Digital Integrated
Circuits
A Design Perspective
Jan M. Rabaey
Anantha Chandrakasan
Borivoje Nikolić
Timing Issues
January 2003
EE141 Integrated
© Digital
Circuits2nd
1
Timing Issues
Synchronous Timing
CLK
In
R1
EE141 Integrated
© Digital
Circuits2nd
Cin
Combinational
Logic
Cout
R2
Out
2
Timing Issues
Timing
Definitions
EE141 Integrated
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Circuits2nd
3
Timing Issues
Latch Parameters
the register maximum propagation delay
tc-q is clock to output and
td-q is data to output delay
D Q
Clk
data D must be stable to be properly registered
in the latch (no unintended changes when the
latch is transparent)
T
Clk
PWm
D
tsu
thold
tc-q
Q
td-q
Intended change must come before the latch closes by at least tsu
Delays can be different for rising and falling data transitions
EE141 Integrated
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4
Timing Issues
Register Parameters
D Q
Data must be stable before the rising edge
of the clock and held sufficiently long to be
processed by the register
Clk
T
Clk
thold
D
tsu
tc-q
Q
Delays can be different for rising and falling data transitions
EE141 Integrated
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5
Timing Issues
Clock Uncertainties
4 Power Supply
3 Interconnect
Devices
2
5 Temperature
6 Capacitive Load
7 Coupling to Adjacent Lines
1 Clock Generation
Sources of clock uncertainty
EE141 Integrated
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6
Timing Issues
Clock Nonidealities

Clock skew (constant delay)
 Spatial variation in temporally equivalent clock
edges; deterministic + random, tSK

Clock jitter (random variations)
 Temporal variations in consecutive edges of the
clock signal; modulation + random noise
 Cycle-to-cycle (short-term) tJS
 Long term tJL

Variation of the pulse width
 Important for level sensitive clocking
EE141 Integrated
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7
Timing Issues
Clock Skew and Jitter
Clk
tSK
Clk
tJS
Both skew and jitter affect the effective cycle time
 Only skew affects the race margin

EE141 Integrated
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8
Timing Issues
Clock Skew
# of registers
Earliest occurrence
of Clk edge
Nominal – /2
Latest occurrence
of Clk edge
Nominal +  /2
Insertion delay
Max Clk skew
Clk delay

EE141 Integrated
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9
Timing Issues
Positive and Negative Skew
In
R1
Combinational
Logic
D Q
CLK
R2
D Q
tCLK1
Combinational
Logic
R3
tCLK2
delay
•••
D Q
tCLK3
delay
(a) Positive skew
In
R1
Combinational
Logic
D Q
tCLK1
R2
D Q
Combinational
Logic
tCLK2
delay
R3
•••
D Q
tCLK3
delay
CLK
(b) Negative skew
EE141 Integrated
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10
Timing Issues
Positive Skew
TCLK + d
CLK1
CLK2
TCLK
1
3
d
2
4
d + th
Launching register clock edge arrives before the
receiving register clock edge
EE141 Integrated
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11
Timing Issues
Negative Skew
TCLK + d
1
CLK1
CLK2
2
d
TCLK
3
4
Receiving register clock edge arrives before the
launching register clock edge
EE141 Integrated
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12
Timing Issues
Timing Constraints
In
R1
D
R2
Q
Combinational
Logic
tCLK1
CLK
tc - q
tc - q, cd
tsu, thold
D
Q
tCLK2
tlogic
tlogic, cd
Minimum clock cycle time:
T -  = tc-q + tsu + tlogic
Were cd stands for a contamination
or a minimum delay both in register
propagation time and combinational
logic delay
Worst case is when receiving edge arrives early (negative )
thus a negative clock skew reduces the clock frequency
EE141 Integrated
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13
Timing Issues
Timing Constraints
R1
In
D
R2
Q
Combinational
Logic
tCLK1
CLK
tc - q
tc - q, cd
tsu, thold
D
Q
tCLK2
tlogic
tlogic, cd
Hold time constraint:
t(c-q, cd) + t(logic, cd) > thold + 
Worst case is when receiving edge arrives late (positive skew)
Race between data and clock is more likely for a positive clock skew
EE141 Integrated
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14
Timing Issues
Impact of Jitter
TC LK

CLK




t j itter
-tji tte r 
Combinational
Logic
REGS
In
CLK
tc-q , tc-q,
ts u, thold
tjitter
cd
t log ic
t log ic, cd
Since jitter is a random delay it increases the minimum clock period
and increases likelihood for race between clock and data
EE141 Integrated
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15
Timing Issues
Longest Logic Path in
Edge-Triggered Systems
TSU
Clk
TClk-Q
Latest point
of launching
TJI + 
TLM
T
Earliest arrival
of next cycle
TLM - the maximum logic delay
EE141 Integrated
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16
Timing Issues
Clock Constraints in
Edge-Triggered Systems
If the launching edge is late and the receiving edge is early,
the data will not be too late if:
Tc-q + TLM + TSU < T – TJI,1 – TJI,2 - 
Minimum cycle time is determined by the maximum delays through the logic
Tc-q + TLM + TSU +  + 2 TJI < T
Skew can be either positive or negative
EE141 Integrated
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17
Timing Issues
Shortest Path
Shortest path effects feedback
connections that typically have
a negative clock skew
Earliest point
of launching
Clk
TClk-Q TLm
TLm - the minimum logic delay
Clk
TH
Nominal
clock edge
EE141 Integrated
© Digital
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Data must not arrive
before this time
18
Timing Issues
Clock Constraints
in Edge-Triggered Systems
If launching edge is early and receiving edge is late:
Tc-q + TLm – TJI,1 > TH + TJI,2 + 
Minimum logic delay
Tc-q + TLm > TH + 2TJI+ 
For clock skew only we had:
t(c-q, cd) + t(logic, cd) > thold + 
EE141 Integrated
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19
Timing Issues
How to counter Clock Skew?


.
REG
REG
In

REG
REG
Negative Skew
log
Out

Positive Skew
Clock Distribution
Data and Clock Routing
EE141 Integrated
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20
Timing Issues
Flip-Flop – Based Timing
Logic propagation must finish
before the next clock’s rising edge
Skew
Flip-flop
delay
Logic delay

TSU
TClk-Q
Flip
-flop
=0
=1
Logic
Clock cycle
Representation after
M. Horowitz, VLSI Circuits 1996.
EE141 Integrated
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21
Timing Issues
Flip-Flops and Dynamic Logic
Logic delay
TSU
TSU
TClk-Q
TClk-Q
=0
=0
=1
=1
Logic delay
Precharge
Evaluate
In dynamic logic gates logic propagation
must finish before the clock’s falling edge
Evaluate
Dual relation holds for the PUN
controlled by inverted clocks
Flip-flops are used only with static logic
EE141 Integrated
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Precharge
22
Timing Issues
Latch timing
When data arrives
to a transparent latch
tD-Q
D
Q
Latch is a ‘soft’ barrier
Clk
tClk-Q
When data arrives
to closed latch
Data has to be ‘re-launched’
EE141 Integrated
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23
Timing Issues
Single-Phase Clock with Latches

Latch
Logic
Tskl
Tskl
Tskt
Tskt
Clk
PW
P
EE141 Integrated
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24
Timing Issues
Latch-Based Design
L1 latch is
transparent
when  = 0
L2 latch is transparent
when  = 1

L1
Latch
Logic
L2
Latch
Logic
EE141 Integrated
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25
Timing Issues
Slack-borrowing
In
L1
D
Q
CLB_A
t pd,A
a
b
CLK1
L2
D Q
CLB_B
t pd,B
c
L1
d
D
CLK2
Q
e
CLK1
TCLK
CLK1




CLK2
t pd,A
a valid
EE141 Integrated
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t DQ
tpd,B
b valid c valid
t DQ
slack passed to next stage
shortening the clock period
requirement
e valid
d valid
26
Timing Issues
Clock Distribution
H-tree
balances the
clock skew
CLK
Clock is distributed in a tree-like fashion
EE141 Integrated
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27
Timing Issues
More realistic H-tree
[Restle98]
EE141 Integrated
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28
Timing Issues
The Grid Clock Distribution
GCL K
•Does not require
rc-matching
Driver
Driver
Driver
GCLK
•Large power dissipation
GCLK
•Easier to satisfy metal
density requirement
in fabrication
Driver
GCL K
EE141 Integrated
© Digital
Circuits2nd
•Good thermal distribution
29
Timing Issues
Example: DEC Alpha 21164
Clock Frequency: 300 MHz - 9.3 Million Transistors
Total Clock Load: 3.75 nF
Power in Clock Distribution network : 20 W (out of 50)
Uses Two Level Clock Distribution:
• Single 6-stage driver at center of chip
• Secondary buffers drive left and right side
clock grid in Metal3 and Metal4
Total driver size: 58 cm!
EE141 Integrated
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30
Timing Issues
21164 Clocking
tcycle= 3.3ns
trise = 0.35ns

tskew = 150ps
Clock waveform





final drivers


pre-driver
Location of clock
driver on die
EE141 Integrated
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2 phase single wire clock,
distributed globally
2 distributed driver channels


Reduced RC delay/skew
Improved thermal distribution
3.75nF clock load
58 cm final driver width
Local inverters for latching
Conditional clocks in caches to
reduce power
More complex race checking
Device variation effects
symmetry
31
Timing Issues
Clock Drivers
EE141 Integrated
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32
Timing Issues
Clock Skew in Alpha Processor
Clock skew
EE141 Integrated
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33
Timing Issues
EV6 (Alpha 21264) Clocking
600 MHz – 0.35 micron CMOS
tcycle= 1.67ns
trise = 0.35ns
Global clock waveform

tskew = 50ps
2 Phase, with multiple conditional
buffered clocks
 2.8 nF clock load
 40 cm final driver width




PLL
EE141 Integrated
© Digital
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Local clocks can be gated “off” to
save power
Reduced load/skew
Reduced thermal issues
Multiple clocks complicate race
checking
34
Timing Issues
21264 Clocking
EE141 Integrated
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35
Timing Issues
EV6 Clock Results
ps
300
305
310
315
320
325
330
335
340
345
ps
5
10
15
20
25
30
35
40
45
50
GCLK Skew
GCLK Rise Times
(at Vdd/2 Crossings)
(20% to 80% Extrapolated to 0% to 100%)
EE141 Integrated
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36
Timing Issues
EV7 Clock Hierarchy
Active Skew Management and Multiple Clock Domains
+ widely dispersed
drivers
DLL
DLL
DLL
NCLK
(Mem Ctrl)
+ DLLs compensate
static and lowfrequency variation
GCLK
(CPU Core)
SYSCLK
EE141 Integrated
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L2R_CLK
(L2 Cache)
PLL
L2L_CLK
(L2 Cache)
+ divides design and
verification effort
- DLL design and
verification is added
work
+ tailored clocks
37
Timing Issues
Self-timed and Asynchronous
Design
Functions of clock in synchronous design
1) Acts as completion signal
2) Ensures the correct ordering of events
Truly asynchronous design
1) Completion is ensured by careful timing analysis
2) Ordering of events is implicit in logic
Self-timed design
1) Completion ensured by completion signal
2) Ordering imposed by handshaking protocol
EE141 Integrated
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38
Timing Issues
Synchronous Pipelined Datapath
R1
D Q
In
CLK
Logic
Block #1
tpd,reg
R2
D Q
tpd1
Logic
Block #2
tpd2
R3
D Q
R4
D Q
Logic
Block #3
tpd3
Make sure that the clock period T is larger than the max delay
T > max(tpd1,tpd2,tpd3 )+tpd,reg
Problems:
Clock skew and jitter
Strong clock currents, induces noise due to package inductance
Power dissipation
Uneven stage delay could be used to support faster processing
EE141 Integrated
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39
Timing Issues
Self-Timed Pipelined Datapath
Req
Req
HS
Ack
HS
Ack
Start
In
Req
Done
R1
F1
tpF1
Start
R2
Req
HS
Ack
Done
F2
tpF2
ACK
Start
R3
Done
F3
Out
tpF3
Necessary for self-timed logic is a completion signal
EE141 Integrated
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40
Timing Issues
Completion Signal Generation
Completion signal can be generated by:
 Replica delay
 Dual-rail coding
LOGIC
In
Out
NETWORK
Start
DELAY MODULE
Critical path replica
Using Delay Element (e.g. in memories)
EE141 Integrated
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Done
41
Timing Issues
Completion Signal Generation
Completion signal generation by dual-rail coding
requires a redundancy in data representation
Below two bits B0 and B1 represent
a single bit value B
value B
Using Redundant Signal Encoding
EE141 Integrated
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42
Timing Issues
Completion Signal in DCVSL
VDD
VDD
B0
Start
Done
B1
B0
B1
In1
In1
In2
In2
PDN
Start
EE141 Integrated
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PDN
Generation of a completion
signal in DCVSL
43
Timing Issues
Self-Timed Adder
VDD
VDD
Start
C0
C0
P0
C1
G0
P1
C2
G1
P2
C3
G2
P3
Start
C4
C4
G3
Start
VDD
Done
C4
C4
C3
C3
C2
C2
C1
C1
Start
Start
C0
C0
P0
C1
K0
P1
K1
C2
P2
K2
Start
(a) Differential carry generation
EE141 Integrated
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C3
P3
C4
C4
(b) Completion signal
K3
Done signal generated
after all carry signals
are stable
44
Timing Issues
Completion Signal Using Current Sensing
Start
Input Register
Inputs
VDD
Start
Output
Static CMOS Logic
A
GNDsense
Current Sensor
tdelay
toverlap
A
B
tMDG
Done
Done
Min Delay Generator
tpd-NOR
B
Output
valid
Current sensor outputs a low value when no current flows
through the logic and a high value when logic is switching
EE141 Integrated
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45
Timing Issues
Hand-Shaking Protocol
Two Phase Handshake
Sender can cannot change its data
once it sends the request signal which finishes its active cycle
Receiver reads the data and produces acknowledge signal,
this will start a new cycle and sender can process new data
Req and Ack signals can be generated in both high-low and
low-high transitions
EE141 Integrated Circuits2nd
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46
Timing Issues
Event Logic – The Muller-C Element
A
F
C
B
(a) Schematic
VDD
A
A
S
B
R
(a) Logic
Q
VDD
A
B
F n+1
0
0
0
0
1
Fn
1
0
Fn
1
1
1
(b) Truth table
VDD
B
F B
F
B
A
A
F
B
B
(b) Majority Function
Implementations of Muller-C element
EE141 Integrated
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(c) Dynamic
47
Timing Issues
2-phase Handshake Protocol
Data
Sender
Receiver
logic
logic
Data Ready
Data Accepted
Req
C
Initially Req, Ack,
& Data Ready are 0
With Data Ready = 1
Req goes high and
Data is transmitted
Ack
Handshake logic
EE141 Integrated
© Digital
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Once this is
finished Ack goes
high and control is
passed to the sender
48
Timing Issues
Example: Self-timed FIFO
Out
In
R1
En
R2
R3
Done
Reqi
Req0
C
C
C
Acko
Acki
Data transferred on positive and negative transmission of En
Done is a delayed En signal
Examine operation of FIFO by plotting signals
EE141 Integrated
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49
Timing Issues
2-Phase Protocol
EE141 Integrated
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50
Timing Issues
Example
From [Horowitz]
EE141 Integrated
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51
Timing Issues
Example
EE141 Integrated
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52
Timing Issues
Example
EE141 Integrated
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53
Timing Issues
Example
EE141 Integrated
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54
Timing Issues
4-Phase Handshake Protocol
Used to initialize
Muller C-elements
in a fixed state
Also known as RTZ
Slower, but unambiguous
EE141 Integrated
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55
Timing Issues
4-Phase Handshake Protocol
Implementation
using Muller-C
elements
Initially Ack=0, Req=0, S=0, Data ready=0
EE141 Integrated
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56
Timing Issues
4-Phase Handshake Protocol
Implementation
using Muller-C
elements
Once Data ready=1 ->Req=1->S=1 and Data is transmitted
EE141 Integrated
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57
Timing Issues
4-Phase Handshake Protocol
Implementation
using Muller-C
elements
At the end of transmition Data ready=0 -> Req=0 , S waits for Ack
once the receiver sets Ack=1 -> S=0 and system waits for new Data ready
EE141 Integrated
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58
Timing Issues
Self-Resetting Logic
completion
detection
(L1)
Precharged
Logic Block
(L1)
completion
detection
(L2)
Precharged
Logic Block
(L2)
completion
detection
(L3)
Precharged
Logic Block
(L3)
VDD
Logic block is precharged as
soon as the successor block
finishes its operation and does
not need the old data
Post-charge
logic
int
out
A
B
EE141 Integrated
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A=1 ->int=0 -> out=1 ->precharge
At this stage A must be low to avoid
conflict
59
Timing Issues
Clock-Delayed Domino
GND
CLK2 (to next stage)
CLK1
VDD
Q1 (also D2)
D1
EE141 Integrated
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No global clock
Clock from one stage drives the next one
Transmission gate always switched on
High speed operation
60
Timing Issues
Asynchronous-Synchronous Interface
fin
Synchronous system
Asynchronous
system
fCLK
Synchronization
EE141 Integrated
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61
Timing Issues
Synchronizers and Arbiters
Arbiter: Circuit to decide which of 2 events
occurred first
 Synchronizer: Arbiter with clock  as one of
the inputs
 Problem: Circuit HAS to make a decision in
limited time - which decision is not important
 Caveat: It is impossible to ensure correct
operation
 But, we can decrease the error probability at
the expense of delay

EE141 Integrated
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62
Timing Issues
A Simple Synchronizer
CLK
int
D
I1
Q
I2
CLK
• Data sampled on rising edge of the clock
• Latch will eventually resolve the signal value,
but ... this might take infinite time!
EE141 Integrated
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63
Timing Issues
Synchronizer: Output Trajectories
Single-pole model
for a flip-flop
2.0
Initial increase
Exponential with
time constant t
Vout
1.0
0.0
0
100
200
300
time [ps]
Transient response of FF around the metastable point VMS
EE141 Integrated
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64
Timing Issues
Synchronizer: Output Trajectories
Error occurs if the signal is still
undefined after waiting period T
A signal is undefined if it falls into
the interval VIH VIL which happens
if the initial value v(0) is
2.0
Vout
1.0
0.0
0
VMS  VMS  VIL  e T /t  v(0)  VMS  VMS  VIL  e T /t
100
200
300
time[ps]
Or when the initial value v(0) is close to VMS in the interval of length
 T  = 2 VMS  VIL  e T /t
Increasing the waiting time T decreases probability of error exponentially
EE141 Integrated
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65
Timing Issues
Mean Time to Failure
Tsignal
Probability that changing signal is
undefined at the beginning of the
sampling time for a
signal duration time Tsignal.
This probability falls down
exponentially with time T used
to decide the signal value
Number of synchronization
errors per second
After time T number of
synchronization errors
drops to
T
EE141 Integrated
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is a synchronization time
66
Timing Issues
Example
Synchronization time and clock frequency T = 10 nsec = T
Average period of input signal transition
Tsignal = 50 nsec
Rise time
Time constant
Undefined region
tr = 1 nsec
t = 310 psec
VIH - VIL = 1 V (VDD = 5 V)
Probability of undefined signal:
mean-time-to-fail MTF (T) = 1 / Nsync (T) with and without synchronizer
for this clock frequency
Number of errors
MTF with synchronizer
MTF without synchronizer
EE141 Integrated
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Nsync(T) = 3.9 10-9 errors/sec
MTF (T) = 2.6 108 sec = 8.3 years
MTF (0) = 2.5 msec
67
Timing Issues
Influence of Noise
p(v)
Uniform distribution
around VM
One would hope that noise
may throw the system out of
undefined range, however
Low amplitude noise does
not influence
synchronization behavior
0
VIL
VIH
Initial Distribution
EE141 Integrated
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Sometimes it helps
sometimes it hurts
68
Timing Issues
Typical Synchronizers
2 phase clocking circuit
2
Q
1
Q
2
1
Using delay line
1
EE141 Integrated
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69
Timing Issues
Cascaded Synchronizers Reduce MTF
O1
In
Sync
O2
Sync
Out
Sync
f
Increased MTF is obtained at the expense of larger latency
For instance cascading synchronizers reduces
exponentially probability of synchronization failure
EE141 Integrated
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70
Timing Issues
Arbiters
Req1
Req2
Ack1
Arbiter
Req1
A
Ack2
B
Ack2
Ack1
Req2
(a) Schematic symbol
Req1
(b) Implementation
Req2
Arbiter decides which of two
events occurred first, so a
VT gap
A
B
metastable
Ack1
(c) Timing diagram
EE141 Integrated
© Digital
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t
synchronizer is a special case of an
arbiter which decides if the signal
came before the clock or not
71
Timing Issues
PLL-Based Synchronization
Chip 1
Chip 2
Data
Digital
System
Digital
System
fsystem = N x fcrystal
Divider
reference
clock
PLL
Clock
Buffer
PLL
fcrystal , 200<Mhz
Crystal
Oscillator
EE141 Integrated
© Digital
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Lower frequency reference clock is increased
to a desired frequency range by PLL
72
Timing Issues
PLL Block Diagram
Reference
clock
Up
Phase
detector
Charge
pump
Loop
filter
vcont
VCO
Down
Local
clock
div
Divide by
N
System
Clock
 Based on up and down signals the charge pump either increases
or decreases the Vcont that controls the voltage controlled oscillator.
 VCO delivers precise system clock and frequency divider divides it
to match with the reference clock.
 Phase detector issues up and down signals based on the phase difference.
EE141 Integrated
© Digital
Circuits2nd
73
Timing Issues
Phase Detector
Output before filtering
Transfer
characteristic
EE141 Integrated
© Digital
Circuits2nd
74
Timing Issues
Phase-Frequency Detector
Rst
D Q
B
UP
B
UP = 0
DN = 1
A
A
UP = 0
DN = 0
UP = 1
DN = 0
A
Rst
D Q
DN
A
B
B
(a) schematic
(b) state transition diagram
A
A
B
B
UP
UP
DN
DN
(c) Timing waveforms
EE141 Integrated
© Digital
Circuits2nd
75
Timing Issues
Phase-Frequency Detector
Response to frequency – B has lower frequency than A
A
B
UP
DN
EE141 Integrated
© Digital
Circuits2nd
76
Timing Issues
PFD Phase Transfer Characteristic
Average (UP-DN)
VDD
-2 p
2p
phase error (deg)
Notice that if the signal shift is by multiplicity of the
clock period it cannot be detected.
EE141 Integrated
© Digital
Circuits2nd
77
Timing Issues
Charge Pump
VDD
UP
To VCO Control Input
DN
Up signals increases the
output voltage and down
signal decreases it.
EE141 Integrated
© Digital
Circuits2nd
78
Timing Issues
PLL Simulation
local
local
EE141 Integrated
© Digital
Circuits2nd
79
Timing Issues
Example of PLL-generated clock
EE141 Integrated
© Digital
Circuits2nd
80
Timing Issues
Clock Generation using DLLs
Delay-Locked Loop DLL (Voltage Controlled Delay Line based
– no frequency conversion)
U
fREF
Phase
Det
D
Charge
Pump
VCDL
Filter
fO
Phase-Locked Loop (VCO-Based)
fREF
U
÷N
PD
D
CP
VCO
Filter
fO
EE141 Integrated
© Digital
Circuits2nd
81
Timing Issues
Delay Locked Loop
EE141 Integrated
© Digital
Circuits2nd
82
Timing Issues
DLL-Based Clock Distribution
VCDL
•••
Digital
Circuit
•••
Digital
Circuit
CP/LF
Phase
Detector
GLOBAL CLK
VCDL
CP/LF
Phase
Detector
EE141 Integrated
© Digital
Circuits2nd
83
Timing Issues