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Combinatorial Logic Circuits
© Digital Integrated Circuits2nd
EE141
1
Combinational Circuits
Index




Basic CMOS gates: Properties
Ratioed Logic
Pass transistor Logic
Dynamic Logic
Adapted from © Digital Integrated Circuits2nd
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Combinational vs. Sequential Logic
In
Combinational
Logic
Circuit
In
Out
Combinational
Logic
Circuit
Out
State
Combinational
Sequential
Output = f(In, Previous In)
Output = f(In)
Adapted from © Digital Integrated Circuits2nd
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Static CMOS Circuit
At every point in time (except during the switching
transients) each gate output is connected to either
VDD or Vss via a low-resistive path.
The outputs of the gates assume at all times the value
of the Boolean function, implemented by the circuit
(ignoring, once again, the transient effects during
switching periods).
This is in contrast to the
dynamic
circuit class, which
relies on temporary storage of signal values on the
capacitance of high impedance circuit nodes.
Adapted from © Digital Integrated Circuits2nd
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Static Complementary CMOS
VDD
In1
In2
F(In1,In2,…InN)=1 produce F=Vdd
PUN
PMOS only
InN
In1
In2
InN
F(In1,In2,…InN)
PDN
NMOS only
F(In1,In2,…InN)=0 produce F=GND
PUN and PDN are dual logic networks
Adapted from © Digital Integrated Circuits2nd
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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
Adapted from © Digital Integrated Circuits2nd
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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
Adapted from © Digital Integrated Circuits2nd
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Complementary CMOS Logic Style
Adapted from © Digital Integrated Circuits2nd
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Example Gate: NAND
Adapted from © Digital Integrated Circuits2nd
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Example Gate: NOR
Adapted from © Digital Integrated Circuits2nd
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Complex CMOS Gate
B
A
C
D
OUT = D + A • (B + C)
A
D
B
Adapted from © Digital Integrated Circuits2nd
C
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Constructing a Complex Gate
VDD
VDD
C
F
SN1
SN4
F
A
SN3
D
B
C
B
SN2
A
D
A
B
D
C
F
(a) pull-down network
(b) Deriving the pull-up network
hierarchically by identifying
sub-nets
A
D
B
C
(c) complete gate
Adapted from © Digital Integrated Circuits2nd
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Cell Design

Standard Cells
 General
purpose logic
 Can be synthesized
 Same height, varying width

Datapath Cells
 For
regular, structured designs (arithmetic)
 Includes some wiring in the cell
 Fixed height and width
Adapted from © Digital Integrated Circuits2nd
EE141
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Standard Cell Layout Methodology – 1980s
Routing
channel
VDD
signals
GND
2nd
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Adapted
Integrated
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Circuits2nd
14
Combinational Circuits
Standard Cell Layout Methodology – 1990s
Mirrored Cell
No Routing
channels
VDD
VDD
M2
M3
GND
Mirrored Cell
2nd
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Adapted
Integrated
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Circuits2nd
GND
15
Combinational Circuits
Standard Cells
N Well
VDD
Cell height 12 metal tracks
Metal track is approx. 3 + 3
Pitch =
repetitive distance between objects
Cell height is “12 pitch”
2
In
Out
GND
Cell boundary
2nd
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Adapted
Integrated
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Rails ~10
16
Combinational Circuits
Standard Cells
VDD
A
2-input ??? gate
B
Out
GND
2nd
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Adapted
Integrated
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17
Combinational Circuits
Stick Diagrams
Contains no dimensions
Represents relative positions of transistors
VDD
VDD
Inverter
NAND2
Out
Out
In
GND
2nd
EE141 from
© Digital
Adapted
Integrated
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Circuits
Integrated
GND
Circuits2nd
A B
18
Combinational Circuits
Stick Diagrams
Logic Graph
A
j
X
C
C
B
A
i
X
X = C • (A + B)
C
PUN
i
B
VDD
j
B
GND
A
B
C
Adapted from © Digital Integrated Circuits2nd
EE141
A
PDN
19
Two Versions of C • (A + B)
A
C
B
A
B
C
VDD
VDD
X
GND
X
GND
Permutation of input signals that produce uninterrupted active strips is important !
2nd
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© Digital
Adapted
Integrated
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20
Combinational Circuits
Euler Paths






There is a systematic approach to uninterrupted strips of active.
Two steps:
Step 1: Construction of logic graph
Step 2: Identification of Euler graphs
Euler path is a path through all nodes such that every edge is
visited once.
Euler path is equivalent to an uninterrupted A-strip (succesive S
and D connections)
Consistency: Same ordering for PUN and PDN
Adapted from © Digital Integrated Circuits2nd
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Euler Path
Node
X
C
i
X
B
Edge =
Transistor
Adapted from © Digital Integrated Circuits2nd
VDD
j
GND
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A
A B C
22
OAI22 Logic Graph
A
C
B
D
X
D
X = (A+B)•(C+D)
C
D
A
B
C
VDD
X
B
A
B
C
D
Adapted from © Digital Integrated Circuits2nd
A
GND
EE141
PUN
PDN
23
Example: x = ab+cd
x
x
c
b
VDD
x
a
c
b
VD D
x
a
d
GND
d
GND
(a) Logic graphs for (ab+cd)
(b) Euler Paths {a b c d}
VD D
x
GND
a
b
c
d
(c) stick diagram for ordering {a b c d}
Adapted from © Digital Integrated Circuits2nd
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CMOS Gates



Static Properties of gates
Delay characteristics
Fan-in and Fan-out considerations
Adapted from © Digital Integrated Circuits2nd
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Static Properties

Depend on input pattern
3V
a) A=B=0 → 1
Vout
c) B=1, A=0 → 1
b) A=1, B=0 → 1
0V
0V
3V
Vin
a) Two pull-up transistors in parallel are more difficult to turn off than one
b) One pull-up transistor, one pull-down. Dynamically, the internal node has
to be discharged (slower)
c) Vds1 produces bulk effect during discharge. More Vin is needed
Adapted from © Digital Integrated Circuits2nd
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Switch Delay Model
Req
A
A
Rp
A
Rp
Rp
B
Rn
Rp
Rp
A
CL
A
Cint
A
NAND2
Adapted from © Digital Integrated Circuits2nd
Cint
A
Rn
B
Rn
B
INV
EE141
CL
Rn
Rn
A
B
CL
NOR2
27
Input Pattern Effects on Delay

Rp
A
Rp


B
Rn
both inputs go low


CL

Cint

A
delay is 0.69 Rp CL
when N transistor A goes off, internal
node has to be charged
High to low transition

both inputs go high

Adapted from © Digital Integrated Circuits2nd
delay is 0.69 Rp/2 CL
one input goes low

B
Rn
Delay is dependent on the pattern
of inputs
Low to high transition
EE141
delay is 0.69 2Rn CL
28
Delay Dependence on Input Patterns
3
Input Data
Pattern
Delay
(psec)
A=B=01
67
A=1, B=01
64
A= 01, B=1
61
0.5
A=B=10
45
0
A=1, B=10
80
A= 10, B=1
81
2.5
A=B=10
2
A=1 0, B=1
Voltage [V]
1.5
1
-0.5
A=1, B=10
0
100
200
300
time [ps]
when N transistor A goes off, internal node has to
be charged (slower)
Adapted from © Digital Integrated Circuits2nd
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400
NMOS = 0.5m/0.25 m
PMOS = 0.75m/0.25 m
CL = 100 fF
29
Transistor Sizing
Rp
2 A
Rp
B
Rn
2
B
2
Rn
Rp
4 B
2
CL
Rp
4
Cint
A
Cint
1
A
Rn
Rn
A
B
CL
1
NAND based implementations are preferred over NOR …
Adapted from © Digital Integrated Circuits2nd
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Transistor Sizing a Complex CMOS Gate
A
B
8 6
C
8 6
4 3
D
4 6
OUT = D + A • (B + C)
A
D
2
1
B
Adapted from © Digital Integrated Circuits2nd
2C
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Fan-In Considerations
A
B
C
D
A
Distributed RC model
(Elmore delay)
CL
B
C3
C
C2
D
C1
tpHL = 0.69 Re (C1+2C2+3C3+4CL)
= Re C1+2 Re C2+3Re C3+4Re CL
* Propagation delay deteriorates
rapidly as a function of fan-in –
quadratically in the worst case. (prop.
to R×C)
* Internal nodes important !!
Adapted from © Digital Integrated Circuits2nd
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tp as a Function of Fan-In
1250
quadratic
1000
tp (psec)
Intrinsec C increases
linearly
Series transistors cause a
double slowdown
750
tpHL
Parallel transistors
increase C
tp
500
tpLH
250
linear
0
2
4
6
8
fan-in
10
12
14
16
Gates with a fan-in greater than 4 should be avoided.
Adapted from © Digital Integrated Circuits2nd
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tp as a Function of Fan-Out
tpNOR2
tpNAND2
tpINV
tp (psec)
2
All gates
have the
same drive
current.
Slope is a
function of
“driving
strength”
4
6
8
10
12
14
16
eff. fan-out
Adapted from © Digital Integrated Circuits2nd
EE141
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tp as a Function of Fan-In and Fan-Out


Fan-in: quadratic due to increasing resistance and
capacitance
Fan-out: each additional fan-out gate adds two gate
capacitances to CL
tp = a1FI + a2FI2 + a3FO
Adapted from © Digital Integrated Circuits2nd
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Fast Complex Gates: Design Technique 1


Transistor sizing
 as long as fan-out capacitance dominates
Progressive sizing
Distributed RC line
InN
MN
In3
M3
C3
In2
M2
C2
In1
M1
C1
CL
Adapted from © Digital Integrated Circuits2nd
M1 > M2 > M3 > … > MN
(the fet closest to the
output is the smallest)
Lower caps see smaller R
Can reduce delay by more than
20%; decreasing gains as
technology shrinks
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Fast Complex Gates: Design Technique 2

Transistor ordering

Transistor with more activity or with latest changes on top
critical path
In3 1 M3
critical path
01
In1
M3
charged
CL
In2 1 M2
C2 charged
In1
M1
01
C1 charged
delay determined by time to
discharge CL, C1 and C2
Adapted from © Digital Integrated Circuits2nd
CLcharged
In2 1 M2
C2 discharged
In3 1 M1
C1 discharged
delay determined by time to
discharge CL
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Fast Complex Gates: Design Technique 3

Alternative logic structures
F = ABCDEFGH
There are techniques to minimize switching time: logical effort
Adapted from © Digital Integrated Circuits2nd
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Fast Complex Gates: Design Technique 4

Isolating fan-in from fan-out using buffer insertion
CL
CL
Adapted from © Digital Integrated Circuits2nd
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Fast Complex Gates: Design Technique 5

Reducing the voltage swing
tpHL = 0.69 (3/4 (CL VDD)/ IDSATn )
= 0.69 (3/4 (CL Vswing)/ IDSATn )
 linear
reduction in delay (only when variation of Req is not
substantial; after this, delay gets worse)
 also reduces power consumption


But the following gate is much slower!
Or requires use of “sense amplifiers” on the receiving
end to restore the signal level (memory design)
Adapted from © Digital Integrated Circuits2nd
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Stages with general logic

What happens in the general case: no longer inverters

Suppose we drive a load using a non-inverter stage
increase the transistors by a factor g so that we have the
same driving as the inverter (per input)
 The input capacitance is g times bigger
 We
t p  kReq  Cint  CL   kReq  Cint  fCint 
t p  kReq  gCINV  fgCINV   t po  p  g  f /  
there’s more than one input
Adapted from © Digital Integrated Circuits2nd
EE141
tpo is the intrinsic time of a min. size inv.
41
Logical Effort
t p  t p0  p  g  f /  
f – effective fanout
p – intrinsic delay factor (multiple times of the inverter
intrinsic delay)
g – logical effort (ratio of its input capacitance to the inverter
capacitance when sized to deliver the same current). Increases
with gate complexity. Depends only on topology
Adapted from © Digital Integrated Circuits2nd
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Logical Effort
Logical effort quantifies how much less driving strength a gate has
compared to an inveter
VDD
A
VDD
A
2
2
B
2
F
F
A
A
VDD
B
4
A
4
2
F
1
A
B
Inverter
g=1
1
B
1
2
2-input NAND
g = 4/3
Adapted from © Digital Integrated Circuits2nd
EE141
2-input NOR
g = 5/3
43
Intrinsic delay factors
Gate Type
P
Inverter
1
N-input NAND
N
N-input NOR
N
N-way mux
2N
XOR, NXOR
Adapted from © Digital Integrated Circuits2nd
N 2^(N-1)
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Normalized delay (d)
Logical Effort of Gates
t pNAND
g = 4/3
p=2
d = (4/3)h+2
t pINV
g=1
p=1
d = h+1
F(Fan-in)
1
2
Adapted from © Digital Integrated Circuits2nd
3
4
5
Fan-out (h)
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6
7
45
Logical Effort of Gates
5
2-input NAND:
p=2; g=4/3
Inverter:
P=1; g=1
4
3
Effort
Delay
2
Normalized Delay
1
Intrinsic
Delay
1
2
Adapted from © Digital Integrated Circuits2nd
3
Fanout f
EE141
4
5
46
Multistage Networks
N
Delay  t p 0   pi  g i  f i 
i 1
Stage effort: hi = gifi
Path electrical effort: F = Cout/Cin
Path logical effort: G = g1g2…gN
F   fi / B
Branching effort: B = b1b2…bN
Path effort: H = GFB
Path delay D  t p 0
N
p  h 
i 1
Adapted from © Digital Integrated Circuits2nd
i
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i
47
Add Branching Effort
Branching effort:
b
Con path  Coff  path
Adapted from © Digital Integrated Circuits2nd
Con path
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Optimum Effort per Stage
When each stage bears the same effort:
hN  H
hN H
Stage efforts: g1f1 = g2f2 = … = gNfN
Effective fanout of each stage: f i  h g i
Adapted from © Digital Integrated Circuits2nd
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Sizing

After the fi’s have been
obtained, the sizing factors
si’s are calculated starting
from the first one:

The others are obtained
iteratively
Reference: Sutherland, Sproull, Harris, “Logical Effort, MorganKaufmann 1999.
Adapted from © Digital Integrated Circuits2nd
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Example: Optimize Path
1
g=1
f=a
b
a
g = 5/3
f = b/a
Adapted from © Digital Integrated Circuits2nd
c
5
g = 5/3
f = c/b
EE141
g=1
f = 5/c
51
Adapted from © Digital Integrated Circuits2nd
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Example – 8-input AND
Adapted from © Digital Integrated Circuits2nd
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Summary
Sutherland,
Sproull
Harris
Adapted from © Digital Integrated Circuits2nd
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Ratioed Logic
© Digital Integrated Circuits2nd
EE141
55
Combinational Circuits
Ratioed Logic
VDD
Resistive
Load
VDD
Depletion
Load
RL
PDN
F
In1
In2
In3
VSS
(a) resistive load
PMOS
Load
VSS
VT < 0
F
In1
In2
In3
VDD
PDN
VSS
(b) depletion load NMOS
F
In1
In2
In3
PDN
VSS
(c) pseudo-NMOS
Goal: to reduce the number of devices over complementary CMOS
Adapted from © Digital Integrated Circuits2nd
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Ratioed Logic
VDD
• N transistors + Load
Resistive
Load
• VOH = V DD
RL
• VOL =
RPN + RL
F
In1
In2
In3
RPN
• Assymetrical response
PDN
• Static power consumption
• tpL= 0.69 RLCL
VSS
Adapted from © Digital Integrated Circuits2nd
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Active Loads
VDD
Depletion
Load
VDD
PMOS
Load
VT < 0
VSS
F
In1
In2
In3
F
In1
In2
In3
PDN
VSS
VSS
depletion load NMOS
Adapted from © Digital Integrated Circuits2nd
PDN
pseudo-NMOS
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Pseudo-NMOS
VDD
A
B
C
D
F
CL
VOH = VDD (similar to complementary CMOS)
2
V OL
kp


2
k n  VDD – V Tn  V OL – -------------  = ------  V DD – VTp 
2 
2

V OL =  VDD – V T  1 –
kp
1 – ------ (assuming that V T = V Tn = VTp )
kn
SMALLER AREA & LOAD BUT STATIC POWER DISSIPATION!!!
Adapted from © Digital Integrated Circuits2nd
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Pseudo-NMOS VTC
3.0
The bigger P, the
fastest the L to H
transition, but more
power and higher
Vol
2.5
W/Lp = 4
Vout [V]
2.0
1.5
W/Lp = 2
i
1.0
0.5
W/Lp = 0.5
W/Lp = 1
W/Lp = 0.25
0.0
0.0
0.5
1.0
1.5
2.0
2.5
Vin [V]
VOL
Adapted from © Digital Integrated Circuits2nd
EE141
V’OL
v
60
Performance of a P-NMOS inverter
Size
Vol
Static P
Tplh
4
0.693
564W
14 ps
2
0.273
298 W
56 ps
1
0.133
160 W
123 ps
½
0.064
80 W
268 ps
1/4
0.031
41 W
569 ps
Adapted from © Digital Integrated Circuits2nd
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Improved Loads (2)
VDD
VDD
M1
M2
Out
A
A
B
B
Out
PDN1
PDN2
VSS
VSS
Differential Cascode Voltage Switch Logic (DCVSL)
Adapted from © Digital Integrated Circuits2nd
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DCVSL Transient Response
Out
AB
B
A
B
B
A
V olta ge [V]
AB
Out
B
2.5
AB
1.5
0.5
-0.5 0
XOR-NXOR gate
Adapted from © Digital Integrated Circuits2nd
EE141
AB
A,B
0.2
A,B
0.4
0.6
Time [ns]
0.8
1.0
63
Pass-Transistor
Logic
© Digital Integrated Circuits2nd
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64
Combinational Circuits
Pass-Transistor Logic
Inputs
B
Switch
Out
A
Out
Network
B
B
• N transistors
• No static consumption
Adapted from © Digital Integrated Circuits2nd
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65
Example: AND Gate

B

Bottom ensures low
impedance path
B=1 and A=1 produces a
weak 1 ouput

A

B
Worsened by body effect
Fewer gates

Smaller capacitance
F = AB
0
Adapted from © Digital Integrated Circuits2nd
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NMOS-Only Logic
3.0
In
In
VDD
x
0.5m/0.25m
Out
0.5m/0.25m
Voltage [V]
1.5m/0.25m
Out
2.0
x
1.0
0.0
0
0.5
1
1.5
2
Time [ns]
Tail end of transient very slow due to the small current available
Adapted from © Digital Integrated Circuits2nd
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Series cascade
Adapted from © Digital Integrated Circuits2nd
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NMOS-only Switch
C = 2.5V
C = 2.5 V
M2
A = 2.5 V
A = 2.5 V
B
Mn
B
M1
CL
Vb does not pull up to 2.5V, but to 2.5V - Vtn
Threshold voltage loss causes static power consumption
NMOS has higher threshold than PMOS (body effect)
Adapted from © Digital Integrated Circuits2nd
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NMOS Only Logic: Level Restoring Transistor
VDD
VDD
Level Restorer
Mr
B
A
Mn
M2
X
Out
M1
• Advantage: Full Swing
• Restorer adds capacitance, takes away pull down current at X
• Ratio problem: Mn has to be able to pull down node X from Vdd to GND
Adapted from © Digital Integrated Circuits2nd
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Restorer Sizing
Voltage [V]
3.0
2.0
W/Lr =1.75/0.25
W/L r =1.50/0.25
1.0
W/Lr =1.0/0.25
0.0
0
100
200
W/L r =1.25/0.25
300
Time [ps]
400
• Upper limit on restorer size
• Pass-transistor pull-down
can have several transistors in
stack
• Fall time is accelerated, rise is
slowed down
500
Transistor Mn is fixed and size of Feedback (Mr) is increased (Switching
threshold of inverter is mid-rail).
Adapted from © Digital Integrated Circuits2nd
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Complementary Pass Transistor Logic
A
A
B
B
Pass-Transistor
F
Network
(a)
A
A
B
B
B
Inverse
Pass-Transistor
Network
B
B
A
F
B
B
A
A
B
F=AB
A
B
F=A+B
F=AB
AND/NAND
A
F=AÝ
(b)
A
A
B
B
F=A+B
B
OR/NOR
Adapted from © Digital Integrated Circuits2nd
EE141
A
F=AÝ
EXOR/NEXOR
73
Complementary Pass Transistor Logic





Complementary data inputs and outputs are always
available
Output are always connected to low-impedance
Design is very modular. The same topology is used.
Permutation of inputs is used.
Complementary signals have to be routed
Restorer has to be used, otherwise static consumption
Adapted from © Digital Integrated Circuits2nd
EE141
74
Solution 3: Transmission Gate
C
A
C
A
B
B
C
C
C = 2.5 V
A = 2.5 V
B
CL
C=0V
Adapted from © Digital Integrated Circuits2nd
EE141
75
Pass-Transistor Based Multiplexer
S
S
S
S
VDD
S
A
VDD
M2
F
S
M1
B
S
GND
In1
Adapted from © Digital Integrated Circuits2nd
EE141
In2
76
Transmission Gate XOR
B
B
M2
A
A
F
M1
M3/M4
B
B
Adapted from © Digital Integrated Circuits2nd
EE141
77
Resistance of Transmission Gate
R [kΩ]
30
2. 5 V
Resistance, ohms
Rn
20
Rp
2.5 V
Rn
Vou t
Rp
10
0
0.0
0V
Rn || Rp
1.0
2.0
Vou t , V
It has a series resistance that can be assumed constant, and equal to a couple of
KΩ
Adapted from © Digital Integrated Circuits2nd
EE141
78
Delay in Transmission Gate Networks
2.5
2.5
V1
In
2.5
Vi
Vi-1
C
0
2.5
C
0
Vn-1
Vi+1
C
0
Vn
C
C
0
(a)
Req
Req
V1
In
Req
Vi
C
Vn-1
Vi+1
C
C
Req
Vn
C
C
(b)
m
Req
Req
Req
Req
Req
Req
In
C
CC
C
C
CC
C
(c)
Adapted from © Digital Integrated Circuits2nd
EE141
79
Delay Optimization
mopt is typically 3 or 4 ..
Adapted from © Digital Integrated Circuits2nd
EE141
80
Dynamic Logic
© Digital Integrated Circuits2nd
EE141
81
Combinational Circuits
Dynamic CMOS

In static circuits at every point in time (except when
switching) the output is connected to either GND or
VDD via a low resistance path.
 fan-in

of n requires 2n (n N-type + n P-type) devices
Dynamic circuits rely on the temporary storage of
signal values on the capacitance of high impedance
nodes.
 requires
on n + 2 (n+1 N-type + 1 P-type) transistors
Adapted from © Digital Integrated Circuits2nd
EE141
82
Dynamic Gate
Clk
Clk
Mp
off
Mp on
Out
In1
In2
In3
Clk
CL
1
Out
((AB)+C)
A
PDN
C
B
Me
Clk
off
Me on
Two phase operation
Precharge (Clk = 0)
Evaluate (Clk = 1)
Adapted from © Digital Integrated Circuits2nd
EE141
84
Conditions on Output



Once the output of a dynamic gate is discharged, it
cannot be charged again until the next precharge
operation.
Inputs to the gate can make at most one transition
during evaluation.
Output can be in the high impedance state during and
after evaluation (PDN off), state is stored on CL
Adapted from © Digital Integrated Circuits2nd
EE141
85
Properties of Dynamic Gates

Logic function is implemented by the PDN only




number of transistors is N + 2 (versus 2N for static complementary CMOS)
Full swing outputs (VOL = GND and VOH = VDD)
Non-ratioed - sizing of the devices does not affect the logic levels
Faster switching speeds



reduced load capacitance due to lower input capacitance (Cin)
reduced load capacitance due to smaller output loading (Cout)
no Isc, so all the current provided by PDN goes into discharging CL
Adapted from © Digital Integrated Circuits2nd
EE141
86
Properties of Dynamic Gates

Overall power dissipation usually higher than static CMOS
 no static current path ever exists between VDD and GND (including Psc)
 no glitching
 higher transition probabilities due to periodic charge and discharge
 extra load on Clk

PDN starts to work as soon as the input signals exceed VTn, so VM,
VIH and VIL equal to VTn


low noise margin (NML)
Needs a precharge/evaluate clock
Adapted from © Digital Integrated Circuits2nd
EE141
87
Issues in Dynamic Design: Charge Leakage
CLK
Clk
Mp
Out
CL
A
Clk
Me
Evaluate
VOut
Precharge
Leakage sources
Dominant component is subthreshold current
Adapted from © Digital Integrated Circuits2nd
EE141
88
Solution to Charge Leakage
Keeper
Clk
Mp
A
Mkp
CL
Out
B
Clk
Me
Same approach as level restorer for pass-transistor logic
Adapted from © Digital Integrated Circuits2nd
EE141
89
Issues in Dynamic Design: Charge Sharing
Clk
Mp
Out
A
CL
B=0
Clk
Charge stored originally on CL is
redistributed (shared) over CL
and CA leading to reduced
robustness
CA
Me
CB
Adapted from © Digital Integrated Circuits2nd
EE141
90
Charge Sharing
VDD
case 1) if V out < VTn
VDD
Clk

Mp
Mp
Out
Out
CL
A
A
=
BB
00
Clk 
CL
Ma
Ma
M
Mb
b
Mee
M
XX
a
CC
a
CC
bb
C L VDD = C L Vout  t  + Ca  VDD – V Tn  V X  
or
Ca
V out = Vout  t  – V DD = – --------  V DD – V Tn  V X  
CL
case 2) if V out > VTn
Ca 
 ---------------------
Vout = –V DD 
C
+
C
 a
L
Adapted from © Digital Integrated Circuits2nd
EE141
91
Solution to Charge Redistribution
Clk
Mp
Mkp
Clk
Out
A
B
Clk
Me
Precharge internal nodes using a clock-driven transistor (at the cost of
increased area and power)
Adapted from © Digital Integrated Circuits2nd
EE141
92
Issues in Dynamic Design: Backgate Coupling
Clk
Mp
A=0
Out1 =1
CL1
Out2 =0
CL2
In
B=0
Clk
Me
Dynamic NAND
Adapted from © Digital Integrated Circuits2nd
Static NAND
EE141
93
Backgate Coupling Effect
3
2
Out1
1
Clk
0
In
Out2
2
Time, ns
-1
0
Adapted from © Digital Integrated Circuits2nd
EE141
4
6
94
Issues in Dynamic Design 4: Clock Feedthrough
Clk
Mp
A
Out
CL
B
Clk
Me
Coupling between Out and Clk
input of the precharge device
due to the gate to drain
capacitance. So voltage of
Out can rise above VDD.
The fast rising (and falling
edges) of the clock couple to
Out.
Signal levels above VDD may cause the normally reverse-biased junction diodes become
forward-biased causing electrons to be injected into the substrate: a) possible latch-up, b)
other nodes disturbed
Adapted from © Digital Integrated Circuits2nd
EE141
95
Clock Feedthrough
Clock feedthrough
Clk
Out
2.5
In1
In2
1.5
In3
In &
Clk
0.5
In4
Clk
Out
-0.5
0
0.5
Time, ns
1
Clock feedthrough
Adapted from © Digital Integrated Circuits2nd
EE141
96
Other Effects




Capacitive coupling
Substrate coupling
Minority charge injection
Supply noise (ground bounce)
Adapted from © Digital Integrated Circuits2nd
EE141
97
Cascading Dynamic Gates
V
Clk
Mp
Clk
Mp
Out1
Clk
Out2
In
In
Clk
Me
Clk
Me
Out1
VTn
V
Out2
t
Due to finite discharge time of first stage, the second stage
output drops when it shouldn’t
Adapted from © Digital Integrated Circuits2nd
EE141
98
Domino Logic
Clk
In1
In2
In3
Clk
Mp
11
10
Out1
PDN
Me
Clk
Mp Mkp
Out2
00
01
In4
In5
Clk
PDN
Me
Output transition always starts at 0, and only 0 →1 transitions occur
Adapted from © Digital Integrated Circuits2nd
EE141
99
Why Domino?
Clk
Ini
Inj
Clk
PDN
Ini
Inj
PDN
Ini
Inj
PDN
Ini
Inj
PDN
Like falling dominos!
Adapted from © Digital Integrated Circuits2nd
EE141
100
Properties of Domino Logic


Only non-inverting logic can be implemented
Very high speed
 static
inverter can be skewed, only L-H transition
 Input capacitance reduced – smaller logical effort
Adapted from © Digital Integrated Circuits2nd
EE141
101
Summary




Static CMOS: Performance is a strong function of fanin. Speed is a linear function of fan-in
Ratioed logic: reduction of complexity at the expense
of static consumption and asymmetrical response
Pass-transistor logic: simple for some functions. Long
switch networks have quadratic delay. NMOS only
networks are even simpler, but suffer from power
consumption and reduced margins
Dynamic logic: Trades off noise margins for
performance. Sensitive to leakage, coupling and charge
sharing. Cascading can cause problems
Adapted from © Digital Integrated Circuits2nd
EE141
102
Appendix I
Elmore Delay
© Digital Integrated Circuits2nd
EE141
103
Combinational Circuits
Y. Ismail, Equivalent Elmore Delays for RLC Trees,
DAC 1999
EE141
Adapted from © Digital Integrated Circuits2nd Proc.
104