Integrated Circuit Design ELCT 701 (Winter 2019)

Notes on Dynamic Behavior of

InvertersDr. Eman Azab

Assistant Professor

Office: C3.315

E-mail: eman.azab@guc.edu.eg

Dr. Eman Azab

Electronics Dept., Faculty of IET

The German University in Cairo

1

Notes on CMOS InverterDynamic Behavior

Dr. Eman Azab

Electronics Dept., Faculty of IET

The German University in Cairo

2

Calculation of Propagation

delays

Dr. Eman Azab

Electronics Dept., Faculty of IET

The German University in Cairo

3

Notes:

In the previous lecture, weassumed that the input voltageis an ideal step with zero riseand fall time

In practice, the input signal hasnon-zero rise and fall time

“𝝉𝒓 & 𝝉𝒇”

We can use the calculatedpropagation delays at idealinput voltage to obtain theactual delays

These equations are empiricalones, yet they provide goodestimation of the actual delays

Calculation of rise and fall time

Dr. Eman Azab

Electronics Dept., Faculty of IET

The German University in Cairo

4

Example:

A CMOS inverter with the following parameters: VDD=5V,

µnCox= 20µA/V2, W/Ln=10, VT,n=1V, Cload=1pF, Calculate

‘tfall’?

tfall is the time that the load capacitor discharge from 90% to 10% ofVOH

Output voltage will drop from 4.5V to 0.5V

Using the average current method:

Assignment, Calculate the fall time using differential equations!

𝐼𝑎𝑣𝑔 =1

2𝐼𝐷,𝑛(𝑉𝑖𝑛 = 5𝑉, 𝑉𝑜𝑢𝑡 = 4.5𝑉) + 𝐼𝐷,𝑛(𝑉𝑖𝑛 = 5𝑉, 𝑉𝑜𝑢𝑡 = 0.5𝑉)

𝐼𝑎𝑣𝑔 =1

2

𝑘𝑛2

(𝑉𝑖𝑛 − 𝑉𝑇,𝑛)2 +

𝑘𝑛2(2 𝑉𝑖𝑛 − 𝑉𝑇,𝑛 𝑉𝑜𝑢𝑡 − 𝑉𝑜𝑢𝑡

2 = 0.9875𝑚𝐴

𝜏𝑓𝑎𝑙𝑙 =𝐶𝑙𝑜𝑎𝑑∆𝑉𝑜𝑢𝑡

𝐼𝑎𝑣𝑔=𝐶𝑙𝑜𝑎𝑑 4.5 − 0.5

𝐼𝑎𝑣𝑔= 4.05 𝑛𝑠

Inverter Design with Delay

Constraints

Dr. Eman Azab

Electronics Dept., Faculty of IET

The German University in Cairo

5

How to select the transistor’s aspect ratio to satisfy delay

constraints?

For simplicity, if we considered Cload as a constant cap. (interconnect only)independent on transistor’s sizing, it’s a straight forward problem, ex.:

We have to balance between delays constraints and the rest of the inverter’sparameters

Note: If we took the parasitic caps of the transistors into consideration, wehave to calculate the capacitance per unit length first

Delay Calculations using

first-order RC approximationDynamic Behavior

Dr. Eman Azab

Electronics Dept., Faculty of IET

The German University in Cairo

6

© Digital Integrated Circuits2nd Inverter

CMOS Inverter: Transient Response

tpHL = f(Ron.CL)

= 0.69 RonCL

V outVout

R n

R p

VDDV DD

V in 5 VDDV in 5 0

(a) Low-to-high (b) High-to-low

CLCL

© Digital Integrated Circuits2nd Inverter

CMOS Inverter Propagation Delay

RC Network Approach

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

© Digital Integrated Circuits2nd Inverter

0 0.5 1 1.5 2 2.5

x 10-10

-0.5

0

0.5

1

1.5

2

2.5

3

t (sec)

Vout(V

)

tp = 0.69 CL (Reqn+Reqp)/2

tpLHtpHL

CMOS Inverter Propagation Delay

RC Network Approach

© Digital Integrated Circuits2nd Inverter

What is a Transistor?

VGS VT

Ron

S D

A Switch!

|VGS|

An MOS Transistor

© Digital Integrated Circuits2nd Inverter

The MOS Transistor

Polysilicon Aluminum

© Digital Integrated Circuits2nd Inverter

MOS Transistors -

Types and Symbols

D

S

G

D

S

G

G

S

D D

S

G

NMOS Enhancement NMOS

PMOS

Depletion

Enhancement

B

NMOS with

Bulk Contact

© Digital Integrated Circuits2nd Inverter

Threshold Voltage: Concept

n+n+

p-substrate

DSG

B

VGS

+

-

Depletion

Region

n-channel

© Digital Integrated Circuits2nd Inverter

The Threshold Voltage

© Digital Integrated Circuits2nd Inverter

The Body Effect

-2.5 -2 -1.5 -1 -0.5 00.4

0.45

0.5

0.55

0.6

0.65

0.7

0.75

0.8

0.85

0.9

VBS

(V)

VT (

V)

© Digital Integrated Circuits2nd Inverter

Current-Voltage Relations

A good ol’ transistor

QuadraticRelationship

0 0.5 1 1.5 2 2.50

1

2

3

4

5

6x 10

-4

VDS

(V)

I D(A

)

VGS= 2.5 V

VGS= 2.0 V

VGS= 1.5 V

VGS= 1.0 V

Resistive Saturation

VDS = VGS - VT

© Digital Integrated Circuits2nd Inverter

Transistor in Linear

n+n+

p-substrate

D

S

G

B

VGS

xL

V(x)+–

VDS

ID

MOS transistor and its bias conditions

© Digital Integrated Circuits2nd Inverter

Transistor in Saturation

n+n+

S

G

VGS

D

VDS > VGS - VT

VGS - VT+-

Pinch-off

© Digital Integrated Circuits2nd Inverter

Current-Voltage Relations

Long-Channel Device

© Digital Integrated Circuits2nd Inverter

A model for manual analysis

© Digital Integrated Circuits2nd Inverter

Current-Voltage Relations

The Deep-Submicron Era

LinearRelationship

-4

VDS

(V)

0 0.5 1 1.5 2 2.50

0.5

1

1.5

2

2.5x 10

I D(A

)

VGS= 2.5 V

VGS= 2.0 V

VGS= 1.5 V

VGS= 1.0 V

Early Saturation

© Digital Integrated Circuits2nd Inverter

Velocity Saturation

x (V/µm)xc = 1.5

un

(m/s

)

usat = 105

Constant mobility (slope = µ)

Constant velocity

© Digital Integrated Circuits2nd Inverter

Perspective

IDLong-channel device

Short-channel device

VDSVDSAT VGS - VT

VGS = VDD

© Digital Integrated Circuits2nd Inverter

ID versus VGS

0 0.5 1 1.5 2 2.50

1

2

3

4

5

6x 10

-4

VGS

(V)

I D(A

)

0 0.5 1 1.5 2 2.50

0.5

1

1.5

2

2.5x 10

-4

VGS

(V)

I D(A

)

quadratic

quadratic

linear

Long Channel Short Channel

© Digital Integrated Circuits2nd Inverter

ID versus VDS

-4

VDS(V)0 0.5 1 1.5 2 2.5

0

0.5

1

1.5

2

2.5x 10

I D(A

)

VGS= 2.5 V

VGS= 2.0 V

VGS= 1.5 V

VGS= 1.0 V

0 0.5 1 1.5 2 2.50

1

2

3

4

5

6x 10

-4

VDS(V)

I D(A

)

VGS= 2.5 V

VGS= 2.0 V

VGS= 1.5 V

VGS= 1.0 V

Resistive Saturation

VDS = VGS - VT

Long Channel Short Channel

© Digital Integrated Circuits2nd Inverter

A unified model

for manual analysis

S D

G

B

© Digital Integrated Circuits2nd Inverter

Simple Model versus SPICE

0 0.5 1 1.5 2 2.50

0.5

1

1.5

2

2.5x 10

-4

VDS

(V)

I D(A

)

VelocitySaturated

Linear

Saturated

VDSAT=VGT

VDS=VDSAT

VDS=VGT

© Digital Integrated Circuits2nd Inverter

A PMOS Transistor

-2.5 -2 -1.5 -1 -0.5 0-1

-0.8

-0.6

-0.4

-0.2

0x 10

-4

VDS (V)

I D(A

)

Assume all variablesnegative!

VGS = -1.0V

VGS = -1.5V

VGS = -2.0V

VGS = -2.5V

© Digital Integrated Circuits2nd Inverter

Transistor Model

for Manual Analysis

© Digital Integrated Circuits2nd Inverter

The Transistor as a Switch

VGS VT

Ron

S D

ID

VDS

VGS = VD D

VDD/2 VDD

R0

Rmid

Dynamic Power

Calculations

Dr. Eman Azab

Electronics Dept., Faculty of IET

The German University in Cairo

31

Dynamic Power Dissipation

Dr. Eman Azab

Electronics Dept., Faculty of IET

The German University in Cairo

32

Switching Power Dissipation:

Changing the input voltage from high to low (or low to high) causescharging and discharging of the load capacitance

This process leads to power dissipation in the form of heat at theseswitching instants

F is the switching frequency

Dynamic Power Dissipation

Dr. Eman Azab

Electronics Dept., Faculty of IET

The German University in Cairo

33

Notes on: Switching Power

Dissipation

Power dissipation is directlyproportional to the circuitswitching speed

Higher speed more power

dissipation

Power dissipation isindependent of transistor sizing

Power-delay product:

A performance parameter to

evaluate the inverter design