Compound gates

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11.1
Unit 11 – Semiconductor
Technology
With focus on MOS Transistors
11.2
Evolution of transistor in ICs
• BJT invention, Bell Labs, 1947
• Single transistor, TI, 1958
• CMOS gate, Fairchild, 1963
• First processor, Intel, 1970
• Very Large Scale Integration, 1978
•
Up to 20k transistor
• Ultra Large Scale Integration, 1989
•
More than 1 million per chip
• System-on-Chip, 2002-2015
•
Form 20-30 million transistors to several
billion transistors
11.3
Invention of the Transistor
• Vacuum tubes ruled in first half of 20th century
Large, expensive, power-hungry, unreliable
• 1947: first point contact transistor
– John Bardeen and Walter Brattain at Bell Labs
– See Crystal Fire
by Riordan, Hoddeson
11.4
Growth Rate
• 53% compound annual growth rate over 50
years
• No other technology has grown so fast so long
• Driven by miniaturization of transistors
– Smaller is cheaper, faster, lower in power!
– Revolutionary effects on society
[Moore65]
Electronics Magazine
11.5
Minimum Feature Size
11.6
Intel 4004 Micro-Processor
1971
1000 transistors
1 MHz operation
11.7
Intel Core I7
2nd Gen. Intel Core i7 Extreme Processor for
desktops launched in Q4 of 2012
• #cores/#threads: 6/12
• Technology node: 32nm
• Clock speed: 3.5 GHz
• Transistor count: Over one billion
• Cache: 15MB
• Addressable memory: 64GB
• Size: 52.5mm by 45.0mm mm2
11.8
ARM Cortex A15
ARM Cortex A15 in 2011 to 2013
• 4 cores per cluster, two clusters per chip
• Technology node: 22nm
• Clock speed: 2.5 GHz
• Transistor count: Over one billion
• Cache: Up to 4MB per cluster
• Addressable memory: up to 1TB
• Size: 52.5mm by 45.0mm
8
11.9
Cortex-A72
11.10
IBM z13 Storage Controller
11.11
Annual Sales
• >1019 transistors manufactured in 2008
– 1 billion for every human on the planet
11.12
Cost per Transistor
cost:
¢-per-transistor
1
0.1
Fabrication capital cost per transistor (Moore’s law)
0.01
0.001
0.0001
0.00001
0.000001
0.0000001
1982
1985
1988
1991
1994
1997
2000
2003
2006
2009
2012
11.13
Internet Traffic Growth
11.14
Transistor Types
• Bipolar transistors
– npn or pnp silicon structure
– Small current into very thin base layer controls
large currents between emitter and collector
– Base currents limit integration density
• Metal Oxide Semiconductor Field Effect
Transistors
– nMOS and pMOS MOSFETS
– Voltage applied to insulated gate controls current
between source and drain
– Low power allows very high integration
11.15
NMOS and PMOS Transistors
• NMOS conducts when gate input is at a high voltage
(logic ‘1’)
• PMOS conducts when gate input is at a low voltage
(logic ‘0’)
Output
( Drain )
Controlling
Input
( Gate )
Source
Controlling
Input
( Gate)
Output
( Drain)
Source
NMOS
(On if G=1)
Indicates a
P-type
PMOS
(On if G=0)
11.16
NMOS and PMOS Transistors
NMOS Transistors
1
0
Current Flows
(Small resistance between
source and output )
No Current Flows
( Large resistance between
source and output )
PMOS Transistors
0
Current Flows
(Small resistance between
source and output)
1
No Current Flows
( Large resistance between
source and output)
11.17
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
A
B
X
Y
Y = X if A and B
A
X
B
Y
Y = X if A OR B
NMOS Transistors pass a “strong” 0 but a “weak” 1
11.18
PMOS Transistors in
Series/Parallel Connection
• PMOS switch closes when switch control input is low
A
B
X
Y
Y = X if A AND B = A + B
A
X
B
Y
Y = X if A OR B = AB
PMOS Transistors pass a “strong” 1 but a “weak” 0
11.19
NMOS and PMOS Transistors
• NMOS transistors work best when one
terminal is connected to a low voltage
source, pulling the other terminal
down to that voltage
– Normally, source terminal is connected to
GND=0V
• PMOS transistors work best when one
terminal is connected to a high
voltage source, pulling the other
terminal down to that voltage
– Normally, source terminal is connected to
power supply voltage (+5V, +3V, etc.)
0V
NMOS
+3V
PMOS
11.20
CMOS
• Complimentary MOS (CMOS)
– Use PMOS to connect output to high
voltage source
+3V
• We call this the Pull-Up Network
– Use NMOS to connect output to low
voltage source (usually = GND)
PMOS
Pull-Up
Network
• We call this the Pull-Down Network
– Either PMOS or NMOS should
create a conductive path to
output, but not both
Pull-up OFF
Inputs
Pull-up ON
Pull-down OFF Z (float)
1
Pull-down ON
X (crowbar)
0
Output
NMOS
Pull-Down
Network
11.21
Signal Strength
• Strength of signal
– How close it approximates ideal voltage source
• VDD and GND rails are strongest 1 and 0
• nMOS passes strong 0
– But degraded or weak 1
• pMOS passes strong 1
– But degraded or weak 0
• Thus nMOSes are best for the pull-down
network, pMOSes are best for the pull-up
11.22
CMOS Inverter
• Inverter can be formed using
one PMOS and NMOS
transistor
• The input value connects to
both gate inputs
• The output is formed at the
junction of the drains
Vdd
A
A
GND
11.23
CMOS Inverter
• When input is 1, NMOS conducts and output is
pulled down to 0V (GND)
• When input is 0, PMOS conducts and output is
pulled up to 3V (VDD)
Vdd
Vdd
OFF
1
0
ON
0
1
ON
OFF
GND
GND
11.24
CMOS ‘NAND’ Gate
• If A and B = 1, the output
of the first circuit is pulled
to 0 (opposite of AND
function)
• If A or B = 0, the output of
the first circuit is pulled to
1 (opposite of AND
function)
Vdd
A
Vdd
B
A•B
A
B
NAND
portion
GND
NAND
11.25
CMOS ‘AND’ Gate
• If A and B = 1, the output
of the first circuit is pulled
to 0 (opposite of AND
function)
• If A or B = 0, the output of
the first circuit is pulled to
1 (opposite of AND
function)
• Inverter is then used to
produce true AND output
Vdd
A
Vdd
Vdd
B
A•B
A
A•B
B
NAND
portion
GND
NAND
Inverter
GND
Inverter to
produce AND
11.26
CMOS ‘NOR’ Gate
• If A or B = 1, the output of
the first circuit is pulled to
0 (opposite of OR
function)
• If A and B = 0, the output
of the circuit is pulled to 1
(opposite of OR function)
Vdd
NOR
portion
A
B
A+B
A
B
GND
NOR
GND
11.27
CMOS ‘NOR’ Gate
• If A or B = 1, the output of
the first circuit is pulled to
0 (opposite of OR
function)
• If A and B = 0, the output
of the circuit is pulled to 1
(opposite of OR function)
• Inverter is then used to
produce true OR output
Vdd
Vdd
NOR
portion
Inverter
A
A+B
B
A+B
A
B
GND
GND
OR
GND
11.28
CMOS (cont.)
• Complementary CMOS gates always produce 0 or 1
• Ex: NAND gate
– Series nMOS: Y=0 when both inputs are 1
– Thus Y=1 when either input is 0
– Requires parallel pMOS
Y
A
B
• Rule of Conduction Complements
– Pull-up network is the dual (complement) of pull-down
– Parallel -> series, series -> parallel
11.29
Compound Gates
• How could you build this gate?
• You could try building each gate
separately
– Two AND gates = ____ transistors
– One NOR gate = ____ transistors
• Or you could take build it as a
single compound gate.
11.30
Compound Gates
• Compound gates can do any inverting function
• Ex: AND-OR-INVERT (AOI)
Y = A•B + C•D
A
C
A
C
B
D
B
D
(a)
A
(b)
B C
D
(c)
D
A
B
(d)
C
D
A
B
A
C
B
D
A
B
C
D
Y
(e)
C
(f)
Y
11.31
Compound Gate Approach
• For an inverting function just look at the
expression (w/o the inversion) and…
– Implement the PDN using:
• Series connections for AND
• Parallel connections for OR
– Implement PUN as dual of PDN
• Swap series and parallel
• If function is non inverting just add an inverter
at the output
11.32
Compound Gate Example
Y = D • (A + B + C)
A
B
C
D
Y
D
A
B
C
11.33
Compound Gate Example
B
A
C
D
OUT = D + A • (B + C)
A
D
B
C
11.34
Compound Gate Example (cont.)
B
A
C
This is really a CMOS
inverter (2 transistors) but
we just show it this way to
save space and focus on the
1st stage cell
D
OUT = D + A • (B + C)
A
D
B
C
11.35
Another Compound Gate Example
OUT = A•D + B(C + E)
Add an inverter at the output
OUT = A•D + B(C + E)
Implement inverting function
using compound CMOS
gate
11.36
BACKUP
11.37
Series and Parallel Summary
•
•
•
•
a
a
nMOS: 1 = ON
pMOS: 0 = ON
Series: both must be ON
Parallel: either can be ON
0
g1
g2
(a)
(b)
a
g1
g2
(c)
a
g1
g2
b
0
1
b
b
OFF
OFF
OFF
ON
a
a
a
a
0
1
1
1
0
1
b
b
b
b
ON
OFF
OFF
OFF
a
a
a
a
0
0
b
1
b
0
b
1
1
0
g2
a
b
a
g1
a
0
0
b
(d)
a
0
1
1
0
1
1
b
b
b
b
OFF
ON
ON
ON
a
a
a
a
0
0
0
1
1
0
1
1
b
b
b
b
ON
ON
ON
OFF
11.38
Complementary CMOS
• Complementary CMOS logic gates
– nMOS pull-down network
– pMOS pull-up network
– a.k.a. static CMOS
Pull-up OFF
Pull-up ON
Pull-down OFF Z (float)
1
Pull-down ON
X (crowbar)
0
pMOS
pull-up
network
inputs
output
nMOS
pull-down
network
11.39
CMOS (cont.)
• Complementary CMOS gates always produce 0 or 1
• Ex: INVERTER gate
– A=0: nMOS is OFF, pMOS is ON, OUT is _______
– A=1: nMOS is ON, pMOS is OFF, OUT is _______
11.40
CMOS (cont.)
• Complementary CMOS gates always produce 0 or 1
• Ex: NOR gate
– Parallel nMOS: Y=0 when either input is 1
– Thus Y=1 when both inputs are 0
– Requires parallel nMOS
• Rule of Conduction Complements
– Pull-up network is complement (aka dual) of pull-down
– Parallel -> series, series -> parallel
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