This presentation is expert talk at Two day's International Webinar on "Testing and Verification of VLSI Design"

1. Department of Electronics and
Communication Engineering
Institute of Technology,
Nirma University
welcomes the participants of
Two-days International Webinar on
Testing and Verification of VLSI Design
September 3-4, 2021
1

2. Concept of
Timing Analysis
Prof. Usha Mehta
Professor,
PG-VLSI Design,
EC, Institute of Technology,
Nirma University, Ahmedabad
usha.mehta@nirmauni.ac.in
usha.mehta@ieee.org
 Does the design
meet a given
timing
requirement?!!
 How fast can I run
the design?!!!

3. 9/6/2021
Static
Timing
Analysis
Acknowledgement
3
This presentation has been summarized
from various books, papers, websites and
presentations and so on …. all over the
world. I couldn’t remember where these
large pull of hints and work come from.
However, I’d like to thank all professors and
scientists who create such a good work on
this emerging field. Without those efforts in
this very emerging technology, these notes
and slides can’t be finished. I am thankful
to them to make my teaching process more
effective.

4. 9/6/2021
Static
Timing
Analysis
Objective of Timing Analysis
Timing verification
• Verifies whether a design meets a given timing
constraint
• Verifies that the design work properly for all possible
combination “EVERY TIME”
Timing optimization
• Needs to identify critical portion of a design for
further optimization
• Critical path identification
• Like component selection
• A slow memory can degrade processor
performance
In both applications, the more accurate, the better 4

5. 9/6/2021
Static
Timing
Analysis
Types of Timing Analysis
• Dynamic Timing Analysis
• Verifies the functionality of design by
applying input vectors and checking the
correctness and timing of output vectors
• Static Timing Analysis
• Checks static delay requirements without
applying any vectors
• It does not check functionality
5

6. 9/6/2021
Static
Timing
Analysis
Static Timing Analysis
• It is a method of validating the timing
performance of a design by checking all
possible paths from timing violations under
worst case conditions
• It considers worst logical delay through each
logic element but not the logical operation of
the circuit.
• Input independent method So no vector
generation is required.
• It does not check the functionality
6

7. 9/6/2021
Static
Timing
Analysis
Static Time Analysis
What it typically does:
• Calculate latest and earliest possible switching
times for each node in the design
• Determine the arrival time of signals for the
worst case (latest or earliest) of all possible
paths leading to a given node in the design
• Compare calculated signal arrival times with
expected (required) arrival times at storage
elements, other clock meets data points (such
as dynamic circuits) and primary outputs in
the design.
7

8. 9/6/2021
Static
Timing
Analysis
Delay/Time Calculation for a design
• The total delay of a path is the sum of all
• Gate/Cell Delays in the path
• Net /Path Delays in the path
8

9. 9/6/2021
Static
Timing
Analysis
Gate/Cell Delays
• Timing Delay between input pin and output pin of a
logic gate/cell in a path
• The cell delay information is contained in the library of
the cell e.g. .lef file
• In ASICs, the delay of a cell is affected by:
• The input transition time (or slew rate)
• The total load “seen” by the output transistors
• Net capacitance and “downstream” pin
capacitances
• These will affect how quickly the input and output
transistors can “switch”
• Inherent transistor delays and “internal” net delays
9

10. 9/6/2021
Static
Timing
Analysis
Gate Delay Models
Unit Delay Model
• Simplest
• Each gate with unit delay
• Longest path delay = 2
Arbitrary but Fixed Delay
Model
• Simple
• Each gate with some
constant delay which does
not depend on circuit or
netlist
10

11. 9/6/2021
Static
Timing
Analysis
Limitation of Fixed Delay Model
Input Waveform
• Slop of the input waveform also affects delay (RC
affects)
• Rising signal vs Falling signal also affects
11

12. 9/6/2021
Static
Timing
Analysis
Limitations of Fixed Delay Model
• Location of pins
• Delay is not actually
through a gate
• but it is actually from
individual input pin to
output
•
12

13. 9/6/2021
Static
Timing
Analysis
Limitation of Fixed Delay Model
• Rising and Falling
Waveforms
• pMOS has larger delay
compared to nMOS.
• Rising and falling delay for
output may be different
• More complicated for Non-
Monotonic functions
13

14. 9/6/2021
Static
Timing
Analysis
Limitation of Fixed Delay Model
• Process Variation
• Delay in its real sense, is a probability distribution function.
• Simplest way to express is in [min, max]
14

15. 9/6/2021
Static
Timing
Analysis
Net/ Wire Delays
• Net delay is the difference between the time
a signal is first applied to the net and the
time it reaches other devices connected to
that net.
Wire delay = function of (Rnet, Cnet+Cpin)
• Total net delays are affected by:
• Characteristics of driver cell and receiver cell
• net material, length and cross sectional are
• net fanout
• Number of vias traversed by the net
• Proximity to other nets (crosstalk)
• The effects of Interconnect Parasitic
• Interconnect parasites cause an increase in propagation
delay (i.e. it slows down working speed)
15

16. 9/6/2021
Static
Timing
Analysis
Elmore Delay Model
• Resistance Oriented Formula
16
,
T R C
delay i downstream i


Tdelay,4=R1(C1+C2+C3+C4+C5)+R2(C2+C4+C5)+R4C4

17. 9/6/2021
Static
Timing
Analysis
STA for Combinational Circuit
• Combinational circuits: Graph model:
• DAG: Directed Acyclic Graph
• Vertices:
• I/O pins of gates
• s and t ( start and stop points)
• Edges:
• Connect each input of a gate to its output
• Show maximum delay paths from the input pin
to the output pin
• Connects the output of each gate to the inputs of
its fanout gates
• Show interconnect delays
• In case of combinational loop:
• Many STA tools break the loop and analyze
17

18. 9/6/2021
Static
Timing
Analysis
Combinational Circuit Representation
: Gate delays only
18

19. 9/6/2021
Static
Timing
Analysis
19
Combinational Circuit Representation
: Gate delays and net delay

20. 9/6/2021
Static
Timing
Analysis
• Add one source to each PI and one sink
node to each PO with 0 – weight edge
• If arrival time of different inputs are different, then the weight
of source edge can represent that delay also.
• For network/algorithm has one clear entry
point and exit point.
• Search algorithms
• Depth First Search Algorithm is most suited to
list all the different possible paths
• Let’s try
20
Combinational Circuit Representation
: Gate delays, net delay and source & Sink node

21. 9/6/2021
Static
Timing
Analysis
STA for Combinational Circuits
Critical Path
 Critical path
Any logical path in the design that violates the timing constraints
The slowest path on the chip between flops or flops and pins.
The critical path limits the maximum clock speed.
The longest path on a DAG graph
21

22. 9/6/2021
Static
Timing
Analysis
Find the Critical path
22
Gate Delay
Not 2
AND 4
OR 4

23. 9/6/2021
Static
Timing
Analysis
Gate Delay
Not 2
AND 4
OR 4
23

24. 9/6/2021
Static
Timing
Analysis
Find the critical Path…..
24
8
1
MUX
12
8
1
MUX
12

25. 9/6/2021
Static
Timing
Analysis
False Path
25
• Paths that physically exist in a design but are not
logic/functional paths
• These paths never get sensitized under any input
conditions

26. 9/6/2021
Static
Timing
Analysis
False Path Solutions
• Solutions:
• Automatic solutions: too complex to be practical
• E.g. if inverter delay > 0
• In practice:
• Designers knows functionalities best 
Designer specifies
26

27. 9/6/2021
Static
Timing
Analysis
STA for Clocked Design
• Sequential circuit is Represented as: a set of combinational
blocks that lie between latches/flipflops.
27
• Transparent Latch, Level Sensitive
• data passes through when clock high, latched when clock low
• D-Type Register or Flip-Flop, Edge-Triggered
• data captured on rising edge of clock, held for rest of cycle

28. 9/6/2021
Static
Timing
Analysis
• For Flipflop,
• there is only one propagation delay,
clock to Q delay
• tclk->Q
• But do remember, for the
latch,
• there are two propagation delays
• tclk->Q and tD->Q
28
STA for Clocked Design

29. 9/6/2021
Static
Timing
Analysis
Three steps in STA
1. Circuit is broken down into sets of timing
paths
2. Delay of each path is calculated
3. Path delays are checked to see if timing
constraints have been met
29

30. 9/6/2021
Static
Timing
Analysis
Data path
• Start Point :
• input port of the design
• clock pin of the flipflop
• End Point:
• outport of the design
• data input pin of the flipflop
30

31. 9/6/2021
Static
Timing
Analysis
Clock Path
• Start Point
• Clock input port
• End Point
• Clock pin of the flipflop/latch/memory
31

32. 9/6/2021
Static
Timing
Analysis
Single Cycle and Multicycle Paths
• Single Cycle Path : It is a timing path that is
designed to take only one clock cycle for the
data to propagate from the start point to
end point.
• Multi Cycle Path
32

33. 9/6/2021
Static
Timing
Analysis
Launch Path and Capture Path
• Launch flipflop and Capture flipflop
• Launch Path : It is part of clock path which is responsible foe launching the data
at launch flipflop
• Capture Path : It is part of clock path which is responsible foe launching the data
at capture flipflop
• Launch path and data path together constitute arrival time of data at the input of
capture flipflop
• Capture clock period and its path delay together constitute required time of data
at the input of the capture register.
33

34. 9/6/2021
Static
Timing
Analysis
Maximum Clock Frequency
• A clock is defined by its period, waveform and slew time.
• The clock frequency for a synchronous sequential circuit is
limited by the timing parameters of its flip-flops and gates.
• The critical path/worst path having the maximum delay
defines the clock frequency of the circuit.
• The minimum clock time period ( reciprocal of maximum clock
frequency) should be equal to or more than maximum time
delay of the longest path of the circuit.
34

35. 9/6/2021
Static
Timing
Analysis
Your chip
clock input
Flip
Flop
Time from clock input (at pin) to
clock input at a given flip flop
Absolute Clock Skew / Latency
35

36. 9/6/2021
Static
Timing
Analysis
Relative Clock Skew
36
Your chip
clock input
Flip
Flop
Time between 2 flip flops receiving
the clock signal
Flip
Flop
delay

37. 9/6/2021
Static
Timing
Analysis
Clock Skew
 Ideally clock skew should be zero. i.e. clock should reach to
each flipflop at the same instant.
 Clock Skew is a measure of the difference in latency between
any two leaf pins in a clock tree.
37
Clock arrival
time at 1.1ns
Clock arrival
time at 1.3ns
Skew = 1.3ns - 1.1ns = .2ns

38. 9/6/2021
Static
Timing
Analysis
Clock Skew and Clock Latency
• The arrival time of a flip-flop's clock pin is its clock latency. The clock
skew between two flip-flops is the difference of their clock latency.
38
Chip
D Q D Q D Q D Q
network latency
(on-chip)
source latency
(off-chip)
Clock
IO
latency
IO
latency

39. 9/6/2021
Static
Timing
Analysis
Clock Skew
• Clock skew is a measure of the difference in latency
between any two leaf pin in a clock tree.
Between CLKA and CLKB
rise = 22 - 8 = 14
fall = 22 -14 = 8
Between CLKB and CLKC
rise = 8 -7 = 1
fall = 14 - 4 = 10
Between CLKC and CLKA
rise = 22 - 7 = 15
fall = 22 - 4 = 18
It is also defined as the difference in time that a single
clock signal takes to reach two different registers
39

40. 9/6/2021
Static
Timing
Analysis
Arrival time (w.r.t input) and Required
time ( w.r.t. output)/Capturing moment
• An arrival time defines the time interval
during which a data signal can arrive at an
input pin in relation to the nearest edge of
the clock signal that triggers the data
transition.
• A required time specifies the data required
time on output ports
40

41. 9/6/2021
Static
Timing
Analysis
Slack
• It is difference between required time and arrival time.
• If required time > arrival time
• Positive slack
• indicates that constraints have been met.
• If required time < arrival time
• Negative slack
• indicates that constraints have not been met
• Set up/Hold violation
• Slack analysis is used to identify timing critical paths in a design
by static timing analysis tool.
41

42. 9/6/2021
Static
Timing
Analysis
Sequential False Path example:
42
• The change in D1-Q never reaches to D4-D.
The value of D4 is always governed by D2.
So clk-D1-AND-OR-D4 is false path.

43. 9/6/2021
Static
Timing
Analysis
Considering the delays….
1. Ideal Condition no delay in any path.
2. Data and Clock path have fixed delays but
no set-up/Hold time for FFs
3. Data and Clock path have fixed delays and
FFs are with set-up/Hold time
4. Data and Clock path have delays, FFs are
with set-up/Hold time ( all delays with min-
max range, not fixed)
43

44. 9/6/2021
Static
Timing
Analysis
Ideal Condition: No delays
44

45. 9/6/2021
Static
Timing
Analysis
Launching, arrival and capture
moments
45

46. 9/6/2021
Static
Timing
Analysis
Delays in Data and Clock Path
46

47. 9/6/2021
Static
Timing
Analysis
Delays in Data Path and Clock Path
contd…
47

48. 9/6/2021
Static
Timing
Analysis
Conditions for
Timings
48

49. 9/6/2021
Static
Timing
Analysis
Set up Time and Hold Time
• Set up Time
• For an edge triggered sequential element, the setup time is
the time interval before the active clock edge during which
the data should remain unchanged.
• This is so that the data can be stored successfully in storage
device
• Because of Long path
• Hold Time
• Time interval after the active clock edge during which the
data should remain unchanged. This is so that the data can
be stored successfully in storage device
• Because of Short Path
49

50. 9/6/2021
Static
Timing
Analysis
Setup Time and Hold Time Consideration
50

51. 9/6/2021
Static
Timing
Analysis
Setup and Hold
Time consideration
contd….
51

52. 9/6/2021
Static
Timing
Analysis
When delays are given in min-max
limits
52

53. 9/6/2021
Static
Timing
Analysis
Set-up Time Violation
53

54. 9/6/2021
Static
Timing
Analysis
Hold Time Violation
54

55. 9/6/2021
Static
Timing
Analysis
Relation between data path delay, clock
path delay, Set-up/Hold and Clock Time
Period…
1. The circuit is given with all delays ( net,
cell, Set-up, hold etc..)
• you are required to calculate the
minimum time period (maximum
frequency) of clock.
2. The circuit is given with all delays ( net,
cell, Set-up, hold etc..) and minimum time
period (maximum frequency) of clock at
which circuit will operate.
• You are required to verify whether any timing
violation exists or not.
55

56. 9/6/2021
Static
Timing
Analysis
Calculate the max. clock frequency
for given circuit…
• Minimum Time Period = tclk-q + tpd + ts = 10 + 5 +2 =
17ns
56

57. 9/6/2021
Static
Timing
Analysis
57
TAB = 11ns, TAC = 15ns , TBC = 16ns.
Minimum clock period =16ns
Calculate the max. clock frequency
for given circuit…

58. 9/6/2021
Static
Timing
Analysis
58
Tclk-Q = 10 ns, NOR/OR = 4 ns, NAND/AND =3 ns,
INV/BUF = 2ns, Ts = 2 ns, Th = 3ns
Calculate the max. clock frequency
for given circuit…

59. 9/6/2021
Static
Timing
Analysis
59
For a minimum clock period, we just want that the data reach ts time
before the clock reach there.
Data path
• Max delay = 26ns
• Min delay = 18ns
Clock Path
• Max delay = 15ns
• Min delay=9ns
Minimum Clock Period = 26 -9 +4 = 21 ns
Calculate the max. clock frequency
for given circuit…

60. 9/6/2021
Static
Timing
Analysis
Find out any set-up violation ?
• For set-up path
• Set-up is checked at next clock cycle
• Maximum delay along the data path
• Minimum delay along the clock path
• Data path is
• CLK->FF1/CLK->FF1/Q->INV->FF2/D
• TD =2ns +11ns+2ns+9ns+2ns = 26ns ( max. delay in data path)
• Clock Path is
• CLK-> BUFF->FF2/CLK
• TCLK= 15 ns + 2ns+5ns+2ns-4ns = 20ns (max. delay in clock
path)
• SET-UP SLACK = TCLK-TD
• 20-26= -6ns < 0 so Set-Up Violation
60
CLK Period = 15ns

61. 9/6/2021
Static
Timing
Analysis
Find out any hold violation?
• For hold path
• Hold is checked at Same clock cycle
• Minimum delay along the data path
• Maximum delay along the clock path
• Data path is
• CLK->FF1/CLK->FF1/Q->INV->FF2/D
• TD =1ns +9ns+1ns+6ns+1ns = 18ns ( min. delay in data path)
• Clock Path is
• CLK-> BUFF->FF2/CLK
• TCLK= 3ns+9ns+3ns+2ns = 17ns (max. delay in clock path)
• SLACK = TD-TCLK
• 18-17=1ns > 0 so No Hold Violation 61

62. 9/6/2021
Static
Timing
Analysis
Fixing Set-up /Hold Violation
:Combinational Delay
• Check for violations
• Data1 reaches to FF2 at 0.5 ns. It should reach before 10 ns – 2ns i.e
8ns Hence, NO set-up violation
• Data2 launched at 10 ns, reaches to FF2 at 10.5 ns. It disturbs the
data1 which should be there upto 11ns. So hold violation.
• To remove hold violation, let’s increase the combinational delay.
Let’s say by 3ns. Then data1 reaches at 3ns which is before 8ns so
still no problem with set-up time and data2 reaches at 13ns so hold
time violation is also solved.
• But what if we increase combination delay to 9ns? Here, while
solving for hold-time, we have violated setup time.
62

63. 9/6/2021
Static
Timing
Analysis
63
Fixing Set-up /Hold Violation
• Check for violations

64. 9/6/2021
Static
Timing
Analysis
Timing Closure
• It is the process of satisfying timing constraints
through layout optimizations and netlist
modifications
• Timing-driven placement: minimizes signal
delays when assigning locations to circuit
elements
• Timing-driven routing : minimizes signal delays
when selecting routing topologies and specific
routes
• Physical synthesis: improves timing by
changing the netlist
• Sizing transistors or gates: increasing the width:length ratio of
transistors to decrease the delay or increase the drive strength
of a gate
• Inserting buffers into nets to decrease propagation delays
• Restructuring the circuit along its critical paths
64

65. 9/6/2021
Static
Timing
Analysis
Ways to fix set-up Violation
(Tdata <= Tclk-Tsetup)
1. Reduce the amount of buffering in the path.
 It will reduce the cell delay but increase the wire delay. So if effective
delay is reduced than, set-up time violation can be fixed.
2. Replace buffer with two inverters place farther apart
 Delay of one buffer is equal to delay of two inverter but because of two
inverters, the transition delays are reduced.
3. Change HVT cells to SVT/LVT to reduce delay
 HVT/SVT/LVT has the same size and pin position so this change will
reduce delay without affecting layout.
4. Increase driver size i.e. driver strength
 It reduces delay
5. Insert Buffer/repeaters
 In case of long wire, the buffer decreases the transition time which
decreases wire delay. If decrease in wire delay is more compared to buffer
delay, overall delay reduces.
65

66. 9/6/2021
Static
Timing
Analysis
Ways to fix set-up Violation
(Tdata <= Tclk-Tsetup) cont…..
6. Adjust Cell position in layout
7. Clock Skew
 By delaying clock to the end point.
66

67. 9/6/2021
Static
Timing
Analysis
Ways to fix hold time violation…
Tdata >= Thold
1. By adding delay
 The hold violation path may have its start or stop point in
other setup violation path
2. Decreasing the size of cells in data path
67

68. 9/6/2021
Static
Timing
Analysis
Negative Set-up and Hold Time
• For a Pure flop(containing no extra gates) setup
and hold time always will be a positive number.
• Now, A flop can be a part of a bigger
component. There are many components
available in stranded cell library that embed a
flop inside. These components will be a part of
our design.
• Setup and hold time can be negative depending
on where you measure the setup and hold time,
if you measure setup and hold time at
component level. These can be negative also.
68

69. 9/6/2021
Static
Timing
Analysis
Negative Set-up and Hold Time
• For pure flipflop
• Tdata < Tclk-Tsetup
• Tdata > Thold
69
Flipflop
(Pure)
Tdata
Tclk
Tsetup Thold

70. 9/6/2021
Static
Timing
Analysis
Negative Set-up and Hold Time
70
Flipflop
(Embedded)
Tdata
Tclk_comp
Tsetup
Thold
Tdata_delay
Tclk_delay
Tcomp_setup Tcomp_hold

71. 9/6/2021
Static
Timing
Analysis
Negative Set-Up Time
• The time when data reaches to flipflop = Tdataflipflop = Tdata+Tdata_delay
• The time when clock reaches to flipflop = Tclkflipflop = Tclk_comp+Tclk_delay
• Considering flipflop, Tdata+Tdata_delay < Tclk_comp+Tclock_delay-Tsetup
• If Tdata_delay= 700, Tclk_delay = 800 and Tsetup=200
• Tdata+700 <= Tclk_comp + 800-200
• Tdata <= Tclk_comp-100
• Tcomp_setup is 100
• But If Tdata_delay= 500, Tclk_delay = 800 and Tffsetup=200
• Tdata+500 <= Tclk_comp+800-200
• Tdata <= Tclk_comp + 100
• Tcomp_setup is negative i.e. -100
71
For Component, Tdata < Tclk_comp-Tcomp_setup

72. 9/6/2021
Static
Timing
Analysis
Negative Hold Time
• The time when data reaches to flipflop = Tdataflipflop = Tdata+Tdata_delay
• The time when clock reaches to flipflop = Tclkflipflop = Tclk_comp+Tclk_delay
• Tdata+Tdata_delay >= Thold
• If Tdata_delay= 100, and Thold=200
• Tdata+100 >= 200
• Tdata >= 100
• Tcomp_hold is 100
• If Tdata_delay= 300 and Thold=200
• Tdata+300 >= 200
• Tdata >= -100
• Tcomp_hold is negative i.e. -100
72
For Component Tdata > Tcomp_hold

73. 9/6/2021
Static
Timing
Analysis
Time Borrowing/ Cycle Stealing
• Technique of borrowing the time from shorter
path of the logic stage to the longer path
• Do remember:
• Edge triggered flipflop changes the stage at the clock edges So
the delay of a combination logic path in a design using such FFs
can not be longer than the clock period of the design ( except for
false or multicycle path)
• While the latch can change the stage as long as clock pin is
enabled. Here, the delay of the longest path can be compensated
by the delay of the shortest path in subsequent logic design
• Hence latch based design can be faster.
73

74. 9/6/2021
Static
Timing
Analysis
Example of Time Borrowing
74

75. 9/6/2021
Static
Timing
Analysis
STA in ASIC Design Flow – Pre layout
75
Logic Synthesis
Design For test
Floor planning
Constraints
(clocks, input drive,
output load)
Static Timing Analysis
Static Timing Analysis
(estimated parasitics)

76. 9/6/2021
Static
Timing
Analysis
STA in ASIC Design Flow – Post Layout
76
Floor planning
Clock Tree Synthesis
Place and Route
Parasitic Extraction
SDF
(extracted parasitics)
Constraints
(clocks, input drive,
output load)
Static Timing Analysis
(estimated parasitics)
Static Timing Analysis
(extracted parasitics)

77. 9/6/2021
Static
Timing
Analysis
Required Inputs
77

78. 9/6/2021
Static
Timing
Analysis
Back Annotation – A process
1. Designer writes the RTL and performs functional simulation
considering delay as zero or some unit value as in simulator’s
library file.
2. The RTL description is converted to gate level netlist by a logic
synthesis tool.
3. The designer estimates the prelayout estimates of delays in the chip
using a delay calculator and information about the IC fabrication
process (.sdf)
4. The designer does timing simulation or static timing verification of
the gate level netlist using this preliminary values to check that the
gate level netlist meets timing constraint
5. The gate level netlist is then converted into layout by place and
route tool
6. The postlayout delays are now calculated from the R and C
information in the layout. This R and C depends on technology and
geometry of IC
7. The post layout delay values are back annotated to modify the delay
estimates of the gate level netlist
8. Again timing simulation or STA to check the timings are still
satisfied.
9. If needed, design changes 78

79. 9/6/2021
Static
Timing
Analysis
Back Annotation
79

80. 9/6/2021
Static
Timing
Analysis
Standard Delay Format
• IEEE standard for the representation and interpretation of
timing data for use at any stage of an electronic design
process.
• It has usually two sections: one for interconnect delays and
the other for cell delays.
• SDF format can be used for back-annotation as well as
forward-annotation.
80