Download Combination Logic

Digital Integrated
Circuits
A Design Perspective
Jan M. Rabaey
Anantha Chandrakasan
Borivoje Nikolić
Designing Combinational
Logic Circuits
November 2002.
EE141 Integrated
© Digital
Circuits2nd
1
Combinational Circuits
Combinational vs. Sequential Logic
Combinational
Logic
Circuit
In
In
Out
Out
Combinational
Logic
Circuit
State
Combinational
Output = f(In)
EE141 Integrated
© Digital
Circuits2nd
Sequential
Output = f(In, Previous In)
2
Combinational Circuits
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.
EE141 Integrated
© Digital
Circuits2nd
3
Combinational Circuits
Static Complementary CMOS
VDD
In1
In2
PUN
InN
In1
In2
InN
PMOS only
F(In1,In2,…InN)
PDN
NMOS only
PUN and PDN are dual logic networks
EE141 Integrated
© Digital
Circuits2nd
4
Combinational Circuits
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
EE141 Integrated
© Digital
Circuits2nd
5
Combinational Circuits
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
EE141 Integrated
© Digital
Circuits2nd
6
Combinational Circuits
Threshold Drops
VDD
PUN
VDD
S
D
VDD
D
0  VDD
VGS
S
CL
VDD  0
PDN
D
VDD
S
EE141 Integrated
© Digital
Circuits2nd
CL
0  VDD - VTn
CL
VGS
VDD  |VTp|
S
CL
D
7
Combinational Circuits
Complementary CMOS Logic Style
EE141 Integrated
© Digital
Circuits2nd
8
Combinational Circuits
Example Gate: NAND
EE141 Integrated
© Digital
Circuits2nd
9
Combinational Circuits
Example Gate: NOR
EE141 Integrated
© Digital
Circuits2nd
10
Combinational Circuits
Complex CMOS Gate
B
A
C
D
OUT = D + A • (B + C)
A
D
B
EE141 Integrated
© Digital
Circuits2nd
C
11
Combinational Circuits
Constructing a Complex Gate
VDD
VDD
C
F
SN4
F
SN1
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
EE141 Integrated
© Digital
Circuits2nd
12
Combinational Circuits
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
EE141 Integrated
© Digital
Circuits2nd
13
Combinational Circuits
Standard Cell Layout Methodology –
1980s
Routing
channel
VDD
signals
GND
EE141 Integrated
© Digital
Circuits2nd
14
Combinational Circuits
Standard Cell Layout Methodology –
1990s
Mirrored Cell
No Routing
channels
VDD
VDD
M2
M3
GND
Mirrored Cell
EE141 Integrated
© Digital
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”
In
2
Cell boundary
EE141 Integrated
© Digital
Circuits2nd
Out
GND
Rails ~10
16
Combinational Circuits
Standard Cells
With minimal
diffusion
routing
VDD
With silicided
diffusion
VDD
VDD
M2
In
Out
In
Out
In
Out
M1
GND
EE141 Integrated
© Digital
Circuits2nd
GND
17
Combinational Circuits
Standard Cells
VDD
2-input NAND gate
VDD
B
A
B
Out
A
GND
EE141 Integrated
© Digital
Circuits2nd
18
Combinational Circuits
Stick Diagrams
Contains no dimensions
Represents relative positions of transistors
VDD
VDD
Inverter
NAND2
Out
Out
In
GND
EE141 Integrated
© Digital
Circuits2nd
GND
A B
19
Combinational Circuits
Stick Diagrams
Logic Graph
A
j
X
C
C
B
X = C • (A + B)
C
i
A
B
A
B
C
EE141 Integrated
© Digital
i
X
VDD
j
B
Circuits2nd
PUN
GND
A
PDN
20
Combinational Circuits
Two Versions of C • (A + B)
A
C
B
A
B
C
VDD
VDD
X
GND
EE141 Integrated
© Digital
X
GND
Circuits2nd
21
Combinational Circuits
Consistent Euler Path
X
C
i
X
B
VDD
j
GND
EE141 Integrated
© Digital
Circuits2nd
A
A B C
22
Combinational Circuits
OAI22 Logic Graph
A
C
B
D
X
D
X = (A+B)•(C+D)
C
D
A
B
EE141 Integrated
© Digital
Circuits2nd
C
VDD
X
B
A
B
C
D
PUN
A
GND
PDN
23
Combinational Circuits
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}
EE141 Integrated
© Digital
Circuits2nd
24
Combinational Circuits
Multi-Fingered Transistors
One finger
Two fingers (folded)
Less diffusion capacitance
EE141 Integrated
© Digital
Circuits2nd
25
Combinational Circuits
Properties of Complementary CMOS Gates
Snapshot
High noise margins:
VOH and VOL are at VDD and GND, respectively.
No static power consumption:
There never exists a direct path between VDD and
VSS (GND) in steady-state mode.
Comparable rise and fall times:
(under appropriate sizing conditions)
EE141 Integrated
© Digital
Circuits2nd
26
Combinational Circuits
CMOS Properties
Full rail-to-rail swing; high noise margins
 Logic levels not dependent upon the relative
device sizes; ratioless
 Always a path to Vdd or Gnd in steady state;
low output impedance
 Extremely high input resistance; nearly zero
steady-state input current
 No direct path steady state between power
and ground; no static power dissipation
 Propagation delay function of load
capacitance and resistance of transistors

EE141 Integrated
© Digital
Circuits2nd
27
Combinational Circuits
Switch Delay Model
Req
A
A
Rp
A
Rp
Rp
B
Rn
Rp
CL
Rn
A
Cint
INV
NAND2
Circuits2nd
Cint
A
A
EE141 Integrated
© Digital
Rp
A
B
Rn
B
CL
Rn
Rn
A
B
CL
NOR2
28
Combinational Circuits
Input Pattern Effects on Delay
Delay is dependent on
the pattern of inputs
 Low to high transition

Rp
A
Rp
B
Rn
 both inputs go low
– delay is 0.69 Rp/2 CL
CL
 one input goes low
B
Rn
– delay is 0.69 Rp CL
Cint
A

High to low transition
 both inputs go high
– delay is 0.69 2Rn CL
EE141 Integrated
© Digital
Circuits2nd
29
Combinational Circuits
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
A=B=10
2.5
Voltage [V]
2
A=1 0, B=1
1.5
A=1, B=10
1
-0.5
0
100
200
time [ps]
EE141 Integrated Circuits2nd
© Digital
300
400
NMOS = 0.5m/0.25 m
PMOS = 0.75m/0.25 m
CL = 100 fF
30
Combinational Circuits
Transistor Sizing
Rp
2 A
Rp
B
Rn
2
B
2
Rn
A
EE141 Integrated
© Digital
Circuits2nd
Rp
4 B
2
CL
Cint
Rp
4
Cint
A
1
Rn
Rn
A
B
CL
1
31
Combinational Circuits
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
1
B
EE141 Integrated
© Digital
Circuits2nd
2
2C
2
32
Combinational Circuits
Fan-In Considerations
A
B
C
D
A
CL
B
C3
C
C2
D
C1
EE141 Integrated
© Digital
Circuits2nd
Distributed RC model
(Elmore delay)
tpHL = 0.69 Reqn(C1+2C2+3C3+4CL)
Propagation delay deteriorates
rapidly as a function of fan-in –
quadratically in the worst case.
33
Combinational Circuits
tp as a Function of Fan-In
1250
quadratic
tp (psec)
1000
Gates with a
fan-in
greater than
4 should be
avoided.
750
tpH
500
tp
L
250
tpL
linear
H
0
2
4
6
8
10
12
14
16
fan-in
EE141 Integrated
© Digital
Circuits2nd
34
Combinational Circuits
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
EE141 Integrated
© Digital
Circuits2nd
35
Combinational Circuits
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
EE141 Integrated
© Digital
Circuits2nd
36
Combinational Circuits
Fast Complex Gates:
Design Technique 1
 Transistor
sizing
 as long as fan-out capacitance dominates
 Progressive
InN
sizing
CL
MN
In3
M3
C3
In2
M2
C2
In1
M1
C1
EE141 Integrated
© Digital
Circuits2nd
Distributed RC line
M1 > M2 > M3 > … > MN
(the fet closest to the
output is the smallest)
Can reduce delay by more than
20%; decreasing gains as
technology shrinks
37
Combinational Circuits
Fast Complex Gates:
Design Technique 2
 Transistor
ordering
critical path
charged
CL
In3 1 M3
In2 1 M2
C2 charged
In1
M1
01
C1 charged
delay determined by time to
discharge CL, C1 and C2
EE141 Integrated
© Digital
Circuits2nd
critical path
01
In1
M3
CLcharged
In2 1 M2
C2 discharged
In3 1 M1
C1 discharged
delay determined by time to
discharge CL
38
Combinational Circuits
Fast Complex Gates:
Design Technique 3
 Alternative
logic structures
F = ABCDEFGH
EE141 Integrated
© Digital
Circuits2nd
39
Combinational Circuits
Fast Complex Gates:
Design Technique 4
 Isolating
fan-in from fan-out using buffer
insertion
CL
EE141 Integrated
© Digital
Circuits2nd
CL
40
Combinational Circuits
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
 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)

EE141 Integrated
© Digital
Circuits2nd
41
Combinational Circuits
Sizing Logic Paths for Speed
Frequently, input capacitance of a logic path
is constrained
 Logic also has to drive some capacitance
 Example: ALU load in an Intel’s
microprocessor is 0.5pF
 How do we size the ALU datapath to achieve
maximum speed?
 We have already solved this for the inverter
chain – can we generalize it for any type of
logic?

EE141 Integrated
© Digital
Circuits2nd
42
Combinational Circuits
Buffer Example
In
Out
1
2
N
CL
N
Delay    pi  g i  f i 
i 1
(in units of tinv)
For given N: Ci+1/Ci = Ci/Ci-1
To find N: Ci+1/Ci ~ 4
How to generalize this to any logic path?
EE141 Integrated
© Digital
Circuits2nd
43
Combinational Circuits
Logical Effort

CL 

Delay  k  RunitCunit 1 
 Cin 
t p  g  f 
p – intrinsic delay (3kRunitCunit) - gate parameter  f(W)
g – logical effort (kRunitCunit) – gate parameter  f(W)
f – effective fanout
Normalize everything to an inverter:
ginv =1, pinv = 1
Divide everything by tinv
(everything is measured in unit delays tinv)
Assume  = 1.
EE141 Integrated
© Digital
Circuits2nd
44
Combinational Circuits
Delay in a Logic Gate
Gate delay:
d=h+p
effort delay
intrinsic delay
Effort delay:
h=gf
logical
effort
effective fanout =
Cout/Cin
Logical effort is a function of topology, independent of sizing
Effective fanout (electrical effort) is a function of load/gate size
EE141 Integrated
© Digital
Circuits2nd
45
Combinational Circuits
Logical Effort
Inverter has the smallest logical effort and
intrinsic delay of all static CMOS gates
 Logical effort of a gate presents the ratio of its
input capacitance to the inverter capacitance
when sized to deliver the same current
 Logical effort increases with the gate
complexity

EE141 Integrated
© Digital
Circuits2nd
46
Combinational Circuits
Logical Effort
Logical effort is the ratio of input capacitance of a gate to the input
capacitance of an inverter with the same output current
VDD
A
VDD
A
2
2
B
F
2
F
A
A
VDD
B
4
A
4
2
F
1
A
B
Inverter
g=1
EE141 Integrated
© Digital
Circuits2nd
1
B
1
2
2-input NAND
g = 4/3
2-input NOR
g = 5/3
47
Combinational Circuits
Normalized delay (d)
Logical Effort of Gates
t pNAND
g=
p=
d=
t pINV
g=
p=
d=
F(Fan-in)
1
EE141 Integrated
© Digital
Circuits2nd
2
3
4
5
Fan-out (h)
6
7
48
Combinational Circuits
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
EE141 Integrated
© Digital
Circuits2nd
2
3
4
5
Fan-out (h)
6
7
49
Combinational Circuits
4/
3;
p
=
2
Logical Effort of Gates
=
D:
g
tN
AN
=
g
r:
e
t
er
1;
p=
1
v
in
3
pu
4
In
2-
Normalized Delay
5
Effort
Delay
2
1
Intrinsic
Delay
1
EE141 Integrated
© Digital
Circuits2nd
2
3
Fanout f
4
5
50
Combinational Circuits
Add Branching Effort
Branching effort:
b
EE141 Integrated
© Digital
Circuits2nd
Con path  Coff  path
Con path
51
Combinational Circuits
Multistage Networks
N
Delay    pi  g i  f i 
i 1
Stage effort: hi = gifi
Path electrical effort: F = Cout/Cin
Path logical effort: G = g1g2…gN
Branching effort: B = b1b2…bN
Path effort: H = GFB
Path delay D = Sdi = Spi + Shi
EE141 Integrated
© Digital
Circuits2nd
52
Combinational Circuits
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
Minimum path delay
Dˆ   gi f i  pi   NH 1/ N  P
EE141 Integrated
© Digital
Circuits2nd
53
Combinational Circuits
Optimal Number of Stages
For a given load,
and given input capacitance of the first gate
Find optimal number of stages and optimal sizing
D  NH 1/ N  Npinv
D
  H 1/ N ln H 1/ N  H 1/ N  pinv  0
N


Substitute ‘best stage effort’
EE141 Integrated
© Digital
Circuits2nd
hH
1/ Nˆ
54
Combinational Circuits
Logical Effort
From Sutherland, Sproull
EE141 Integrated
© Digital
Circuits2nd
55
Combinational Circuits
Example: Optimize Path
1
a
g=1
f=a
g = 5/3
f = b/a
b
c
5
g = 5/3
f = c/b
g=1
f = 5/c
Effective fanout, F =
G=
H=
h=
a=
b=
EE141 Integrated
© Digital
Circuits2nd
56
Combinational Circuits
Example: Optimize Path
1
a
g=1
f=a
g = 5/3
f = b/a
Effective fanout, F = 5
G = 25/9
H = 125/9 = 13.9
h = 1.93
a = 1.93
b = ha/g2 = 2.23
c = hb/g3 = 5g4/f = 2.59
EE141 Integrated
© Digital
Circuits2nd
b
c
5
g = 5/3
f = c/b
g=1
f = 5/c
57
Combinational Circuits
Example: Optimize Path
1
g1 = 1
a
g2 = 5/3
Effective fanout, H = 5
G = 25/9
F = 125/9 = 13.9
f = 1.93
a = 1.93
b = fa/g2 = 2.23
c = fb/g3 = 5g4/f = 2.59
EE141 Integrated
© Digital
Circuits2nd
b
c
5
g3 = 5/3
g4 = 1
58
Combinational Circuits
Example – 8-input AND
EE141 Integrated
© Digital
Circuits2nd
59
Combinational Circuits
Method of Logical Effort
Compute the path effort: F = GBH
 Find the best number of stages N ~ log4F
 Compute the stage effort f = F1/N
 Sketch the path with this number of stages
 Work either from either end, find sizes:
Cin = Cout*g/f

Reference: Sutherland, Sproull, Harris, “Logical Effort, Morgan-Kaufmann 1999.
EE141 Integrated
© Digital
Circuits2nd
60
Combinational Circuits
Summary
Sutherland,
Sproull
Harris
EE141 Integrated
© Digital
Circuits2nd
61
Combinational Circuits
Ratioed Logic
VDD
Resistive
Load
VDD
Depletion
Load
RL
PDN
VSS
(a) resistive load
PMOS
Load
VSS
VT < 0
F
In1
In2
In3
VDD
F
In1
In2
In3
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
EE141 Integrated
© Digital
Circuits2nd
62
Combinational Circuits
Ratioed Logic
VDD
• N transistors + Load
Resistive
Load
• VOH = V DD
RL
• VOL =
F
In1
In2
In3
RPN + RL
• Assymetrical response
PDN
• Static power consumption
VSS
EE141 Integrated
© Digital
RPN
Circuits2nd
• tpL= 0.69 RLCL
63
Combinational Circuits
Active Loads
VDD
Depletion
Load
VDD
PMOS
Load
VT < 0
VSS
F
In1
In2
In3
PDN
VSS
depletion load NMOS
EE141 Integrated
© Digital
Circuits2nd
F
In1
In2
In3
PDN
VSS
pseudo-NMOS
64
Combinational Circuits
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

kp
V OL =  VDD – V T  1 – 1 – -----(assuming that V T = V Tn = VTp )
kn
SMALLER AREA & LOAD BUT STATIC POWER DISSIPATION!!!
EE141 Integrated
© Digital
Circuits2nd
65
Combinational Circuits
Pseudo-NMOS VTC
3.0
2.5
W/Lp = 4
Vout [V]
2.0
1.5
W/Lp = 2
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]
EE141 Integrated
© Digital
Circuits2nd
66
Combinational Circuits
Improved Loads
VDD
M1
Enable
M2
M1 >> M2
F
A
B
C
D
CL
Adaptive Load
EE141 Integrated
© Digital
Circuits2nd
67
Combinational Circuits
Improved Loads (2)
VDD
M1
VDD
M2
Out
A
A
B
B
Out
PDN1
PDN2
VSS
VSS
Differential Cascode Voltage Switch Logic (DCVSL)
EE141 Integrated
© Digital
Circuits2nd
68
Combinational Circuits
DCVSL Example
Out
Out
B
B
A
B
B
A
XOR-NXOR gate
EE141 Integrated
© Digital
Circuits2nd
69
Combinational Circuits
DCVSL Transient Response
V olta ge [V]
2.5
AB
1.5
0.5
-0.5 0
EE141 Integrated
© Digital
Circuits2nd
AB
A,B
0.2
A,B
0.4
0.6
Time [ns]
0.8
1.0
70
Combinational Circuits
Pass-Transistor Logic
Inputs
B
Switch
Out
A
Out
Network
B
B
• N transistors
• No static consumption
EE141 Integrated
© Digital
Circuits2nd
71
Combinational Circuits
Example: AND Gate
B
A
B
F = AB
0
EE141 Integrated
© Digital
Circuits2nd
72
Combinational Circuits
NMOS-Only Logic
3.0
In
1.5m/0.25m
VDD
x
Out
0.5m/0.25m
0.5m/0.25m
Voltage [V]
In
Out
2.0
x
1.0
0.0
0
0.5
1
1.5
2
Time [ns]
EE141 Integrated
© Digital
Circuits2nd
73
Combinational Circuits
NMOS-only Switch
C = 2.5V
C = 2.5 V
M2
A = 2.5 V
A = 2.5 V
B
B
Mn
CL
M1
VB does not pull up to 2.5V, but 2.5V - VTN
Threshold voltage loss causes
static power consumption
NMOS has higher threshold than PMOS (body effect)
EE141 Integrated
© Digital
Circuits2nd
74
Combinational Circuits
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
EE141 Integrated
© Digital
Circuits2nd
75
Combinational Circuits
Restorer Sizing
Voltage [V]
3.0
2.0
•Upper limit on restorer size
•Pass-transistor pull-down
can have several transistors in
stack
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
EE141 Integrated
© Digital
200
Circuits2nd
W/L r =1.25/0.25
300
Time [ps]
400
500
76
Combinational Circuits
Solution 2: Single Transistor Pass Gate with
VT=0
VDD
VDD
0V
2.5V
VDD
0V
Out
2.5V
WATCH OUT FOR LEAKAGE CURRENTS
EE141 Integrated
© Digital
Circuits2nd
77
Combinational Circuits
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
EE141 Integrated
© Digital
Circuits2nd
A
F=AÝ
(b)
A
A
B
B
F=A+B
B
OR/NOR
A
F=AÝ
EXOR/NEXOR
78
Combinational Circuits
Solution 3: Transmission Gate
C
A
C
A
B
B
C
C
C = 2.5 V
A = 2.5 V
B
CL
C=0V
EE141 Integrated
© Digital
Circuits2nd
79
Combinational Circuits
Resistance of Transmission Gate
30
2.5 V
Resistance, ohms
Rn
20
Rp
2.5 V
Rn
Vou t
Rp
0V
10
Rn || Rp
0
0.0
EE141 Integrated
© Digital
1.0
Circuits2nd
Vou t , V
2.0
80
Combinational Circuits
Pass-Transistor Based Multiplexer
S
S
S
S
VDD
S
A
VDD
M2
F
S
M1
B
S
GND
In1
EE141 Integrated
© Digital
Circuits2nd
In2
81
Combinational Circuits
Transmission Gate XOR
B
B
M2
A
A
F
M1
M3/M4
B
B
EE141 Integrated
© Digital
Circuits2nd
82
Combinational Circuits
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)
EE141 Integrated
© Digital
Circuits2nd
83
Combinational Circuits
Delay Optimization
EE141 Integrated
© Digital
Circuits2nd
84
Combinational Circuits
Transmission Gate Full Adder
P
VDD
Ci
A
P
A
A
P
B
VDD
Ci
A
P
Ci
VDD
S Sum Generation
Ci
P
B
VDD
A
P
Co Carry Generation
Ci
A
Setup
P
Similar delays for sum and carry
EE141 Integrated
© Digital
Circuits2nd
85
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
EE141 Integrated
© Digital
Circuits2nd
86
Combinational Circuits
Dynamic Gate
Clk
Clk
Mp
off
Mp on
Out
In1
In2
In3
Clk
CL
PDN
1
Out
((AB)+C)
A
C
B
Me
Clk
off
Me on
Two phase operation
Precharge (Clk = 0)
Evaluate (Clk = 1)
EE141 Integrated
© Digital
Circuits2nd
88
Combinational Circuits
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
EE141 Integrated
© Digital
Circuits2nd
89
Combinational Circuits
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
EE141 Integrated
© Digital
Circuits2nd
90
Combinational Circuits
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
 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
EE141 Integrated
© Digital
Circuits2nd
91
Combinational Circuits
Issues in Dynamic Design 1:
Charge Leakage
CLK
Clk
Mp
Out
CL
A
Clk
Evaluate
VOut
Me
Precharge
Leakage sources
Dominant component is subthreshold current
EE141 Integrated
© Digital
Circuits2nd
92
Combinational Circuits
Solution to Charge Leakage
Keeper
Clk
Mp
A
Mkp
CL
Out
B
Clk
Me
Same approach as level restorer for pass-transistor logic
EE141 Integrated
© Digital
Circuits2nd
93
Combinational Circuits
Issues in Dynamic Design 2:
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
EE141 Integrated
© Digital
CB
Circuits2nd
94
Combinational Circuits
Charge Sharing Example
Clk
A
A
B
B
B
Cc=15fF
C
C
Ca=15fF
Out
CL=50fF
!B
Cb=15fF
Cd=10fF
Clk
EE141 Integrated
© Digital
Circuits2nd
95
Combinational Circuits
Charge Sharing
VDD
case 1) if V out < VTn
VDD
Clk

Mp
Mp
Out
Out
CL
A
A
=
BB
00
Clk 
CL
Ma
Ma
XX
M
Mb
b
Mee
M
EE141 Integrated
© Digital
a
CC
a
CC
bb
Circuits2nd
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
96
Combinational Circuits
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)
EE141 Integrated
© Digital
Circuits2nd
97
Combinational Circuits
Issues in Dynamic Design 3:
Backgate Coupling
Clk
Mp
A=0
Out1 =1
CL1
Out2 =0
CL2
In
B=0
Clk
Me
Dynamic NAND
EE141 Integrated
© Digital
Circuits2nd
Static NAND
98
Combinational Circuits
Backgate Coupling Effect
3
2
Out1
1
Clk
0
In
Out2
2
Time, ns
-1
0
EE141 Integrated
© Digital
Circuits2nd
4
6
99
Combinational Circuits
Issues in Dynamic Design 4: Clock
Feedthrough
Clk
Mp
A
Out
CL
B
Clk
Me
EE141 Integrated
© Digital
Circuits2nd
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.
100
Combinational Circuits
Clock Feedthrough
Clock feedthrough
Clk
Out
2.5
In1
1.5
In2
In3
In &
Clk
0.5
In4
Out
Clk
-0.5
0
0.5
Time, ns
1
Clock feedthrough
EE141 Integrated
© Digital
Circuits2nd
101
Combinational Circuits
Other Effects
 Capacitive
coupling
 Substrate coupling
 Minority charge injection
 Supply noise (ground bounce)
EE141 Integrated
© Digital
Circuits2nd
102
Combinational Circuits
Cascading Dynamic Gates
V
Clk
Clk
Mp
Mp
Out1
Clk
Me
Out2
In
In
Clk
Clk
Me
Out1
VTn
V
Out2
t
Only 0  1 transitions allowed at inputs!
EE141 Integrated
© Digital
Circuits2nd
103
Combinational Circuits
Domino Logic
Clk
In1
In2
In3
Clk
EE141 Integrated
© Digital
Mp
11
10
PDN
Me
Circuits2nd
Out1
Clk
Mp Mkp
Out2
00
01
In4
In5
Clk
PDN
Me
104
Combinational Circuits
Why Domino?
Clk
Ini
Inj
Clk
PDN
Ini
Inj
PDN
Ini
Inj
PDN
Ini
Inj
PDN
Like falling dominos!
EE141 Integrated
© Digital
Circuits2nd
105
Combinational Circuits
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
EE141 Integrated
© Digital
Circuits2nd
106
Combinational Circuits
Designing with Domino Logic
VDD
VDD
VDD
Clk
Mp
Clk
Mp
Out1
Mr
Out2
In1
In2
In3
PDN
PDN
In4
Can be eliminated!
Clk
Me
Clk
Me
Inputs = 0
during precharge
EE141 Integrated
© Digital
Circuits2nd
107
Combinational Circuits
Footless Domino
VDD
Clk
VDD
Mp
Clk
Mp
Out1
0
Clk
1
0
Outn
1
0
In2
0
Mp
Out2
In1
1
VDD
1
0
In3
1
0
1
Inn
1
0
The first gate in the chain needs a foot switch
Precharge is rippling – short-circuit current
A solution is to delay the clock for each stage
EE141 Integrated
© Digital
Circuits2nd
108
Combinational Circuits
Differential (Dual Rail) Domino
off
Mp Mkp
Clk
Out = AB
1
on
Mkp
0
Clk
Mp
1
A
!A
0
Out = AB
!B
B
Clk
Me
Solves the problem of non-inverting logic
EE141 Integrated
© Digital
Circuits2nd
109
Combinational Circuits
np-CMOS
Clk
In1
In2
In3
Mp
11
10
PDN
Clk
Me
Out1
Clk
Me
In4
In5
PUN
00
01
Clk
Mp
Out2
(to PDN)
Only 0  1 transitions allowed at inputs of PDN
Only 1  0 transitions allowed at inputs of PUN
EE141 Integrated
© Digital
Circuits2nd
110
Combinational Circuits
NORA Logic
Clk
In1
In2
In3
Mp
11
10
Out1
PDN
Clk
In4
In5
PUN
Clk
to other
PDN’s
WARNING: Very sensitive to noise!
EE141 Integrated
© Digital
Me
00
01
Me
Circuits2nd
Clk
Mp
Out2
(to PDN)
to other
PUN’s
111
Combinational Circuits