Noise Model for Multiple Segmented Coupled RC Interconnects

1
Noise Model for Multiple Segmented Coupled RC
Interconnects

• Andrew B. Kahng, Sudhakar Muddu,
• Niranjan A. Pol and Devendra Vidhani
• UCSD CSE and ECE Department, abk_at_ucsd.edu
• Sanera Systems, Inc., muddu_at_sanera.net
• Cadence Design Systems, npol_at_cadence.com
• Sun Microsystems, dv_at_eng.sun.com

2
Outline of Talk

• Signal Integrity Issues
• Previous Works
• Our Contributions
• Transformed ? Model for Segmented Aggressors
• Multiple Aggressors
• Simulation Results
• Conclusions

3
Outline of Talk

• Signal Integrity Issues
• Previous Works
• Our Contributions
• Transformed ? Model for Segmented Aggressors
• Multiple Aggressors
• Simulation Results
• Conclusions

4
Factors Affecting Signal Integrity

• 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

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

6
Outline of Talk

• Signal Integrity Issues
• Previous Works
• Our Contributions
• Transformed ? Model for Segmented Aggressors
• Multiple Aggressors
• Simulation Results
• Conclusions

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

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

9
Outline of Talk

• Signal Integrity Issues
• Previous Works
• Our Contributions
• Transformed ? Model for Segmented Aggressors
• Multiple Aggressors
• Simulation Results
• Conclusions

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

11
Circuit Model

• Two parallel coupled lines
• Aggressor - Green Victim - Red
• Coupling capacitance - Cc
• Supply voltages - Vs1, Vs2

Driver 1
Load 1
Aggressor Line
Vs1
Cc
Load 2
Driver 2
Victim Line
Vs2
12
Lumped ? - Model
Cga2
Cga1

• 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
13
Peak Noise For ? Model

• Vpeak is given at vc( tpeak)
• where

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

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

VA
RdA
CgA
CLA
Aggressor Net
RWA
CC
RdA
L2
L3
L1
RWV
Victim Net
CgV
RdV
CLV
L1 L2 L3 1
16
Victim Resistance Modeling

• 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 RdvRwv L1

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 (dont worry about receiver
  end correction)
• Cc1 0.5 Cc (1-L1)
• Cc2 0.5 Cc (1L1)

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 changed
• Cgv1 0.5 Cgv (1L1-L3)
• Cgv2 0.5 Cgv (1-L1L3)

19
Outline of Talk

• Signal Integrity Issues
• Previous Works
• Our Contributions
• Transformed ? Model for Segmented Aggressors
• Multiple Aggressors
• Simulation Results
• Conclusions

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 aggressors 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

21
Outline of Talk

• Signal Integrity Issues
• Previous Works
• Our Contributions
• Transformed ? Model for Segmented Aggressors
• Multiple Aggressors
• Simulation Results
• Conclusions

22
Simulation Configuration

• 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

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
• 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

VA
RdA
CgA
CLA
Aggressor Net
RWA
CC
RdA
L2
L3
L1
RWV
Victim Net
CgV
RdV
CLV
L1 L2 L3 1
24
Peak Noise Results for Configuration 1
Peak noise results for configuration 1 L10.2,
L20.6, L30.2
25
Segmented Aggressor Net Configuration 2

• 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) Driver Resistance
• RdA(RdV) Aggressor(Victim) Wire Resistance
• CgA(CgV) Aggressor(Victim) Capacitance to
  ground
• CgA(CgV) Aggressor(Victim) Load Capacitance
• Cc Coupling Capacitance

Aggressor Net
VA
RdA
CgA
CLA
RWA
CC
L2
L3
RWV
Victim Net

RdV
Cgv
CLA
L1 L2 L3 L
26
Peak Noise Results for Configuration 2
Peak noise results for configuration 1 L10,
L20.6, L30.4
27
Segmented Aggressor Net Configuration 3

• 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) Driver Resistance
• RdA(RdV) Aggressor(Victim) Wire Resistance
• CgA(CgV) Aggressor(Victim) Capacitance to
  ground
• CgA(CgV) Aggressor(Victim) Load Capacitance
• Cc Coupling Capacitance

Aggressor Net
VA
RdA
CgA
CLA
RWA
CC
L1
L2
RWV
Victim Net
RdV
Cgv
CLV
L1 L2 L3 L
28
Peak Noise Results for Configuration 3
Peak noise results for configuration 1 L10.4,
L20.6, L30
29
Peak Noise Results for Two Aggressor
Peak noise results for two aggressors
configurations. Aggressor1 L10, L20.6, L30.4
Aggressor2 L10.4, L20.6, L30
30
Peak Noise Results for Three Aggressors
Peak noise results for three aggressors
configurations. Aggressor1 L10, L20.6, L30.4
Aggressor2 L10.2, L20.6, L30.2 Aggressor3
L10.6, L20.4, L30
31
Outline of Talk

• Signal Integrity Issues
• Previous Works
• Our Contributions
• Transformed ? Model for Segmented Aggressors
• Multiple Aggressors
• Simulation Results
• Conclusions

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

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