6.002
CIRCUITS AND
ELECTRONICS
Inside the Digital Gate
Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT
OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
6.002 Fall 2000
Lecture 5
Review
The Digital Abstraction
z Discretize value 0, 1
z Static discipline
meet voltage thresholds
sender
VOH
VOL
receiver
VIH
VIL
forbidden
region
Specifies how gates must be designed
Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT
OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
6.002 Fall 2000
Lecture 5
Review
Combinational gate abstraction
outputs function of input alone
satisfies static discipline
A
B
C
NAND
A
0
0
1
1
B
0
1
0
1
C
1
1
1
0
Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT
OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
6.002 Fall 2000
Lecture 5
For example:
a digital circuit
Demo
A⋅ B
A
B
D
C
D = (C ⋅ (A ⋅ B ))
3 gates here
„ A Pentium III class microprocessor
is a circuit with over 4 million gates !!
„ The RAW chip (http://www.cag.lcs.mit.edu/raw)
being built at the
Lab for Computer Science at MIT
has about 3 million gates.
Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT
OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
6.002 Fall 2000
Lecture 5
How to build a digital gate
Analogy
l ike
power
supply
A
(li
taps
s)
e
h
c
t
i
ke sw
B
C
if A=ON AND B=ON
C has H20
else
C has no H20
Use this insight to build an AND gate.
Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT
OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
6.002 Fall 2000
Lecture 5
How to build a digital gate
OR gate
A
C
B
Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT
OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
6.002 Fall 2000
Lecture 5
Electrical Analogy
C
B
A
V +
–
Bulb C is ON if A AND B are ON,
else C is off
Key: “switch” device
Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT
OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
6.002 Fall 2000
Lecture 5
Electrical Analogy
equivalent ckt
Key: “switch” device
control
in
C =0
in
out
C
in
out
C=1
3-Terminal device
if C = 0
else
out
short circuit between in and out
open circuit between in and out
For mechanical switch,
control
mechanical pressure
Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT
OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
6.002 Fall 2000
Lecture 5
Consider
VS
RL
RL
VOUT
+ VS
–
VOUT
IN
C
VS =
C
“1”
OUT
VS
VOUT
C =0
Truth table for
C VOUT
0 1
1 0
VS
VOUT
C =1
Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT
OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
6.002 Fall 2000
Lecture 5
What about?
VS
Truth table for
c1 c2 VO
0 0 1
0 1 1
1 0 1
1 1 0
VOUT
c1
c2
Truth table for
VS
VOUT
c1
c2
c1 c2 VO
0 0 1
0 1 0
1 0 0
1 1 0
Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT
OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
6.002 Fall 2000
Lecture 5
What about?
can also build compound gates
VS
D
A
C
D = (A ⋅ B) + C
B
Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT
OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
6.002 Fall 2000
Lecture 5
The MOSFET Device
Metal-Oxide
Semiconductor
Field-Effect
Transistor
drain
D
G
gate
≡
S
source
3 terminal lumped element
behaves like a switch
G : control terminal
D, S : behave in a symmetric
manner (for our needs)
Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT
OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
6.002 Fall 2000
Lecture 5
The MOSFET Device
Understand its operation by viewing it
as a two-port element —
out k
k
c
e
Ch extboo l
the t s interna
for it ture.
iG
c
u
r
t
s
D
iDS
G
+
vGS
–
vDS
S
–
D
off
G
vGS < VT
G
vGS ≥ VT
S
+
D
iDS
on
S
VT ≈ 1V typically
“Switch” model (S model) of the MOSFET
Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT
OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
6.002 Fall 2000
Lecture 5
Demo
Check the MOS device
on a scope.
i
DS
+
vDS
+
vGS
–
–
iDS
vGS ≥ VT
vGS < VT
vDS
iDS vs vDS
Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT
OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
6.002 Fall 2000
Lecture 5
A MOSFET Inverter
VS = 5V
RL
vOUT
A
B
IN
A
B
Note the power of abstraction.
The abstract inverter gate representation
hides the internal details such as power
supply connections, RL, GND, etc.
(When we build digital circuits, the
and
are common across all gates!)
Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT
OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
6.002 Fall 2000
Lecture 5
Example
vOUT
5V
vOUT
vIN
v IN
0V V
T =1V
5V
The T1000 model laptop desires gates that satisfy
the static discipline with voltage thresholds. Does
out inverter qualify?
1:
VOL = 0.5V
VIL = 0.9V
VOH = 4.5V
VIH = 4.1V
sender
5
4.5 V
OH
receiver
5
4.1
0.9
0.5 VOL
0:
0
0
Our inverter satisfies this.
1
VIH
VIL
0
Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT
OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
6.002 Fall 2000
Lecture 5
E.g.:
Does our inverter satisfy the static
discipline for these thresholds:
VOL = 0.2V
VIL = 0.5V
VOH = 4.8V
VIH = 4.5V
yes
x
VOL = 0.5V
VIL = 1.5V
VOH = 4.5V
VIH = 3.5V
no
Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT
OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
6.002 Fall 2000
Lecture 5
Switch resistor (SR) model
of MOSFET
…more accurate MOS model
D
D
G
G
G
S
D
vGS < VT
S
RON
vGS ≥ VT S
e.g. RON = 5 KΩ
Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT
OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
6.002 Fall 2000
Lecture 5
SR Model of MOSFET
D
D
G
G
G
vGS < VT
S
S
MOSFET
S model
RON
vGS ≥ VT S
MOSFET
SR model
vGS ≥ VT
vGS ≥ VT
iDS
D
iDS
vGS < VT
1
RON
vGS < VT
vDS
vDS
Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT
OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
6.002 Fall 2000
Lecture 5
Using the SR model
VS
RL
RL
vOUT
+ VS
–
vOUT
IN
C
VS =
C
“1”
OUT
Truth table for
VS
RL
vOUT
C VOUT
0 1
1 0
RON
C =0
VS
RL
C =1
vGS ≥ VT
vOUT
RON
Choose RL, RON, VS such that:
V R
v
= S ON ≤ V
OL
OUT R
+R
L
ON
Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT
OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
6.002 Fall 2000
Lecture 5