Circuits & Electronics P5

6.002 CIRCUITS ANDELECTRONICS Inside the Digital Gate... For example:D A B C A Pentium III class microprocessor is a circuit with over 4 million gates !!. The RAW chip being built at the

6.002 CIRCUITS AND

ELECTRONICS

Inside the Digital Gate

z Discretize value 0, 1

z Static discipline

meet voltage thresholds

Specifies how gates must be designed

sender receiver

forbidden region

OL

V

OH

V

IL

V IH V

The Digital Abstraction

C

A B

0 0 1

0 1 1

1 0 1

1 1 0

A

NAND

Combinational gate abstraction

outputs function of input alone satisfies static discipline

For example:

D

A B C

A Pentium III class microprocessor

is a circuit with over 4 million gates !!

The RAW chip

being built at the

Lab for Computer Science at MIT

has about 3 million gates

„

„

3 gates here

( )

(C A B )

D = ⋅ ⋅

B A⋅

How to build a digital gate

Analogy

C

like

power

supply

(like switches)

taps

if A=ON AND B=ON

C has H 0 else C has no H 02 2 Use this insight to build an AND gate

How to build a digital gate

C B

A

OR gate

Electrical Analogy

+

–

Bulb C is ON if A AND B are ON, else C is off

Key: “switch” device

C

Electrical Analogy

Key: “switch” device

C

in

out

control

3-Terminal device

if C = 0

short circuit between in and out else

open circuit between in and out

For mechanical switch,

control mechanical pressure

in

out

1

=

C

equivalent ckt

0

=

C

in

out

=

S

V “1”

+– V S

L

R

C

IN

OUT

OUT

V

S

V

0

=

C

OUT

V

S

V

1

=

C

OUT

V

S

V

L

R

C

OUT

V

Truth table for

C

0 1

1 0

OUT

V

What about?

Truth table for

O

V

2

c

0 0 1

0 1 1

1 0 1

1 1 0

1

c

Truth table for

O

V

2

c

0 0 1

0 1 0

1 0 0

1 1 0

1

c

S

V

OUT

V

1

c

2

c

S

V

OUT

V

1

What about?

can also build compound gates

S

V

D A

B

C D = (A⋅B)+C

The MOSFET Device

3 terminal lumped element behaves like a switch

Metal-Oxide Semiconductor Field-Effect Transistor

: control terminal : behave in a symmetric manner (for our needs)

G

S D,

source

D

S G

drain

The MOSFET Device

Understand its operation by viewing it

as a two-port element —

“Switch” model (S model) of the MOSFET

D S

G

GS

v+

–

DS

v

DS

–

for its intern

al structure.

T

V

V T ≈1 typically

on

G

D

S

DS

i

D

S

Check the MOS device

on a scope.

Demo

GS

v+

–

DS

v

DS

i

+

–

T

DS

i

DS

v

T

v <

DS

i vs v DS

A MOSFET Inverter

S

V

L

R

B

V

5

=

Note the power of abstraction.

The abstract inverter gate representation

hides the internal details such as power

supply connections, , , etc.

(When we build digital circuits, the

and are common across all gates!)

L

R GND

v OUT

The T1000 model laptop desires gates that satisfy the static discipline with voltage thresholds Does out inverter qualify?

IN

OUT

v

IN

v

5V

5V

0V =1V

T

V

= 0.5V

OL

V

= 4.5V

OH

V

= 0.9V

IL

V

= 4.1V

IH

V

Our inverter satisfies this

receiver

OL

V

OH

V

IL

V

IH

V

5 4.5

0.5 0

sender

5 4.1 0.9 0

1:

0:

1

0

Example

Does our inverter satisfy the static discipline for these thresholds:

= 0.2V

OL

V

= 4.8V

OH

V

= 0.5V

IL

V

= 4.5V

IH

V

= 0.5V

OL

V

= 4.5V

OH

V

= 1.5V

IL

V

= 3.5V

IH

V

yes no

x

Switch resistor (SR) model

of MOSFET

…more accurate MOS model

D

S G

D

S

T

v <

G

T

ON

R D

S G

e.g R ON = K5 Ω

SR Model of MOSFET

MOSFET

S model

T

T

v <

DS

i

DS

v

MOSFET

SR model

T

v ≥

T

v <

DS

i

DS

v

ON

R

1

D

S G

D

S

T

v <

G

T

ON

R D

S G

Using the SR model

=

S

V “1”

+– V S

L

R

C

IN

OUT

OUT

v

S

V

0

=

C

OUT

v

S

V

1

=

C OUT

v

S

V

L

R

C

OUT

v

Truth table for

C

0 1

1 0

OUT

V

T

v ≥

ON

R

ON

L

R ON R

ON

R S

V OUT

+

=

L

R

L

R Choose RL, RON, VS such that: