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Unformatted text preview: ELEC 7770
ELEC
Advanced VLSI Design
Spring 2010
Timing Simulation and STA
Vishwani D. Agrawal
James J. Danaher Professor
ECE Department, Auburn University, Auburn, AL 36849
vagrawal@eng.auburn.edu
http://www.eng.auburn.edu/~vagrawal/COURSE/E7770_Spr10/course.html
Spring 10, Jan 25 . .
Spring ELEC 7770: Advanced VLSI Design (Agrawal) 1 Digital Circuit Timing
Digital
Input
Signal
changes Synchronized
With clock Outputs Comb.
logic Spring 10, Jan 25 . . Transient
region Inputs Output
Observation
instant ELEC 7770: Advanced VLSI Design (Agrawal) time Clock period 2 Timing Analysis and Optimization
Timing Timing analysis Dynamic analysis: Simulation. Static timing analysis (STA): Vectorless topological analysis of
Static
circuit.
circuit. Timing optimization Performance Clock design
Other forms of design optimization Chip area Testability Power Spring 10, Jan 25 . . ELEC 7770: Advanced VLSI Design (Agrawal) 3 Circuit Delays
Circuit Switching or inertial delay is the interval between input
Switching
change and output change of a gate:
change Depends on input capacitance, device (transistor)
Depends characteristics and output capacitance of gate.
characteristics
Also depends on input rise or fall times and states of other
Also
inputs (secondorder effects).
inputs
Approximation: fixed rise and fall delays (or minmax delay
Approximation:
range, or single fixed delay) for gate output.
range, Propagation or interconnect delay is the time a transition
Propagation
takes to travel between gates:
takes Depends on transmission line effects (distributed R, L, C
Depends Spring 10, Jan 25 . . parameters, length and loading) of routing paths.
parameters,
Approximation: modeled as lumped delays for gate inputs.
ELEC 7770: Advanced VLSI Design (Agrawal) 4 Spice
Spice Circuit/device level analysis Circuit modeled as network of transistors, capacitors,
Circuit
resistors and voltage/current sources.
resistors Node current equations using Kirchhoff’s current law. Analysis is accurate but expensive Used to characterize parts of a larger circuit.
Original references: L. W. Nagel and D. O. Pederson, “SPICE – Simulation
L.
Program With Integrated Circuit Emphasis,” Memo ERLProgram
M382, EECS Dept., University of California, Berkeley, Apr.
M382,
1973.
1973. L. W. Nagel, SPICE 2, A Computer program to Simulate
L.
Semiconductor Circuits, PhD Dissertation, University of
Semiconductor
PhD
California, Berkeley, May 1975.
California, Spring 10, Jan 25 . . ELEC 7770: Advanced VLSI Design (Agrawal) 5 Logic Model of MOS Circuit
Logic
pMOS FETs VDD a a
Ca c
Cc b
Cb nMOS
FETs Cd Ca , Cb , Cc and Cd are
node capacitances
Spring 10, Jan 25 . . b Da
Db c Dc Da and Db are
interconnect or
propagation delays
Dc is inertial delay
of gate ELEC 7770: Advanced VLSI Design (Agrawal) 6 Spice Characterization
Spice
Input data pattern Delay (ps) Dynamic energy (pJ) a=b=0→1 69 1.55 a = 1, b = 0 → 1 62 1.67 a = 0 → 1, b = 1 50 1.72 a=b=1→0 35 1.82 a = 1, b = 1 → 0 76 1.39 a = 1 → 0, b = 1 57 1.94 Spring 10, Jan 25 . . ELEC 7770: Advanced VLSI Design (Agrawal) 7 Spice Characterization (Cont.)
Spice
Input data pattern
a=b=0 5.05 a = 0, b = 1 13.1 a = 1, b = 0 5.10 a=b=1 Spring 10, Jan 25 . . Static power (pW) 28.5 ELEC 7770: Advanced VLSI Design (Agrawal) 8 Complex Gates: SwitchLevel Partitions
Complex Circuit partitioned into channelconnected components for Spice
Circuit
channelconnected characterization.
characterization.
Reference: R. E. Bryant, “A SwitchLevel Model and Simulator for
Reference:
MOS Digital Systems,” IEEE Trans. Computers, vol. C33, no. 2, pp.
IEEE
vol.
160177, Feb. 1984.
160177, Internal
switching
nodes not
seen by
logic
simulator Spring 10, Jan 25 . . G2 G1 G3 ELEC 7770: Advanced VLSI Design (Agrawal) 9 Interconnect Delay: Elmore Delay Model
Interconnect W. Elmore, “The Transient Response of Damped Linear Networks with
W.
Particular Regard to Wideband Amplifiers,” J. Appl. Phys., vol. 19,
J.
.,
no.1, pp. 5563, Jan. 1948.
no.1,
2 R2
s R1 C2 1 4
R4 C1
Shared resistance: C4 R3
3 R5 C3 R45 = R1 + R3
R15 = R1
R34 = R1 + R3
Spring 10, Jan 25 . . 5
C5
ELEC 7770: Advanced VLSI Design (Agrawal) 10 Elmore Delay Formula
Elmore
N
Delay at node k = 0.69 Σ Cj × Rjk
j =1
where N = number of capacitive nodes in the network
Example:
Delay at node 5 = 0.69 [ R1 C1 + R1 C2 + (R1+R3)C3 + (R1+R3)C4
(R1+R3+R5)C5 ] Spring 10, Jan 25 . . ELEC 7770: Advanced VLSI Design (Agrawal) 11 Event Propagation Delays
Event
Single lumped inertial delay modeled for each gate
PI transitions assumed to occur without time skew
Path P1
1 0 13 P2 0 0 Spring 10, Jan 25 . . 2 1 3
2 246 P3
5 ELEC 7770: Advanced VLSI Design (Agrawal) 12 Circuit Outputs
Circuit Each path can potentially produce one signal
Each transition at the output.
transition
The location of an output transition in time is
The
determined by the delay of the path.
determined
Clock period Final value Initial value
Slow transitions Fast transitions time
Initial value
Spring 10, Jan 25 . . Final value
ELEC 7770: Advanced VLSI Design (Agrawal) 13 Delay and DiscreteEvent Simulation
Delay
Inputs (NAND gate)
Transient
region a
b
c (CMOS) Logic simulation c (zero delay)
c (unit delay)
X c (multiple delay) Unknown (X) c (minmax delay)
0 Spring 10, Jan 25 . . 5 ELEC 7770: Advanced VLSI Design (Agrawal) rise=5, fall=5
min =2, max =5
Time units
14 EventDriven Simulation
EventDriven
(Example)
2 e =1
g =1 2 2 d=0
4 b =1 f =0 Time stack a =1
c =1→0 Scheduled
events
t=0
1
2
3
4
5
6
7
8 Activity
list c=0 d, e d = 1, e = 0 f, g g=0
f=1 g g=1 g
0
Spring 10, Jan 25 . . 4 8 Time, t ELEC 7770: Advanced VLSI Design (Agrawal) 15 Time Wheel (Circular Stack)
Time
Current
time
pointer max
t=0
1 Event linklist 2
3
4
5
6
7 Spring 10, Jan 25 . . ELEC 7770: Advanced VLSI Design (Agrawal) 16 Timing Design and Delay Test
Timing Timing simulation: Critical paths are identified by static (vectorless)
Critical
timing analysis tools like Primetime (Synopsys).
Primetime Timing or circuitlevel simulation using designergenerated functional vectors verifies the design. Layout optimization: Critical path data are used in
Layout placement and routing. Delay parameter
extraction, timing simulation and layout are
repeated for iterative improvement.
repeated
Testing: Some form of atspeed test is necessary.
Testing:
Critical paths and all gate transition delays are
tested. Spring 10, Jan 25 . .
Spring ELEC 7770: Advanced VLSI Design (Agrawal) 17 Static Timing Analysis (STA)
Static Finds maximum and minimum delays between
Finds
Flipflops Combinational
circuit Flipflops Flipflops all clocked flipflops.
all Spring 10, Jan 25 . . ELEC 7770: Advanced VLSI Design (Agrawal) 18 Early References
Early T. I. Kirkpatrick and N. R. Clark, “PERT as an
T. Aid to Logic Design,” IBM J. Res. Dev., vol. 10,
IBM
.,
no. 2, pp. 135141, March 1966.
no.
R. B. Hitchcock, Sr., “Timing Verification and the
R.
Timing Analysis Program,” Proc. 19th Design
Proc.
Automation Conf., 1982, pp. 594604.
Automation
V. D. Agrawal, “Synchronous Path Analysis in
V.
MOS Circuit Simulator,” Proc. 19th Design
Proc.
Automation Conf., 1982, pp. 629635.
Automation Spring 10, Jan 25 . . ELEC 7770: Advanced VLSI Design (Agrawal) 19 Basic Ideas
Basic Adopted from project management Frederick W. Taylor (18561915) Henry Gantt (18611919) PERT – Program Evaluation and Review
PERT
Technique
Technique CPM – Critical Path Method Spring 10, Jan 25 . . ELEC 7770: Advanced VLSI Design (Agrawal) 20 A Gantt Chart in Microsoft Excel
Gantt Spring 10, Jan 25 . . ELEC 7770: Advanced VLSI Design (Agrawal) 21 Using a Gantt Chart
Using Track progress of subtasks and project. Assess resource needs as a function of time. Spring 10, Jan 25 . . ELEC 7770: Advanced VLSI Design (Agrawal) 22 Pert Chart
Pert Spring 10, Jan 25 . . ELEC 7770: Advanced VLSI Design (Agrawal) 23 Example: Thesis Research
Example:
Begin Defense
done Analysis
completed 4, 4, 4 2, 4, 6 weeks 2, 3, 4 4, 5, 6
Problem
selected 3, 4, 5 minimum
average
maximum
Spring 10, Jan 25 . . 2, 2, 2 Background
study
completed 5, 7, 9
Program
and
Experiment
completed Thesis
Draft
done Thesis
submitted 4, 4, 4 ELEC 7770: Advanced VLSI Design (Agrawal) 24 Critical Path
Critical
Begin Defense
done Analysis
completed 4, 4, 4 2, 4, 6 weeks 2, 3, 4 4, 5, 6
Problem
selected 3, 4, 5 minimum
average
maximum
Spring 10, Jan 25 . . 2, 2, 2 Background
study
completed 5, 7, 9
Program
and
Experiment
completed Thesis
Draft
done Thesis
submitted 4, 4, 4
Critical path is path
of maximum average
delay (24 weeks). ELEC 7770: Advanced VLSI Design (Agrawal) 25 A Basic Timing Analysis Algorithm
Basic Combinational logic. Circuit represented as an acyclic directed graph
Circuit (DAG).
(DAG).
Gates characterized by delays. Spring 10, Jan 25 . . ELEC 7770: Advanced VLSI Design (Agrawal) 26 Example
Example
Levelize graph. Initialize arrival times at primary inputs.
0
0 A
1 0
0 B
3 0
0 C
1 0
0
evel 0 H
3
E
1 G
2
F
1 D
2
1 Spring 10, Jan 25 . . J
1 2 3 ELEC 7770: Advanced VLSI Design (Agrawal) 4 5
27 Example (Cont.)
Example Determine output arrival time when all input arrival times
are known.
0
A1
H 10
1
0
3
0
0 B3
3 0
0 C1
1 0
0
evel 0 D2
2
1 Spring 10, Jan 25 . . E4
1 G7
2
J8
1 F5
1
2 3 ELEC 7770: Advanced VLSI Design (Agrawal) 4 5
28 Example (Cont.)
Example
Trace critical path from the output with longest arrival time.
0
A1
H 10
1
0
3
0
0 B3
3 0
0 C1
1 0
0
evel 0 D2
2
1 Spring 10, Jan 25 . . E4
1 G7
2
J8
1 F5
1
2 3 ELEC 7770: Advanced VLSI Design (Agrawal) 4 5
29 Finding Earliest and Longest Times
Finding
0
0 A 1,1
1 0
0 B 3,3
3 0
0 C 1,1
1 0
0 D 2,2
2 evel 0 1 Spring 10, Jan 25 . . H 4,10
3
E 2,4
1 G 4,7
2
J 4,8
1 F 3,5
1
2 3 ELEC 7770: Advanced VLSI Design (Agrawal) 4 5
30 Shortest and Longest Paths
Shortest
0
0 A 1,1
1 0
0 B 3,3
3 0
0 C 1,1
1 0
0 D 2,2
2 Spring 10, Jan 25 . . H 4,10
3
E 2,4
1 G 4,7
2
F 3,5
1 ELEC 7770: Advanced VLSI Design (Agrawal) J 4,8
1 31 Characteristics of STA
Characteristics Linear time analysis, Complexity is O(n), n is
Linear number of gates and interconnects.
number
Variations: Find k longest paths: S. Kundu, “An Incremental Algorithm for Identification of
S.
Longest (Shortest) Paths,” Integration, the VLSI Journal, vol.
Longest
Integration,
17, no. 1, pp. 2535, August 1994.
17, Find worstcase delays from an input to all outputs. Linear programming methods. Spring 10, Jan 25 . . ELEC 7770: Advanced VLSI Design (Agrawal) 32 Algorithms for Directed Acyclic Graphs
(DAG)
(DAG) Graph size: n = V + E, for V vertices and E
Graph edges.
edges.
Levelization: O(n) (lineartime) algorithm finds
Levelization:
the maximum (or minimum) depth.
the
Path counting: O(n2) algorithm. Number of paths
algorithm.
can be exponential in n.
can
Finding all paths: Exponentialtime algorithm.
Shortest (or longest) path between two nodes: Dijkstra’s algorithm: O(n2) BellmanFord algorithm: O(n3) Spring 10, Jan 25 . . ELEC 7770: Advanced VLSI Design (Agrawal) 33 References
References Delay modeling, simulation and testing: M. L. Bushnell and V. D. Agrawal, Essentials of Electronic
M.
Testing for Digital, Memory and MixedSignal VLSI Circuits,
Testing
Springer, 2000.
Springer, Analysis and Design: G. De Micheli, Synthesis and Optimization of Digital Circuits,
G.
Synthesis McGrawHill, 1994.
McGrawHill,
N. Maheshwari and S. S. Sapatnekar, Timing Analysis and
N.
Optimization of Sequential Circuits, Springer, 1999.
Optimization PrimeTime (Static timing analysis tool): H. Bhatnagar, Advanced ASIC Chip Synthesis, Second Edition,
H.
Advanced
Springer, 2002
Springer, Spring 10, Jan 25 . . ELEC 7770: Advanced VLSI Design (Agrawal) 34 ...
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