Spring 08, Jan 31.. ELEC 7770: Advanced VLSI Design (Agrawal) 1 ELEC 7770 Advanced VLSI Design Spring 2008 Timing Simulation and STA Vishwani D. Agrawal

Spring 08, Jan 31 . .Spring 08, Jan 31 . . ELEC 7770: Advanced VLSI Design (Agrawal)ELEC 7770: Advanced VLSI Design (Agrawal) 11

ELEC 7770ELEC 7770Advanced VLSI DesignAdvanced VLSI Design

Spring 2008Spring 2008 Timing Simulation and STA Timing Simulation and STA

Vishwani D. AgrawalVishwani D. Agrawal

James J. Danaher ProfessorJames J. Danaher Professor

ECE Department, Auburn University, Auburn, AL 36849ECE Department, Auburn University, Auburn, AL 36849

[email protected]@eng.auburn.eduhttp://www.eng.auburn.edu/~vagrawal/COURSE/E7770_Spr08/course.htmlhttp://www.eng.auburn.edu/~vagrawal/COURSE/E7770_Spr08/course.html


Digital Circuit TimingDigital Circuit Timing

Inpu

tsO

utpu

ts

time

Transientregion

Clock period

Comb.logic

OutputObservation

instant

InputSignal

changes

SynchronizedWith clock


Timing Analysis and OptimizationTiming Analysis and Optimization

Timing analysisTiming analysis Dynamic analysis: Simulation.Dynamic analysis: Simulation. Static timing analysis (STA): Vector-less topological analysis of Static timing analysis (STA): Vector-less topological analysis of

circuit.circuit.

Timing optimizationTiming optimization PerformancePerformance Clock designClock design

Other forms of design optimizationOther forms of design optimization Chip areaChip area TestabilityTestability PowerPower


Circuit DelaysCircuit Delays Switching or inertial delay is the interval between input Switching or inertial delay is the interval between input

change and output change of a gate:change and output change of a gate: Depends on input capacitance, device (transistor) Depends on input capacitance, device (transistor)

characteristics and output capacitance of gate.characteristics and output capacitance of gate. Also depends on input rise or fall times and states of other Also depends on input rise or fall times and states of other

inputs (second-order effects).inputs (second-order effects). Approximation: fixed rise and fall delays (or min-max delay Approximation: fixed rise and fall delays (or min-max delay

range, or single fixed delay) for gate output.range, or single fixed delay) for gate output.

Propagation or interconnect delay is the time a transition Propagation or interconnect delay is the time a transition takes to travel between gates:takes to travel between gates:

Depends on transmission line effects (distributed Depends on transmission line effects (distributed RR, , LL, , CC parameters, length and loading) of routing paths.parameters, length and loading) of routing paths.

Approximation: modeled as lumped delays for gate inputs.Approximation: modeled as lumped delays for gate inputs.


SpiceSpice Circuit/device level analysisCircuit/device level analysis

Circuit modeled as network of transistors, capacitors, Circuit modeled as network of transistors, capacitors, resistors and voltage/current sources.resistors and voltage/current sources.

Node current equations using Kirchhoff’s current law.Node current equations using Kirchhoff’s current law.

Analysis is accurate but expensiveAnalysis is accurate but expensive Used to characterize parts of a larger circuit.Used to characterize parts of a larger circuit.

Original references:Original references: L. W. Nagel and D. O. Pederson, “SPICE – Simulation L. W. Nagel and D. O. Pederson, “SPICE – Simulation

Program With Integrated Circuit Emphasis,” Memo ERL-Program With Integrated Circuit Emphasis,” Memo ERL-M382, EECS Dept., University of California, Berkeley, Apr. M382, EECS Dept., University of California, Berkeley, Apr. 1973.1973.

L. W. Nagel, L. W. Nagel, SPICE 2, A Computer program to Simulate SPICE 2, A Computer program to Simulate Semiconductor CircuitsSemiconductor Circuits, PhD Dissertation, University of , PhD Dissertation, University of California, Berkeley, May 1975.California, Berkeley, May 1975.


Ca

Logic Model of MOS CircuitLogic Model of MOS Circuit

Cc

Cb

VDD

a

b

c

pMOS FETs

nMOSFETs

Ca , Cb , Cc and Cd are

node capacitances

Dc

Da ca

b

Da and Db are

interconnect or propagation delays

Dc is inertial delay

of gate

Db

Cd


Spice CharacterizationSpice Characterization

Input data patternInput data pattern Delay (ps)Delay (ps) Dynamic energy (pJ)Dynamic energy (pJ)

aa = = bb = 0 → 1 = 0 → 1 6969 1.551.55

aa = 1, = 1, bb = 0 → 1 = 0 → 1 6262 1.671.67

aa = 0 → 1, = 0 → 1, bb = 1 = 1 5050 1.721.72

aa = = bb = 1 → 0 = 1 → 0 3535 1.821.82

aa = 1, = 1, bb = 1 → 0 = 1 → 0 7676 1.391.39

aa = 1 → 0, = 1 → 0, bb = 1 = 1 5757 1.941.94


Spice Characterization (Cont.)Spice Characterization (Cont.)

Input data patternInput data pattern Static power (pW)Static power (pW)

aa = = bb = 0 = 0 5.055.05

aa = 0, = 0, bb = 1 = 1 13.113.1

aa = 1, = 1, bb = 0 = 0 5.105.10

aa = = bb = 1 = 1 28.528.5


Complex Gates: Switch-Level PartitionsComplex Gates: Switch-Level Partitions Circuit partitioned into Circuit partitioned into channel-connected componentschannel-connected components for Spice for Spice

characterization.characterization. Reference: R. E. Bryant, “A Switch-Level Model and Simulator for Reference: R. E. Bryant, “A Switch-Level Model and Simulator for

MOS Digital Systems,” MOS Digital Systems,” IEEE Trans. ComputersIEEE Trans. Computers, vol. C-33, no. 2, pp. , vol. C-33, no. 2, pp. 160-177, Feb. 1984.160-177, Feb. 1984.

G1

G2

G3

Internal switching nodes not seen by logic simulator


Interconnect Delay: Elmore Delay ModelInterconnect Delay: Elmore Delay Model W. Elmore, “The Transient Response of Damped Linear Networks with W. Elmore, “The Transient Response of Damped Linear Networks with

Particular Regard to Wideband Amplifiers,” Particular Regard to Wideband Amplifiers,” J. Appl. PhysJ. Appl. Phys., vol. 19, ., vol. 19, no.1, pp. 55-63, Jan. 1948.no.1, pp. 55-63, Jan. 1948.

s 1

2

3

4

5

R1

R2

R3

R4

R5

C1

C2

C3

C5

C4

Shared resistance:

R45 = R1 + R3R15 = R1R34 = R1 + R3


Elmore Delay FormulaElmore Delay Formula

NDelay 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]


Event Propagation DelaysEvent Propagation Delays

2 4 61

1 3

5

3

10

0

0

2

2

Path P1

P2

P3

Single lumped inertial delay modeled for each gatePI transitions assumed to occur without time skew


Circuit OutputsCircuit Outputs Each path can potentially produce one signal Each path can potentially produce one signal

transition at the output.transition at the output. The location of an output transition in time is The location of an output transition in time is

determined by the delay of the path.determined by the delay of the path.

Initial value

Initial value

Final value

Final value

Clock period

Fast transitions Slow transitions

time


Delay and Discrete-Event SimulationDelay and Discrete-Event Simulation(NAND gate)(NAND gate)

b

a

c (CMOS)

Time units 0 5

c (zero delay)

c (unit delay)

c (multiple delay)

c (minmax delay)

Inp

uts

Log

ic s

imul

atio

n

min =2, max =5

rise=5, fall=5

Transient region

Unknown (X)

X


Event-Driven SimulationEvent-Driven Simulation(Example)(Example)

2

2

4

2

a =1

b =1

c =1→0

d = 0

e =1

f =0

g =1

Time, t 0 4 8

g

t = 0 12345678

Scheduledevents

c = 0

d = 1, e = 0

g = 0

f = 1

g = 1

Activitylist

d, e

f, g

gTim

e s

tack


Time Wheel (Circular Stack)Time Wheel (Circular Stack)

t=0

1

2

3

4

5

6

7

maxCurrenttimepointer Event link-list


Timing Design and Delay TestTiming Design and Delay Test Timing simulation:Timing simulation:

Critical paths are identified by static (vector-less) Critical paths are identified by static (vector-less) timing analysis tools like timing analysis tools like PrimetimePrimetime (Synopsys). (Synopsys).

Timing or circuit-level simulation using designer-Timing or circuit-level simulation using designer-generated functional vectors verifies the design.generated functional vectors verifies the design.

Layout optimization: Critical path data are used in Layout optimization: Critical path data are used in placement and routing. Delay parameter placement and routing. Delay parameter extraction, timing simulation and layout are extraction, timing simulation and layout are repeated for iterative improvement.repeated for iterative improvement.

Testing: Some form of at-speed test is necessary. Testing: Some form of at-speed test is necessary. Critical paths and all gate transition delays are Critical paths and all gate transition delays are tested. tested.


Static Timing Analysis (STA)Static Timing Analysis (STA) Finds maximum and minimum delays between Finds maximum and minimum delays between

all clocked flip-flops.all clocked flip-flops.

Combinationalcircuit

Flip

-flo

ps

Flip

-flo

ps

Flip

-flo

ps


Early ReferencesEarly References

T. I. Kirkpatrick and N. R. Clark, “PERT as an T. I. Kirkpatrick and N. R. Clark, “PERT as an Aid to Logic Design,” Aid to Logic Design,” IBM J. Res. DevIBM J. Res. Dev., vol. 10, ., vol. 10, no. 2, pp. 135-141, March 1966.no. 2, pp. 135-141, March 1966.

R. B. Hitchcock, Sr., “Timing Verification and the R. B. Hitchcock, Sr., “Timing Verification and the Timing Analysis Program,” Timing Analysis Program,” Proc. 19Proc. 19thth Design Design Automation ConfAutomation Conf., 1982, pp. 594-604.., 1982, pp. 594-604.

V. D. Agrawal, “Synchronous Path Analysis in V. D. Agrawal, “Synchronous Path Analysis in MOS Circuit Simulator,” MOS Circuit Simulator,” Proc. 19Proc. 19thth Design Design Automation ConfAutomation Conf., 1982, pp. 629-635.., 1982, pp. 629-635.


Basic IdeasBasic Ideas Adopted from project managementAdopted from project management

Frederick W. Taylor (1856-1915)Frederick W. Taylor (1856-1915) Henry Gantt (1861-1919)Henry Gantt (1861-1919)

PERT – Program Evaluation and Review PERT – Program Evaluation and Review TechniqueTechnique

CPM – Critical Path MethodCPM – Critical Path Method


A Gantt Chart in Microsoft ExcelA Gantt Chart in Microsoft Excel


Using a Gantt ChartUsing a Gantt Chart

Track progress of subtasks and project.Track progress of subtasks and project. Assess resource needs as a function of time.Assess resource needs as a function of time.


Pert ChartPert Chart


Example: Thesis ResearchExample: Thesis Research

Begin

Problemselected

Backgroundstudy

completed

Programand

Experimentcompleted

Analysiscompleted

ThesisDraftdone

Defensedone

Thesissubmitted

2, 4, 6 weeks

3, 4, 5

4, 5, 6

5, 7, 9

4, 4, 4

4, 4, 4

2, 3, 4

2, 2, 2

minimumaveragemaximum


Critical PathCritical Path

Begin

Problemselected

Backgroundstudy

completed

Programand

Experimentcompleted

Analysiscompleted

ThesisDraftdone

Defensedone

Thesissubmitted

2, 4, 6 weeks

3, 4, 5

4, 5, 6

5, 7, 9

4, 4, 4

4, 4, 4

2, 3, 4

2, 2, 2

minimumaveragemaximum

Critical path is pathof maximum averagedelay (24 weeks).


A Basic Timing Analysis AlgorithmA Basic Timing Analysis Algorithm Combinational logic.Combinational logic. Circuit represented as an acyclic directed graph Circuit represented as an acyclic directed graph

(DAG).(DAG). Gates characterized by delays.Gates characterized by delays.


ExampleExample

A1

B3

D2

E1

F1

J1

G2

H3

0

0

0

0

0

0

0

0

Levelize graph. Initialized arrival times at primary inputs.

Level 0 1 2 3 4 5

C1


Example (Cont.)Example (Cont.)

A1

B3

C1

D2

E1

F1

J1

G2

H3

0

0

0

0

0

0

0

0

Determine output arrival time when all input arrival times are known.

1

3

1

2

4

5

7

10

8

Level 0 1 2 3 4 5


Example (Cont.)Example (Cont.)

A1

B3

C1

D2

E1

F1

J1

G2

H3

0

0

0

0

0

0

0

0

Trace critical path from the output with longest arrival time.

1

3

1

2

4

5

7

10

8

Level 0 1 2 3 4 5


Finding Earliest and Longest TimesFinding Earliest and Longest Times

A1

B3

C1

D2

E1

F1

J1

G2

H3

0

0

0

0

0

0

0

0

1,1

3,3

1,1

2,2

2,4

3,5

4,7

4,10

4,8

Level 0 1 2 3 4 5


Shortest and Longest PathsShortest and Longest Paths

A1

B3

C1

D2

F1

J1

G2

H3

0

0

0

0

0

0

0

0

1,1

3,3

1,1

2,2

2,4

3,5

4,7

4,10

4,8

E1


Characteristics of STACharacteristics of STA

Linear time analysis, Complexity is O(n), n is Linear time analysis, Complexity is O(n), n is number of gates and interconnects.number of gates and interconnects.

Variations:Variations: Find k longest paths:Find k longest paths:

S. Kundu, “An Incremental Algorithm for Identification of S. Kundu, “An Incremental Algorithm for Identification of Longest (Shortest)Longest (Shortest) P Paths,”aths,” Integration, the VLSI Journal,Integration, the VLSI Journal, vol. vol. 17, no. 1, pp. 25-35, August 1994.17, no. 1, pp. 25-35, August 1994.

Find worst-case delays from an input to all outputs.Find worst-case delays from an input to all outputs. Linear programming methods.Linear programming methods.


Algorithms for Directed Acyclic Graphs Algorithms for Directed Acyclic Graphs (DAG)(DAG)

Graph size: n = |V| + |E|, for |V| vertices and |E| Graph size: n = |V| + |E|, for |V| vertices and |E| edges.edges.

Levelization: O(n) (linear-time) algorithm finds Levelization: O(n) (linear-time) algorithm finds the maximum (or minimum) depth.the maximum (or minimum) depth.

Path counting: O(nPath counting: O(n22) algorithm. Number of paths ) algorithm. Number of paths can be exponential in n.can be exponential in n.

Finding all paths: Exponential-time algorithm.Finding all paths: Exponential-time algorithm. Shortest (or longest) path between two nodes:Shortest (or longest) path between two nodes:

Dijkstra’s algorithm: O(nDijkstra’s algorithm: O(n22)) Bellman-Ford algorithm: O(nBellman-Ford algorithm: O(n33))


ReferencesReferences Delay modeling, simulation and testing:Delay modeling, simulation and testing:

M. L. Bushnell and V. D. Agrawal, M. L. Bushnell and V. D. Agrawal, Essentials of Electronic Essentials of Electronic Testing for Digital, Memory and Mixed-Signal VLSI CircuitsTesting for Digital, Memory and Mixed-Signal VLSI Circuits, , Springer, 2000.Springer, 2000.

Analysis and Design:Analysis and Design: G. De Micheli, G. De Micheli, Synthesis and Optimization of Digital CircuitsSynthesis and Optimization of Digital Circuits, ,

McGraw-Hill, 1994.McGraw-Hill, 1994. N. Maheshwari and S. S. Sapatnekar, N. Maheshwari and S. S. Sapatnekar, Timing Analysis and Timing Analysis and

Optimization of Sequential CircuitsOptimization of Sequential Circuits, Springer, 1999., Springer, 1999.

PrimeTime (Static timing analysis tool):PrimeTime (Static timing analysis tool): H. Bhatnagar, H. Bhatnagar, Advanced ASIC Chip Synthesis, Second EditionAdvanced ASIC Chip Synthesis, Second Edition, ,

Springer, 2002Springer, 2002

Documents

Spring 08, Jan 31.. ELEC 7770: Advanced VLSI Design (Agrawal) 1 ELEC 7770 Advanced VLSI Design Spring 2008 Timing Simulation and STA Vishwani D. Agrawal