Noise Model for Multiple Segmented Coupled RC Interconnects Andrew B. Kahng, Sudhakar Muddu †,...

Noise Model for Multiple Segmented Coupled RC Interconnects

Andrew B. Kahng, Sudhakar Muddu†,

Niranjan A. Pol ‡ and Devendra Vidhani*UCSD CSE and ECE Department, [email protected]

†Sanera Systems, Inc., [email protected]‡Cadence Design Systems, [email protected]

*Sun Microsystems, [email protected]

KMPV2001 2

Outline of Talk

• Signal Integrity Issues

• Previous Works

• Our Contributions

– Transformed Model for Segmented Aggressors

– Multiple Aggressors

• Simulation Results

• Conclusions

KMPV2001 3

Outline of Talk


• Previous Works





• Conclusions

KMPV2001 4

• Interconnect Induced Issues– scaled linewidths, increased aspect ratios, larger die sizes

greater wire and via RC, electromigration, IR drop, skin effect

– more metal layers higher coupling to ground ratio– long wider metal wires magnetic field / inductance

• Process Induced Issues– low device thresholds, low VDD

increased susceptibility to low noise margins

• Design Induced Issues– high frequency

faster slew times, inductive effects, ground bounce

Factors Affecting Signal Integrity

KMPV2001 5

Focus: Crosstalk Issues

• Cross talk caused by coupling between neighboring signals– Victim Net: Net being affected by coupling– Aggressor Net: Net affecting victim net due to its coupling to victim

• Coupling capacitance is one of major contributors• Functionality Issues

– peak noise• false switching of noise sensitive nodes in the design

• Timing Issues– positive/negative delay impact due to crosstalk– issues with timing closure

• Motivation: find coupling related noise issues ASAP!!– In general, find signal integrity problem earlier in design– provide sufficient conditions for finding problem

KMPV2001 6

Outline of Talk


• Previous Works





• Conclusions

KMPV2001 7

Previous Works on Crosstalk

• 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; does full chip simulation

• Kahng et. al., 99: model; Assume single, full length aggressor

KMPV2001 8

Previous Works on Crosstalk

• Circuit models issues– use lumped capacitance models

– cannot handle segmented aggressors configurations

• Noise models issues– estimations very pessimistic

– assumptions about R and C

– some are simulation based

KMPV2001 9

Outline of Talk


• Previous Works





• Conclusions

KMPV2001 10

Our Work

• Improved circuit model for peak noise– facilitates segmented aggressors– superposition for multiple aggressors

• Methodology– for coupled RC interconnects only– takes drivers into account– considers slew times– considers lumped -Model– considers both local and global line

KMPV2001 11

Circuit Model

• Two parallel coupled lines

• Aggressor - Green; Victim - Red

• Coupling capacitance - Cc

• Supply voltages - Vs1, Vs2

Aggressor Line

Victim Line

Vs1

Vs2

Driver 1

Driver 2

Load 1

Load 2Cc

KMPV2001 12

Lumped - Model

C

B

Vs1

Vs2

Rd2

Cc1

D

ARa

Rv

CL1

Aggressor Line

Victim Line

Rd1

Cc2

Cgv1Cgv2 CL2

Cga1Cga2

Rd1, Rd2: Driver Resistances

Cgv1, Cgv2: Leg of model for ground cap for victim

Cga1, Cga2: Leg of model for ground cap for aggressor

Ra, Rv: Wire resistances of used in the model

Cc1, Cc2: Left and right leg of model for coupling cap

CL1, CL2: Load caps

KMPV2001 13

Peak Noise For Model

• Vpeak is given at vc( tpeak)

where

ST

peakt

sTs

e

sTs

e

sk

sk

sspeakt

ST

peakt

sk

sk

sspeakt

2

11

11

22

11ln22

12

10

22

11ln22

11

KMPV2001 14

Segmented Aggressor Nets• Simple lumped model deficiencies for general case

– general case is when aggressor and victim nets are not overlapped completely

– for segmented aggressor overlaps, lumped model gives pessimistic results

• Extensions to lumped model for general case– improved victim wire and victim driver resistance modeling– improved victim coupling and ground capacitance modeling

• For multiple segmented aggressor nets coupling to victim net, use superposition to compute noise peak value

KMPV2001 15

Segmented Aggressor Net Configuration

• L1 = Left fraction of Victim to the Aggressor Overlap

• L2 = Fraction of Victim overlapped by Aggressor

• L3 = Right fraction of Victim to the Aggressor Overlap

• RdA(RdV) = Aggressor(Victim) Driver Resistance

• RwA(RwV) = Aggressor(Victim) Wire Resistance

• CgA(CgV) = Aggressor(Victim) Capacitance to ground

• CLA(CLV) = Aggressor(Victim) Load Capacitance

• Cc = Coupling Capacitance

CLV

VA

Aggressor Net

L3L2L1

L1+ L2+ L3 = 1

RdA

RdV

RWA

CLA

RWV

CgV

CgA

Victim Net

CC RdA

KMPV2001 16

• Victim wire resistance modeling– Wire resistance to left and right of overlap region not considered part of

wire resistance in the model– Assumed proportional to length of the victim net overlap region with the

aggressor, I.e.,Rv = Rwv* L2

• Victim driver resistance modeling– Assumed to consist of the actual driver resistance and the resistance of

portion of wire to the left of the overlap region, I.e.,Rd2 = Rdv+Rwv* L1

Victim Resistance Modeling

KMPV2001 17

Non Uniform Coupling Capacitance Distribution• Coupling capacitance distribution in model and real circuit

– In real circuit, coupling capacitance starts L1 distance away from the keeper end of the victim net

– In the model, the left leg of the coupling capacitance is at the keeper end of the victim net

• Discrepancy between model and real circuit– In real circuit, capacitance is shielded by the wire resistance – In the model, the keeper end of the victim net is at zero potential– This causes more discharge from the left leg of coupling cap

• Solution– Lower the coupling cap on the keeper end of the victim net in the model– Keep it pessimistic (don’t worry about receiver end correction)

Cc1 = 0.5 * Cc* (1-L1)Cc2 = 0.5 * Cc* (1+L1)

KMPV2001 18

Non Uniform Victim Ground Cap Distribution• Ground capacitance distribution / discrepancy

– In real circuit, the ground capacitance is distributed all along the victim wire

– In the model, the ground capacitance is visible equally at driver and receiver end of the wire

• Solution– Make left (right) leg of ground cap account for the ground cap for the

portion of the victim wire to the left (right) of the overlap region– Adjust total ground capacitance such that the total ground capacitance is

not changedCgv1 = 0.5* Cgv * (1+L1-L3)Cgv2 = 0.5* Cgv * (1-L1+L3)

KMPV2001 19

Outline of Talk


• Previous Works





• Conclusions

KMPV2001 20

Multiple Aggressors

• In real life layouts, need to see contributions of not more than 3 worst aggressors

• Our model report noise by superposition for individual aggressor’s noise contribution

• Noise function due to each aggressor is added in time domain to obtain the superimposed peak noise

• Could potentially be huge number of aggressor configurations

• Presented results for two and three aggressors

KMPV2001 21

Outline of Talk


• Previous Works





• Conclusions

KMPV2001 22

Criteria– global wires (case 2 and 3) and local wires (case 1 and 4)– different coupling to ground capacitance ratios– The values shown here are corresponding to Rint, Cint per unit length of the

victim wire and coupling cap to the aggressor with L2 assumed equals 1.0– To compare results for model with spice, we construct multiple model

with 45 nodes in the spice circuit

CasesWidth

(in m)Spacing(in m)

Length(in m)

Rint/length(in )

Cgnd/length(in fF)

Ccoup/length(in fF/mm)

1 0.49 0.46 1000 122.9 63.2 115.02

2 0.49 0.46 5000 122.9 63.15 115.00

3 1.00 0.46 10000 60.53 98.40 118.0

4 0.49 1.30 1000 122.9 109.3 46.2

Simulation Configuration

KMPV2001 23

Segmented Aggressor Net Configuration 1

• L1 = Left fraction of Victim to the Aggressor Overlap = 0.2

• L2 = Fraction of Victim overlapped by Aggressor = 0.6

• L3 = Right fraction of Victim to the Aggressor Overlap = 0.2


• RwA(RwV) = Aggressor(Victim) Wire Resistance


• CLA(CLV) = Aggressor(Victim) Load Capacitance


CLV

VA

Aggressor Net

L3L2L1

L1+ L2+ L3 = 1

RdA

RdV

RWA

CLA

RWV

CgV

CgA

Victim Net

CC RdA

KMPV2001 24

Peak Noise Results for Configuration 1

Peak noise results for configuration 1: L1=0.2, L2=0.6, L3=0.2

SPICE Our Model % Error SPICE Our Model % Error1 0.114 0.119 4.84 0.058 0.061 4.562 0.49 0.451 -8 0.436 0.421 -3.513 0.521 0.457 -12.22 0.502 0.45 -10.524 0.046 0.048 4.98 0.023 0.025 4.57

Ts = 200 psCases

Ts = 400 ps

SPICE Our Model % Error SPICE Our Model % Error1 0.255 0.269 5.67 0.18 0.197 9.612 0.515 0.462 -10.42 0.506 0.459 -9.363 0.52 0.46 -11.52 0.526 0.459 -12.684 0.103 0.109 5.65 0.072 0.079 10.66

Ts = 1 psCases

Ts = 100 ps

KMPV2001 25


VA

Aggressor Net

L3L2

RdA

RdV

RWA

RWV

CC

Cgv

CgA

Victim Net

CLA

CLA

• L1 = Left fraction of Victim to the Aggressor Overlap = 0.0• L2 = Fraction of Victim overlapped by Aggressor = 0.6• L3 = Right fraction of Victim to the Aggressor Overlap = 0.4


• RdA(RdV) = Aggressor(Victim) Wire Resistance


• CgA(CgV) = Aggressor(Victim) Load Capacitance


L1+ L2+ L3 = L

KMPV2001 26


Peak noise results for configuration 1: L1=0, L2=0.6, L3=0.4


Ts = 200 psCases

Ts = 400 ps


Ts = 1 psCases

Ts = 100 ps

KMPV2001 27


CLV

VA

Aggressor Net

L2L1

RdA

RdV

RWA

RWV

CC

Cgv

CgA

Victim Net

CLA

• L1 = Left fraction of Victim to the Aggressor Overlap = 0.4• L2 = Fraction of Victim overlapped by Aggressor = 0.6• L3 = Right fraction of Victim to the Aggressor Overlap = 0.0


• RdA(RdV) = Aggressor(Victim) Wire Resistance


• CgA(CgV) = Aggressor(Victim) Load Capacitance


L1+ L2+ L3 = L

KMPV2001 28


Peak noise results for configuration 1: L1=0.4, L2=0.6, L3=0


Ts = 200 psCases

Ts = 400 ps


Ts = 1 psCases

Ts = 100 ps

KMPV2001 29

Peak Noise Results for Two Aggressor

Peak noise results for two aggressors configurations. Aggressor1: L1=0, L2=0.6, L3=0.4; Aggressor2: L1=0.4, L2=0.6, L3=0

SPICE Our Model % Error SPICE Our Model % Error1 0.222 0.237 6.78 0.117 0.112 4.662 0.726 0.793 7.17 0.658 0.732 9.853 0.851 0.887 4.57 0.828 0.872 5.414 0.091 0.096 5.54 0.047 0.049 4.59

Ts = 200 psCases

Ts = 400 ps


Ts = 1 psCases

Ts = 100 ps

KMPV2001 30

Peak Noise Results for Three Aggressors

Peak noise results for three aggressors configurations. Aggressor1: L1=0, L2=0.6, L3=0.4; Aggressor2: L1=0.2, L2=0.6, L3=0.2; Aggressor3: L1=0.6, L2=0.4, L3=0


Ts = 200 psCases

Ts = 400 ps


Ts = 1 psCases

Ts = 100 ps

KMPV2001 31

Outline of Talk


• Previous Works





• Conclusions

KMPV2001 32

Conclusions• Model works for point to point victim net and segmented

multiple aggressors

• Results are accurate for peak noise

• Pessimism increases with the number of aggressors– One segmented aggressor: 16% max error– Two segmented aggressor: 17%– Three segmented aggressor: 31%

• Can be used as a quick pruning step in an analytical noise tool

KMPV2001 33

Future Work

• More scalable for large system of aggressors

• Extension to tree like structures (multiple fanouts)

• Report pulse width / slew degradation and effective switch factor

• Form a complete analytical system for post layout noise analysis

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Noise Model for Multiple Segmented Coupled RC Interconnects Andrew B. Kahng, Sudhakar Muddu †,...

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