Noise and delay uncertainty studies for coupled rc interconnects
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Noise and Delay Uncertainty Studies for Coupled RC Interconnects. Andrew B. Kahng, Sudhakar Muddu † and Devendra Vidhani ‡ UCLA Computer Science Department, [email protected] † Silicon Graphics Inc., [email protected] ‡ Sun Microsystems, [email protected] Outline of Talk.

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Noise and Delay Uncertainty Studies for Coupled RC Interconnects

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Noise and delay uncertainty studies for coupled rc interconnects

Noise and Delay Uncertainty Studies for Coupled RC Interconnects

Andrew B. Kahng, Sudhakar Muddu† and Devendra Vidhani‡

UCLA Computer Science Department, [email protected]

†Silicon Graphics Inc., [email protected]

‡Sun Microsystems, [email protected]


Outline of talk

Outline of Talk

  • Signal Integrity issues

  • Previous works

  • Our Contributions

    • Circuits Models

    • Delay and Noise Equations

  • Simulation results

  • Conclusions


Factors affecting signal integrity

Factors Affecting Signal Integrity

  • Interconnect induced issues

    • scaled linewidths greater wire and via RC

    • increased aspect ratios greater wire and via RC

    • larger die sizes greater wire and via RC

    • more metal layers higher coupling to ground ratio

  • Process Induced Issues

    • low device thresholds increased susceptibility to low noise margins

    • low VDD increased susceptibility to low noise margins

    • high frequency faster slew times


Focus crosstalk issues

Focus: Crosstalk Issues

  • Functionality Issues

    • peak noise

      • false switching of noise sensitive nodes in the design

  • Timing Issues

    • delay uncertainty

      • maximum difference between maximum and minimum victim line delay over all possible cases of switching activity on neighboring aggressor line(s)

  • Motivation: find noise issues ASAP!!

    • find signal integrity problem earlier in deisgn

    • provide sufficient conditions for finding problem


Outline of talk1

Outline of Talk

  • Signal Integrity issues

  • Previous works

  • Our Contributions

    • Circuits Models

    • Delay and Noise Equations

  • Simulation results

  • Conclusions


Previous work on signal integrity

Previous Work on Signal Integrity

  • Vittal et. Al., 97: L model; step input; ignore Rint, Cint

  • Kawaguchi et. Al., 98: diffusion equations; step input; same peak noise expressions as Vittal

  • Nakagawa et. Al., 98: L model; assumptions about peak noise time

  • Shepard et. Al., 97: L model; ignores R and C of aggressors; uses ramp with heuristics


Previous work on signal integrity issues

Previous Work on Signal Integrity Issues

  • Circuit models issues

    • use lumped capacitance models

    • use charge sharing models

  • Noise models issues

    • estimations very pessimistic

    • assumptions about R and C

    • assume zero slew rate

    • some are simulation based


Outline of talk2

Outline of Talk

  • Signal Integrity issues

  • Previous works

  • Our Contributions

    • Circuits Models

    • Delay and Noise Equations

  • Simulation results

  • Conclusions


Our work

Improved peak noise and delay and noise models

better peak noise estimates

analytical equations for delay uncertainty

Methodology

for coupled RC interconnects only

takes drivers into account

considers slew times

considers both lumped L-Model and -Model

considers both local and global lines

Our Work


Our work1

Circuit model

L model

 model

Noise analysis and peak noise expressions

Delay analysis and delay uncertainty

Our Work


Circuit model

Two parallel coupled lines

Aggressor - Green; Victim - Red

Coupling capacitance - Cc

Supply voltages - Vs1, Vs2

Circuit Model

Driver 1

Load 1

Aggressor Line

Vs1

Cc

Load 2

Driver 2

Victim Line

Vs2


Charge sharing model

Charge Sharing Model

  • No resistance

  • Lumped capacitance - C1, C2

  • Load capacitance - CL1, CL2

  • Node C has noise voltage

Aggressor Line

Vs1

CL1

C1

B

Cc1

C

C’1

CL2

Vs2

Victim Line


Noise analysis for charge sharing model

Noise Analysis For Charge Sharing Model

  • Basic noise analysis model

    • Victim line quiet

    • Aggressor line switching

  • Peak noise defined by ratio of coupling capacitance to total capacitance of wire


Lumped l model

Lumped L Model

  • All resistances considered

  • Lumped capacitances

  • Different slew times considered

Aggressor Line

Vs1

CL1

C1

R1

Rd1

B

Cc1

R’1

Rd2

C

C’1

CL2

Vs2

Victim Line

  • Solve using nodal equations at B and C


Solving l model

Solving L Model

  • M1,M2,a1,and a2,are given as

  • Transfer functions for nodes B and C are


Noise analysis for l model

Noise Analysis For L Model

  • L model voltage function for ramp input at victim node C (TS is slew time)

  • L model peak noise expression for step input reduces to Vittal et. Al. peak noise expression


Peak noise for l model

Peak Noise For L Model

  • Differentiate vc(t) to get tpeak

  • L Model peak noise at tpeak


Lumped model

Aggressor Line

Vs1

CL1

C2

C1

R1

Rd1

B

A

Cc2

Cc1

R’1

Rd2

C

D

C’2

CL2

C’1

Vs2

Victim Line

Lumped  - Model


Peak noise for model

Peak Noise For  Model

  • Vpeak is given at vc(tpeak)

    where


Delay uncertainty

Delay Uncertainty

  • Maximum difference between maximum and minimum delay

  • Caused by crosstalk between victim and aggressor switching simultaneously

  • Maximum delay by worst case

    • Aggressor and victim switching in opposite directions

  • Minimum delay by best case

    • Aggressor and victim switching in same direction


Simultaneous switching of victim aggressor

Vs1

V0

0

V0

Vs2

0

Ts2

Ts1

Simultaneous Switching of Victim & Aggressor

  • General Case

    • both victim ramp (TS2) and aggressor ramp (TS2) and four regimes of operation

  • Our Case: first region is empty

Time


Delay uncertainty1

Delay Uncertainty

  • Our delay uncertainty study based on  Model

  • Corresponding voltage function at node C


Delay function

Delay Function

  • Delay Function at node C


Outline of talk3

Outline of Talk

  • Signal Integrity issues

  • Previous works

  • Our Contributions

    • Circuits Models

    • Delay and Noise Equations

  • Simulation results

  • Conclusions


Simulation results

Simulation Results

  • Simulation configuration

    • 0.25 micron technology

    • analyzing different metal layer wires

    • analyze different factors like slew, coupling cap, etc.

  • Peak noise results w.r.t. slew

  • Best and worst delay result

  • Delay uncertainty w.r.t. aggressor slew and coupling


Simulation configuration

Simulation Configuration

  • Criteria

    • global wires (case 2 and 3) and local wires (case 1 and 4)

    • different coupling to ground capacitance ratios


Peak noise results

Peak Noise Results

  • Peak noise for different models

  • Comparison with previous work (Vittal et. Al. and Kawaguchi et. Al.)

  • Our results considered different slew times at aggressor


Peak noise results1

Peak Noise Results

  • Peak noise for different models

  • Comparison with previous work (VittalM97 and Kawaguchi-Sakurai)

  • Our results considered different slew times at aggressor


Peak noise variation for local wires

Peak Noise Variation For Local Wires

  • Peak noise variation with respect to slew of aggressor for local wire case 1


Peak noise variation for global wires

Peak Noise Variation For Global Wires

  • Peak noise variation with respect to slew of aggressor for global wire case 3


Victim delay results best worst case

Victim Delay Results (Best/Worst Case)

  • Worst case delay values using 50% threshold delay

  • Aggressor and victim switching in opposite directions

  • Same slew time on victim and aggressor

  • Case 1 and 4 - local

  • Case 2 and 3 - global


Victim delay uncertainty with slew times

Victim Delay Uncertainty With Slew Times

  • Delay uncertainty constant with same slew time on victim and aggressor

  • accuracy within 15% of spice


Victim delay variation w r t coupling

Victim Delay Variation W.R.T. Coupling

  • Best and worst case delays variation with coupling capacitance variation

  • Same slew time on victim and aggressor

  • Case 1 is local interconnect and case 2 is global interconnect


Victim delay variation with aggressor slew

Victim Delay Variation With Aggressor Slew

  • Impact of aggressor slew on delay

  • Victim slew constant at 400 ps

  • 15% accuracy w.r.t. spice

  • Local interconnect (case1) delay highly sensitive to slew time


Victim delay variation with aggressor slew1

Victim Delay Variation With Aggressor Slew

  • Impact of aggressor slew on delay

  • Victim slew constant at 400 ps

  • 15% accuracy w.r.t. spice

  • Local interconnect (case1) delay highly sensitive to slew time


Conclusions

Conclusions

  • Provide simple, fast and accurate analytical expressions for peak noise and delay estimates

  • Consider all R and C and all slew times

  • Provide noise awareness methodology possibility earlier in design phase

  • Easy extensions

    • multiple aggressor lines

    • slew offsets


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