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Digital Integrated
Circuits
A Design Perspective
Jan M. Rabaey
Anantha Chandrakasan
Borivoje Nikolic
Designing Sequential
Logic Circuits
Revised from Digital Integrated Circuits, © Jan M. Rabaey el
© Digital Integrated Circuits2nd
Sequential Circuits
Sequential Logic
Inputs
Outputs
COMBINATIONAL
LOGIC
Current State
Registers
Q
Next state
D
CLK
2 storage mechanisms
• positive feedback
• charge-based
© Digital Integrated Circuits2nd
Sequential Circuits
Naming Conventions
 In
our text:
 a latch is level sensitive
 a register is edge-triggered
 There
are many different naming
conventions
 For instance, many books call edgetriggered elements flip-flops
 This leads to confusion however
© Digital Integrated Circuits2nd
Sequential Circuits
Memory elements
 At high level , memory is classified as background memory
and foreground memory.
 Memory that is embedded into logic is foreground memory.
 Large amounts of centralized memory core is background
memory, which achieves higher area density through efficient
use of array structures.
 Here, we focus on foreground memory elements.
© Digital Integrated Circuits2nd
Sequential Circuits
Latch versus Register

Latch
stores data when
clock is high

D Q
D Q
Clk
Clk
Clk
Clk
D
D
Q
Q
© Digital Integrated Circuits2nd
Register
stores data when
clock rises or falls
Sequential Circuits
Latches
© Digital Integrated Circuits2nd
Sequential Circuits
Latch-Based Design
• P latch is transparent
when f = 1
• N latch is transparent
when f = 0
f
N
Latch
Logic
P
Latch
Logic
© Digital Integrated Circuits2nd
Sequential Circuits
Timing Definitions
CLK
t
tsu
D
D
thold
DATA
STABLE
Q
CLK
t
tc 2
Q
Register
q
DATA
STABLE
t
Tsetup: setup time is the time that data input D must be valid before
clock transition
Thold: hold time is the time that data input D must remain valid after
the clock edge
Tc2q: propagation delay of copying D to Q output (with respect to clk)
© Digital Integrated Circuits2nd
Sequential Circuits
Characterizing Timing
tD 2
D
Q
Clk
tC 2
Q
Clk
Q
Register
© Digital Integrated Circuits2nd
D
Q
tC 2
Q
Latch
Sequential Circuits
Maximum Clock Frequency
FF’s
f
tc2q + tp,comb + tsetup <= T
Clock period T must
accommodate the
longest possible delay
LOGIC
tp,comb
Also another constraint: tcdreg + tcdlogic > =thold
tcd: contamination delay = minimum delay
This constraint ensures the input data of the sequential circuits is
held long enough after the clock edge and not modified too soon
by the new coming-in data
© Digital Integrated Circuits2nd
Sequential Circuits
Positive Feedback: Bi-Stability
Vi2
V o1
V i1
V o2
A
V i 2 = V o1
C
B
V i 1 = V o2
When the gain of inverter in transient region is larger than 1,
A & B are the only stable operating points, C is metastable.
© Digital Integrated Circuits2nd
Sequential Circuits
Meta-Stability
Gain should be larger than 1 in the transition region
Hence, cross coupling of two inverters results in a bistable
circuit, that is a circuit with two stable states. The circuit
serves as a memory, storing either a 1 or 0 (A or B)
© Digital Integrated Circuits2nd
Sequential Circuits
Bistable circuit
 In absence of triggering, a bistable circuit remains in a
single state (static memory as long as power is on). Another
common name for a bistable circuit is flip-flop
 A FF is only useful when there is a mean to bring it from
one state to the other one.
 Two approaches can achieve that:
 cutting the feedback loop, once the feedback loop is
open, a new value can be written. This is called
multiplexer based.
 Overpowering the feedback loop, by applying a trigger
signal at the input of the FF, a new value is forced into the
circuit by overpowering the previous stored value.
© Digital Integrated Circuits2nd
Sequential Circuits
Mux-Based Latches
Negative latch
(transparent when CLK= 0)
1
D
CLK
Q  Clk  Q  Clk  In
Q
0
Q
0
© Digital Integrated Circuits2nd
Positive latch
(transparent when CLK= 1)
D
1
CLK
Q  Clk  Q  Clk  In
Sequential Circuits
Mux-based Static Latch
 The most robust and common technique to build a latch is
to use transmission-gate multiplexers.
 Use the clock as a decoupling signal, that distinguishes
between the transparent and opaque states
CLK
Q
Clock load is 4,
clock activity
factor is 1, so
more power
CLK
D
© Digital Integrated Circuits2nd
CLK
Sequential Circuits
Mux-Based Latch
Clock load reduced to 2 at the cost
of static power consumption
CLK
QM
CLK
QM
CLK
CLK
NMOS only
© Digital Integrated Circuits2nd
Non-overlapping clocks
Sequential Circuits
Static Latch: an alternative
CLK
I1
D
D
T1
I2
CLK
 Eliminating the feedback, we can obtain another
implementation of a latch by cross-coupling the inverters. In
this case, the transmission gate and source driver D must
overpower the feedback to switch the state.
 So now sizing is important. If minimum-sized devices are
used in transmission gates, it is essential that transistors of
inverter I2 be made even weaker.
© Digital Integrated Circuits2nd
Sequential Circuits
Master-Slave (Edge-Triggered)
Register
The most common approach for constructing an edge-triggered
Register is to use a master-slave configuration, which consists
of cascading a (negative/positive) latch with a
(positive/negative) one.
© Digital Integrated Circuits2nd
Sequential Circuits
Master-Slave Register design
I2
D
T2
I3
I5
T4
I4
T3
I6
Q
QM
I1
T1
CLK
• At low phase of the clock, master stage is transparent and D is passed to
QM. (During this time, slave stage is in hold mode, keeping its value using
feedback).
• On the rising edge, master stage stops sampling and slave starts sampling.
• At high phase of the clock, slave samples output QM, while master is in hold
mode. Since QM is constant now, Q makes one transition per clock cycle.
The value of Q is the value of D right before the rising edge.
© Digital Integrated Circuits2nd
Sequential Circuits
Clk-Q Delay
2.5
Volts
CLK
1.5
D
Tsetup
0.5
2 0.5
0
© Digital Integrated Circuits2nd
tc 2
q(lh)
tc 2
q(hl)
Q
0.5
1
1.5
time, nsec
2
2.5
Sequential Circuits
Setup Time
© Digital Integrated
Circuits2nd
Voltage at input of T2
Sequential Circuits
Timing properties of Master-Slave
Register (first order estimation)
I2
D
T2
I3
I5
T4
I4
T3
I6
Q
QM
I1
T1
CLK
Assume inverters have the same delay Tinv and transmission gates
have the same delay Ttp
Setup time: 2Tinv + Ttp
Propagation time: Ttp + 2Tinv
Hold time: 0
© Digital Integrated Circuits2nd
Sequential Circuits
Reduced Clock Load Master-Slave
Register
CLK
D
T1
CLK
CLK
I1
I2
T2
CLK
I3
Q
I4
Reverse conduction
When I4 is a weak device, it is not a major problem
Does this problem appear in the previous register?
© Digital Integrated Circuits2nd
Sequential Circuits
Avoiding Clock Overlap
Direct path from D to Q
CLK
CLK
Q
X
A
D
B
Driving the
same node
CLK
CLK
(a) Schematic diagram
CLK
CLK
(b) Overlapping clock pairs
© Digital Integrated
Circuits2nd
Problem at 0-0 overlap?
Sequential Circuits
Avoiding Clock Overlap
 When clock goes high, master stage should stop
sampling the input and go into hold mode. Since CLK and
CLK are both high for a short period of time, there is a direct
path from D to Q. As a result, Q might change during the
overlap period, which is undesired for edge-trigger registers.
This is known as a race condition in which Q is a function of
whether D arrives at node X before or after the falling edge
of the CLK.
 Also, if there is clock overlap between CLK and CLK,
node A can be driven by both D and B, which may result in
an undefined state.
 These problems can be avoided by using two nonoverlapping clocks.
© Digital Integrated Circuits2nd
Sequential Circuits
2 phase non-overlapping clocks
f
f
D
In
f
f
Note: During non-overlap time,
both latches are in highimpedance state (feedback loop
is open, gain is 0). So, this
duration should not be long.
f
f
tf12
© Digital Integrated Circuits2nd
Sequential Circuits
Overpowering the Feedback Loop ─
Cross-Coupled Pairs
NOR-based set-reset
S
R
S
R
Q
Q
0
0
Q
Q
1
0
1
0
0
1
1
1
0
0
1
0
Q
S
Q
R
Q
Q
Forbidden State
Cross-coupled NANDs
S
Q
What if they need to be clocked?
© Digital Integrated
Circuits2nd
R
Q
Sequential Circuits
Ratioed CMOS SR latch
VDD
M2
M4
Q
Q
Added clock
CLK
M6
S
M5
M1
M3
M8
CLK
M7
R
This is not used in datapaths any more,
but is a basic building memory cell
© Digital Integrated Circuits2nd
Sequential Circuits
Sizing Issues
2.0
3
Q
S
W = 0.5 m m
2
W = 0.6 m m
W = 0.7 m m
Volts
Q (Volts)
1.5
1.0
1
W = 0.8 m m
0.5
0.0
2.0
2.5
3.0
W/L 5 and 6
3.5
4.0
(a)
0
W = 1m m
W = 0.9 m m
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
time (ns)
(b)
Output voltage dependence
on transistor width
Transient response
Boundary condition: current equal
© Digital Integrated Circuits2nd
Sequential Circuits
Storage Mechanisms
Static latch
Dynamic (charge-based) latch
CLK
CLK
Q
CLK
D
Q
D
CLK
CLK
A stored value remains
valid as long as power
supply is applied.
Drawback: complexity
© Digital Integrated Circuits2nd
Temporary storage of
charge on parasitic
capacitors, similar to
dynamic logic. Periodic
refresh may be necessary.
Sequential Circuits
Dynamic transmission gate register
CLK
CLK
B
A
D
CLK
Q=D
CLK
This implementation is very efficient since it requires only 8 transistors
(6 if NMOS only switches). The reduced transistor count is attractive for
high-performance data path.
Setup time: Ttp
Propagation time: Ttp + 2Tinv
Hold time: 0
© Digital Integrated Circuits2nd
Sequential Circuits
Correct operation of dynamic register
CLK
CLK
D
Q
CLK
CLK
Positive-edge triggered register
 Since registers are periodically clocked, the storage nodes are
constantly updated.
 Clock overlap might be an important concern. During 0-0 overlap
period, a direct path for data flow from D to Q exists (a race condition
occurs). The same is true for 1-1 overlap period.
 0-0 overlap can be addressed if there is enough delay between D
input and Q. 1-1 overlap can be taken care of by enforcing that the hold
time larger than the overlap duration.
© Digital Integrated Circuits2nd
Sequential Circuits
Correct operation of dynamic register
CLK
CLK
D
Q
CLK
CLK
Positive-edge triggered register
CLK
CLK
© Digital Integrated Circuits2nd
Ensure
enough delay
Hold time
constraint
Sequential Circuits
2-phase dynamic register
f
f
In
D
Input Sampled
f
f
Output Enable
© Digital Integrated Circuits2nd
Sequential Circuits
Making a Dynamic Latch Pseudo-Static
CLK
D
D
CLK
 Dynamic register is very appealing from perspectives of complexity,
performance and power consumption. But robustness limit its use. The
storage node is prone to coupling, noise and leakage.
 Fortunately, most of the problems can be adequately addressed by
adding a weak feedback inverter and making it pseudostatic (at slight cost
of delay).
© Digital Integrated Circuits2nd
Sequential Circuits
More Precise Setup Time
© Digital Integrated Circuits2nd
Sequential Circuits
Setup/Hold Time Illustrations
Circuit before clock arrival (Setup-1 case)
CN
TG1
D
Inv2
SM
D1
QM
Clk-Q Delay
Inv1
CP
TClk-Q
TSetup-1
Data
Time
Clock
TSetup-1
t=0
© Digital Integrated Circuits2nd
Time
Sequential Circuits
Setup/Hold Time Illustrations
Circuit before clock arrival (Setup-1 case)
CN
TG1
D
Inv2
SM
D1
QM
Clk-Q Delay
Inv1
CP
TClk-Q
TSetup-1
Data
Time
Clock
TSetup-1
t=0
© Digital Integrated Circuits2nd
Time
Sequential Circuits
Setup/Hold Time Illustrations
Circuit before clock arrival (Setup-1 case)
CN
TG1
D
Inv2
SM
D1
QM
Clk-Q Delay
Inv1
CP
TClk-Q
TSetup-1
Data
Time
Clock
TSetup-1
t=0
© Digital Integrated Circuits2nd
Time
Sequential Circuits
Setup/Hold Time Illustrations
Circuit before clock arrival (Setup-1 case)
CN
TG1
D
Inv2
SM
D1
Clk-Q Delay
QM
Inv1
TClk-Q
CP
TSetup-1
Data
Time
Clock
TSetup-1
t=0
© Digital Integrated Circuits2nd
Time
Sequential Circuits
Setup/Hold Time Illustrations
Circuit before clock arrival (Setup-1 case)
CN
TG1
D
Inv2
SM
D1
Clk-Q Delay
TClk-Q
QM
Inv1
CP
TSetup-1
Data
Time
Clock
TSetup-1
t=0
© Digital Integrated Circuits2nd
Time
Sequential Circuits
Setup/Hold Time Illustrations
Hold-1 case
CN
TG1
SM
D1
D
Inv2
Clk-Q Delay
QM
Inv1
CP
0
TClk-Q
THold-1
Clock
Data
THold-1
t=0
© Digital Integrated Circuits2nd
Time
Sequential Circuits
Time
Setup/Hold Time Illustrations
Hold-1 case
CN
TG1
SM
D1
D
Inv2
Clk-Q Delay
QM
Inv1
CP
0
TClk-Q
THold-1
Clock
Data
THold-1
t=0
© Digital Integrated Circuits2nd
Time
Sequential Circuits
Time
Setup/Hold Time Illustrations
Hold-1 case
CN
TG1
SM
D1
D
Inv2
Clk-Q Delay
QM
Inv1
CP
0
TClk-Q
THold-1
Clock
Data
THold-1
t=0
© Digital Integrated Circuits2nd
Time
Sequential Circuits
Time
Setup/Hold Time Illustrations
Hold-1 case
CN
TG1
SM
D1
D
Inv1
Inv2
Clk-Q Delay
QM
TClk-Q
CP
0
THold-1
Clock
Data
THold-1
t=0
© Digital Integrated Circuits2nd
Time
Sequential Circuits
Time
Setup/Hold Time Illustrations
Hold-1 case
CN
TG1
SM
D1
D
Inv2
Clk-Q Delay
QM
TClk-Q
Inv1
CP
0
THold-1
Clock
Data

THold-1
t=0
© Digital Integrated Circuits2nd
Time
Sequential Circuits
Time
Other Latches/Registers:
2
C MOS
Clock overlap insensitive register: embed clock signal in
VDD
VDD
the inverter
M2
CLK
M6
M4
CLK
M8
X
D
CLK
M3
M1
Master Stage
Q
CL1
CLK
M7
CL2
M5
Slave Stage
“Keepers” can be added to make circuit pseudo-static
© Digital Integrated Circuits2nd
Sequential Circuits
Insensitive to Clock-Overlap
0
VDD
VDD
VDD
VDD
M2
M6
M2
M6
M4
0
M8
X
D
Q
X
D
1
M1
M5
(a) Equivalent circuit in (0-0) overlap
X can make only
0->1 transition,
but can not make
it to Q
© Digital Integrated Circuits2nd
M3
M1
Q
1
M7
M5
(b) Equivalent circuit (1-1) overlap
No direct path
from D to Q
CLK
CLK
Overlapping clock pairs
Sequential Circuits
C2MOS
 The circuit is insensitive to clock overlaps since overlaps
activate either the pull-up or the pull-down network in
master/slave stage (never both)
 One potential problem is slow rise and fall of the clocks,
where both NMOS and PMOS are on. This could create a
path between input and output that can destroy the state.
CLK
CLK
 Timing (delay) characteristics may be improved compared
to transmission-gate-based static register.
© Digital Integrated Circuits2nd
Sequential Circuits