists a direct path between V DD and

V SS ( GND ) in steady-state mode .

Comparable rise and fall times:

(under appropriate sizing conditions)

www.ppttopics.com

SWITCH 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

INV

www.ppttopics.com

INPUT PATTERN EFFECTS ON DELAY

• Delay is dependent on the pattern of inputs

• Low 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 transition

– both inputs go high

• delay is 0.69 2Rn CL

CL

B

Rn

A

Rp

B

Rp

A

Rn Cint

www.ppttopics.com

TRANSISTOR 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

1 1

4

4

www.ppttopics.com

FAN-IN CONSIDERATIONS

D C B A

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.

www.ppttopics.com

Fast Complex Gates:

Design Technique 1

• Transistor sizing

– as long as fan-out capacitance dominates

• Progressive sizing

InN CL

C3

C2

C1 In1

In2

In3

M1

M2

M3

MN

Distributed RC line

M1 > M2 > M3 > … > MN

(the fet closest to the

output is the smallest)

www.ppttopics.com

FAST COMPLEX GATES:

DESIGN TECHNIQUE 2

Transistor ordering

C2

C1 In1

In2

In3

M1

M2

M3 CL

C2

C1 In3

In2

In1

M1

M2

M3 CL

critical path critical path

charged 1

01 charged

charged 1

delay determined by time to

discharge CL, C1 and C2

delay determined by time to

discharge CL

1

1

01

www.ppttopics.com

FAST COMPLEX GATES:

DESIGN TECHNIQUE 3

F = ABCDEFGH

www.ppttopics.com

Delay in a Logic Gate

Gate delay:

d = h + p

effort delay intrinsic delay

Effort delay:

h = g f

logical effort effective fanout = Cout/Cin

Logical effort is a function of topology, independent of sizing

Effective fanout (electrical effort) is a function of load/gate size

www.ppttopics.com

LOGICAL EFFORT

fgp

C

CCRkDelay

in

Lunitunit

1

g – logical effort ,which is defined as how much more

input capacitance a gate presents to deliver the same

output current as inverter.

P-intrincsic delay:ratio of intrinsic delays of gate and

inverter

F-effective fanout

www.ppttopics.com

EXAMPLES OF LOGICAL EFFORT

B

A

A B

F

VDDVDD

A B

A

B

F

VDD

A

A

F

1

2 2 2

2

2

1 1

4

4

Inverter 2-input NAND 2-input NOR

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

www.ppttopics.com

LOGICAL EFFORT OF GATES

Intrinsic�Delay

EffortDelay

1 2 3 4 5

Fanout f

1

2

3

4

5

Inverte

r:g =

1; p = 1

2-input N

AND: g = 4

/3; p =

2N

orm

aliz

ed D

elay

www.ppttopics.com

LOGICAL EFFORT OF COMMON LOGIC GATES

www.ppttopics.com

MULTISTAGE NETWORKS

N

i

iii fgpDelay1

Stage effort: hi = gifi

Path electrical effort: F = Cout/Cin

Path logical effort: G = g1g2…gN

Branching effort: B = b1b2…bN

Path effort: H = GFB

Path delay D = Sdi = Spi + Shi

www.ppttopics.com

BRANCHING EFFORT

Branching effort:

pathon

pathoffpathon

C

CCb

www.ppttopics.com

OPTIMUM EFFORT PER STAGE

HhN

When each stage bears the same effort:

N Hh

PNHpfgD N

iii /1ˆ

Minimum path delay

Effective fanout of each stage: ii ghf

Stage efforts: g1f1 = g2f2 = … = gNfN

www.ppttopics.com

Example: Optimize Path

g = 1

f = a g = 5/3

f = b/a

g = 5/3

f = c/b

g = 1

f = 5/c

1a

b c

5

www.ppttopics.com

EXAMPLE – 8-INPUT AND

www.ppttopics.com

RATIOED LOGIC

www.ppttopics.com

IMPROVED LOADS

V DD

V SS

PDN1

Out

V DD

V SS

PDN2

Out

A A B B

M1 M2

Differential Cascode Voltage Switch Logic (DCVSL)

www.ppttopics.com

DCVSL EXAMPLE

B

A A

B B B

Out

Out

XOR-NXOR gate

www.ppttopics.com

PASS-TRANSISTOR LOGIC In

puts

Switch

Network

OutOut

A

B

B

B

• N transistors

• No static consumption

Pass transistors require low switching energy to charge up a node

due to the reduced voltage swing

www.ppttopics.com

EXAMPLE: AND GATE

B

B

A

F = AB

0

www.ppttopics.com

DIFFERENTIAL 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=AÝ

F=AÝ

OR/NOR EXOR/NEXORAND/NAND

F

F

Pass-Transistor

Network

Pass-Transistor

Network

A

ABB

A

ABB

Inverse

(a)

(b)

NMOS ONLY LOGIC:

LEVEL RESTORING TRANSISTOR

M 2

M 1

M n

M r

Out A

B

V DD

V DD Level Restorer

X

• Advantage: Full Swing

• Ratio problem

www.ppttopics.com

TRANSMISSION GATE

A B

C

C

A B

C

C

B

C L

C = 0 V

A = 2.5 V

C = 2.5 V

www.ppttopics.com

TRANSMISSION GATE BASED

MULTIPLEXER

AM2

M1

B

S

S

S F

VDD

www.ppttopics.com

TRANSMISSION GATE XOR

A

B

F

B

A

B

B

M1

M2

M3/M4

www.ppttopics.com

Vout

0 V

2.5 V

2.5 VRn

Rp

0.0 1.0 2.00

10

20

30

Vout, V

Resis

tance

, oh

ms

Rn

Rp

Rn || Rp

www.ppttopics.com

DELAY IN TRANSMISSION GATE NETWORKS

V 1 V i-1

C

2.5 2.5

0 0

V i V i+1

C C

2.5

0

V n-1 V n

C C

2.5

0

In

V 1 V i V i+1

C

V n-1 V n

C C

In

R eq R eq R eq R eq

C C

(a)

(b)

C

R eq R eq

C C

R eq

C C

R eq R eq

C C

R eq

C

In

m

(c)

www.ppttopics.com

www.ppttopics.com

PROS AND CONS:

Pros:

Robustness

good performance

No Static Power Dissipation

Cons:

Requires 2N transistors with a fan in of N

www.ppttopics.com

CONCLUSION:

Static CMOS circuits can be used for devices

that have no extreme area,complexity or speed

constraints

www.ppttopics.com

REFERENCES:

1.DIGITAL INTEGRATED CIRCUTS BY

JAN RABAEY,

ANANTHA CHANDRAKASAN,

BORIVOJE NIKOLIC

2.http://bwrc.eecs.berkeley.edu/ICbook

www.ppttopics.com

THANK U

www.ppttopics.com