THE INVERTERS

Digital Integrated Circuits © Prentice Hall 1995InverterInverter

THE INVERTERS


DIGITAL GATES Fundamental Parameters

Functionality Reliability, Robustness Area Performance

» Speed (delay)» Power Consumption» Energy


Noise in Digital Integrated Circuits

VDDv(t)

i(t)

(a) Inductive coupling (b) Capacitive coupling (c) Power and ground

noise


DC Operation: Voltage Transfer Characteristic

V(x)

V(y)

VOH

VOL

VM

VOHVOL

fV(y)=V(x)

Switching Threshold

Nominal Voltage Levels

V(y)V(x)


Mapping between analog and digital signals

"1"

"0"

VOH

VIH

VIL

VOL

UndefinedRegion

V(x)

V(y)

VOH

VOL

VIH

VIL

Slope = -1

Slope = -1


Definition of Noise Margins

VIH

VIL

UndefinedRegion

"1"

"0"

VOH

VOL

NMH

NML

Gate Output Gate Input

Noise Margin High

Noise Margin Low


The Regenerative Property

(a) A chain of inverters.

v0, v2, ...

v1, v3, ... v1, v3, ...

v0, v2, ...

(b) Regenerative gate

f(v)

finv(v)

finv(v)

f(v)

(c) Non-regenerative gate

v0 v1 v2 v3 v4 v5 v6

...


Fan-in and Fan-out

N

M

(a) Fan-out N

(b) Fan-in M


The Ideal Gate

Vin

Vout

g=

Ri =

Ro = 0


VTC of Real Inverter

0.0 1.0 2.0 3.0 4.0 5.0Vin (V)

1.0

2.0

3.0

4.0

5.0

Vo

ut (V

)

VMNMH

NML


Delay Definitions

tpHL

tpLH

t

t

Vin

Vout

50%

50%

tr

10%

90%

tf


Ring Oscillator

v0 v1 v2 v3 v4 v5

v0 v1 v5

T = 2 tp N


Power Dissipation


CMOS INVERTER


The CMOS Inverter: A First Glance

VDD

Vin Vout

CL


CMOS Inverters

Polysilicon

InOut

Metal1

VDD

GND

PMOS

NMOS

1.2 m=2


Switch Model of CMOS Transistor

Ron

|VGS| < |VT||VGS| > |VT|

|VGS|


CMOS Inverter: Steady State Response

VDD VDD

VoutVout

Vin = VDD Vin = 0

Ron

Ron

VOH = VDD

VOL= 0

VM = Ronp) f(Ronn,


CMOS Inverter: Transient Response

VDD

Vout

Vin = VDD

Ron

CL

tpHL = f(Ron.CL)

= 0.69 RonCL

t

Vout

VDD

RonCL

1

0.5

ln(0.5)

0.36


CMOS Properties

Full rail-to-rail swing Symmetrical VTC Propagation delay function of load

capacitance and resistance of transistors No static power dissipation Direct path current during switching


Voltage TransferCharacteristic


CMOS Inverter VTC

Vout

Vin1 2 3 4 5

12

34

5

NMOS linPMOS off

NMOS satPMOS sat

NMOS offPMOS lin

NMOS satPMOS lin

NMOS linPMOS sat


Simulated VTC

0.0 1.0 2.0 3.0 4.0 5.0Vin (V)

0.0

2.0

4.0

Vo

ut (V

)


Gate Switching Threshold

0.1 0.3 1.0 3.2 10.01.0

2.0

3.0

4.0

kp/kn

VM


MOS Transistor Small Signal Model

rogmvgsvgs

+

-

S

DG


Determining VIH and VIL


Propagation Delay


CMOS Inverter: Transient Response

VDD

Vout

Vin = VDD

Ron

CL

tpHL = f(Ron.CL)

= 0.69 RonCL

t

Vout

VDD

RonCL

1

0.5

ln(0.5)

0.36


CMOS Inverter Propagation Delay

VDD

Vout

Vin = VDD

CLIav

tpHL = CL Vswing/2

Iav

CL

kn VDD

~


Computing the Capacitances

VDD VDD

VinVout

M1

M2

M3

M4Cdb2

Cdb1

Cgd12

Cw

Cg4

Cg3

Vout2

Fanout

Interconnect

VoutVin

CL

SimplifiedModel


CMOS Inverters

Polysilicon

InOut

Metal1

VDD

GND

PMOS

NMOS

1.2 m=2


The Miller Effect

Vin

M1

Cgd1Vout

V

V

Vin

M1

Vout V

V

2Cgd1

“A capacitor experiencing identical but opposite voltage swings at both its terminals can be replaced by a capacitor to ground, whose value is two times the original value.”


Computing the Capacitances


Impact of Rise Time on Delayt p

HL(n

sec

)

0.35

0.3

0.25

0.2

0.15

trise (nsec)10.80.60.40.20


Delay as a function of VDD

0

4

8

12

16

20

24

28

2.00 4.001.00 5.003.00

Nor

mal

ized

Del

ay

VDD (V)


Where Does Power Go in CMOS?

• Dynamic Power Consumption

• Short Circuit Currents

• Leakage

Charging and Discharging Capacitors

Short Circuit Path between Supply Rails during Switching

Leaking diodes and transistors


Dynamic Power Dissipation

Energy/transition = CL * Vdd2

Power = Energy/transition * f = CL * Vdd2 * f

Need to reduce CL, Vdd , and f to reduce power.

Vin Vout

CL

Vdd

Not a function of transistor sizes!


Impact ofTechnology

Scaling


Technology Evolution


Technology Scaling (1)

Minimum Feature Size


Technology Scaling (2)

Number of components per chip


Propagation Delay Scaling


Technology Scaling Models

• Full Scaling (Constant Electrical Field)

• Fixed Voltage Scaling

• General Scaling

ideal model — dimensions and voltage scaletogether by the same factor S

most common model until recently —only dimensions scale, voltages remain constant

most realistic for todays situation —voltages and dimensions scale with different factors


Scaling Relationships for Long Channel

Devices


Scaling of Short Channel

Devices

Documents

THE INVERTERS