1. Chapter 3b Static Noise AnalysisCx
Victim net
Aggressor net
Prof. Lei He
Electrical Engineering Department
University of California, Los Angeles
URL: eda.ee.ucla.edu

2. Outline Introduction and Motivation Noise Models RC Model
J. Cong, Z. Pan and P. V. Srinivas, "Improved Crosstalk Modeling for Noise Constrained Interconnect Optimization", ASPDAC 2001
Worst case noise for RC
Lauren Hui Chen, Malgorzata Marek-Sadowska: Aggressor alignment for worst-case coupling noise. ISPD 2000: 48-54
Worst case noise for RLC
Jun Chen and Lei He, "Worst-Case Crosstalk Noise for Non-Switching Victims in High-speed Buses", TCAD, Volume 24, Issue 8, Aug. 2005, Pages:

3. Victim net Aggressor net
Introduction
Coupling Capacitance Dominates
Signal delay
Crosstalk noise
What is Crosstalk noise?
Capacitive coupling between an aggressor net and a victim net leads to coupled noise
Aggressor net: switches states; source of noise for victim net
Victim net: maintains present state; affected by coupled noise from aggressor net Cx
Victim net
Aggressor net
output

4. Noise Models RC model Worst case noise for RC Worst case noise for RLC
J. Cong, Z. Pan and P. V. Srinivas, "Improved Crosstalk Modeling for Noise Constrained Interconnect Optimization", ASPDAC 2001
Worst case noise for RC
Lauren Hui Chen, Malgorzata Marek-Sadowska: Aggressor alignment for worst-case coupling noise. ISPD 2000: 48-54
Worst case noise for RLC
Jun Chen and Lei He, "Worst-Case Crosstalk Noise for Non-Switching Victims in High-speed Buses", TCAD, Volume 24, Issue 8, Aug. 2005, Pages:

5. Aggressor / Victim Network
Assuming idle victim net
Ls: Interconnect length before coupling
Lc: Interconnect length of coupling
Le: Interconnect length after coupling
Aggressor has clock slew tr

6. Victim net is modeled as 2-π -RC circuits Rd: Victim drive resistance
Cx is assumed to be in middle of Lc
Rise time
victim / aggressor
coupling capacitance

7. 2- π Model Parameters
Aggressor
Victim

8. Analytical Solution

9. Analytical Solution part 2
s-domain output voltage
Transform function H(s)

10. Analytical Solution part 3
Aggressor input signal
Output voltage

11. Simplification of Closed Form Solution
Closed form solution complicated
Non-intuitive
Noise peak amplitude, noise width?
Dominant-pole approximation method

12. Dominant-Pole Simplification
RC delay from upstream resistance of coupling element
Elmore delay of victim net

13. Intuition of Dominant Pole Simplification
vout rises until tr and decays after
vmax evaluated at tr

14. Extension to RC Trees
Similar to previous model with addition of lumped capacitances
Extended to a victim net in general RC tree structure

15. Results
Average errors of 4% comparing to HSPICE in peak noise and noise width.
Devgan model 589%
Vittal model 9%
95% of nets have errors less than 10%

16. Spice Comparison
peak noise noise width

17. Effect of Aggressor Location
As aggressor is moved close to receiver, peak noise is increased
Ls varies from 0 to 1mm
Lc has length of 1mm
Le varies from 1mm to 0

18. Optimization Rules Rule 1: If RsC1 < ReCL
Sizing up victim driver will reduce peak noise
If RsC1 > ReCL and tr << tv
Driver sizing will not reduce peak noise
Rule 2:
Noise-sensitive victims should avoid near-receiver coupling

19. Optimization Rules part 2
Preferred position for shield insertion is near a noise sensitive receiver
Rule 4:
Wire spacing is an effective way to reduce noise
Rule 5:
Noise amplitude-width product has lower bound
And upper bound

20. Noise Models Shield Insertion and Net Ordering (SINO) Devgan’s model
Anirudh Devgan, "Efficient Coupled Noise Estimation for On-chip Interconnects", ICCAD, 1997.
2-Pi model
J. Cong, Z. Pan and P. V. Srinivas, "Improved Crosstalk Modeling for Noise Constrained Interconnect Optimization", ASPDAC 2001
Worst case noise for RC
Lauren Hui Chen, Malgorzata Marek-Sadowska: Aggressor alignment for worst-case coupling noise. ISPD 2000: 48-54
Shield Insertion and Net Ordering (SINO)
L. He and K. M. Lepak, "Simultaneous shield insertion and net ordering for capacitive and inductive coupling minimization", ISPD 2000
Worst case noise for RLC
Jun Chen and Lei He, "Worst-Case Crosstalk Noise for Non-Switching Victims in High-speed Buses", TCAD, Volume 24, Issue 8, Aug. 2005, Pages:

21. Worst Case Noise Model Consider multiple-aggressors situation:
Each aggressor (A1, …, A5) has its switching signal.
Each switching aggressor will result in a coupling noise on victim at variable arrival times.

22. Worst Case Noise Model To consider Worst Case Noise (WCN):
Make alignment of aggressor inputs (change arrival time)
The coupling noise at victim output can occur at the same time.
Aggressor Alignment Problem Formulation:
Find the relative relationships among arrival times for all aggressor inputs such that all individual peak noises are aligned, assuming all the other conditions are fixed.

23. WCN Superposition Consider two aggressors (V1 and V2) case
N1: when V1 is switching, V2 is quiet;
N2: when V2 is switching, V1 is quiet;
Individual noise waveforms

24. WCN Superposition
To consider WCN, the aggressor alignment is performed:
Change the arrival time of V2
Two noise signals can occur at the same time

25. WCN Analysis strategies
Four WCN analysis strategies based on aggressor alignment
Explicit Aggressor Alignment (AS: Aligned switching)
Noise output is obtained by aligning switching of all aggressors. The largest amplitude is WCN.
No Aggressor Alignment (SS: simultaneous switching)
Simultaneous switching of all aggressors.
Implicit Aggressor Alignment (SP: Superposition)
Each noise output is obtained with only one aggressor switching;
Total peak noise is the summation over all individual peak noise.
Extension of Implicit Aggressor Alignment
“back-annotates”: use output noise to determine the aggressor input skews, and estimate the coupling stage again.

26. Peak Noise Comparisons with no timing constraints
Experiment
Peak Noise Comparisons with no timing constraints
WCN analysis can provide higher accuracy than superposition does.

27. Peak Noise Comparisons when timing constraints are given
Experiment
Peak Noise Comparisons when timing constraints are given
Similarly, WCN analysis can provide higher accuracy than superposition does.

28. Noise Models Shield Insertion and Net Ordering (SINO) Devgan’s model
Anirudh Devgan, "Efficient Coupled Noise Estimation for On-chip Interconnects", ICCAD, 1997.
2-Pi model
J. Cong, Z. Pan and P. V. Srinivas, "Improved Crosstalk Modeling for Noise Constrained Interconnect Optimization", ASPDAC 2001
Worst case noise for RC
Lauren Hui Chen, Malgorzata Marek-Sadowska: Aggressor alignment for worst-case coupling noise. ISPD 2000: 48-54
Shield Insertion and Net Ordering (SINO)
L. He and K. M. Lepak, "Simultaneous shield insertion and net ordering for capacitive and inductive coupling minimization", ISPD 2000
Worst case noise for RLC
Jun Chen and Lei He, "Worst-Case Crosstalk Noise for Non-Switching Victims in High-speed Buses", TCAD, Volume 24, Issue 8, Aug. 2005, Pages:

29. Vdd s1 s2 s3 s4 Gnd Vdd Gnd s1 G s2 s3 s4 Problem Formulation
Assume coplanar parallel interconnect structures (termed a “placement”),
Vdd s1 s2 s3 s4
Gnd
Cx coupling has been considered, but Lx coupling can not be neglected.
Simultaneous shield insertion and net ordering (SINO)
Net ordering eliminates Cx noise
Shield insertion removes Lx noise
Vdd
Gnd s1 G s2 s3 s4

30. Characteristics of Lx Coupling
# of Shields
Noise (% of Vdd)
0 (a)
0.71V (55%)
2 (b)
0.38V (29%)
5 (c)
0.17V (13%)
(18 bit bus structure from He et. al., CICC 1999)
(a)
(b)
(c)
Lx coupling between non-adjacent nets is non-trivial
Shielding is effective to reduce Lx coupling

31. Net Sensitivity
Two nets are considered sensitive if a switching event on signal s1 happens during a sample time window for s2
error occurs
Signal levels (V)
aggressor
VIH
victim1
victim2
time
Sampling window
no error occurs

32. SINO/NF Problem Formulation
Given: An initial placement P
Find: A new placement P’ via simultaneous shield insertion and net ordering such that:
P’ is capacitive noise free
Sensitive nets are not adjacent to each other
P’ is inductive noise free
Sensitive nets do not share a block
P’ has minimal area

33. SINO/NB Problem Formulation
Given: An initial placement P
Find: A new placement P’ via simultaneous shield insertion and net ordering such that:
P’ is capacitive noise free
All nets in P’ have inductive noise less than a given value
P’ has minimal area

34. Quality of SINO/NB Solutions
Max. clique size in the sensitivity graph
SINO/NF
SINO/NB
Kthresh
Graph Coloring
Greedy SI
NO+SI GC SA
Net Sensitivity Rate: 10%
1.0
3.2
(2.0)
5.0
2.8
2.0
1.8
4.2
1.2
Net Sensitivity Rate: 30%
6.0
(3.8)
13.2
4.4
3.0
3.8
Net Sensitivity Rate: 60%
13.6
(8.2)
22.4
5.4
8.2
4.0
3.4
# of shields is fewer than lower bound for SINO/NF
CPU time is much less than existing net ordering algorithms

35. Shield Insertion and Net Ordering (SINO)
Noise Models
2-Pi model
J. Cong, Z. Pan and P. V. Srinivas, "Improved Crosstalk Modeling for Noise Constrained Interconnect Optimization", ASPDAC 2001
Worst case noise for RC
Lauren Hui Chen, Malgorzata Marek-Sadowska: Aggressor alignment for worst-case coupling noise. ISPD 2000: 48-54
Shield Insertion and Net Ordering (SINO)
L. He and K. M. Lepak, "Simultaneous shield insertion and net ordering for capacitive and inductive coupling minimization", ISPD 2000
Worst case noise for RLC
Jun Chen and Lei He, "Worst-Case Crosstalk Noise for Non-Switching Victims in High-speed Buses", TCAD, Volume 24, Issue 8, Aug. 2005, Pages:

36. Worst Case Noise (WCN) for RLC tree
Problem Formulation:
Given a non-switching victim and multiple aggressors in a pre-routed interconnect structure
Object: find switching patterns and switching times for all aggressors such that the noise in the victim has maximal amplitude.
Recall basic WCN analyses for RC model:
SS: Simultaneous switching
SP: Superposition
AS: Aligned switching
How to extend WCN analysis to the RCL model?

37. Shielding: Vdd s1 s2 s3 s4 Gnd WCN under the RCL model
Dedicated shields can reduce crosstalk noise.
Assume there are shields at both edges of the bus structure.
Vdd s1 s2 s3 s4
Gnd

38. Switching Pattern WCN under the RCL model
Waveform can have resonance due to inductance under RCL model
Resonance leads to multiple noise peaks with opposite polarities.
WCN may happen when aggressors switch in the same or different direction.
V – quiet victim
q – q quiet wire
a - aggressor
S - shield

39. Routing Direction: WCN under the RCL model
Same direction or Opposite direction
Consider two routing directions
One is aggressor and the other is victim
Same direction routing leads to smaller crosstalk noise
Noise difference results from different current flow, and different loop inductance.

40. WCN analysis under RLC model
Extension to Existing Algorithm for RC
Simultaneous Switching (SS):
All aggressors switch simultaneously in the same direction
WCN is the maximum noise on the victim
Superposition (SP)
Find maximum noise peak for each aggressor when only this aggressor switches.
WCN is the summation of amplitudes of all such peaks.

41. WCN analysis under RLC model
AS (Aligned Switching)
Find individual noise with only one aggressor switching;
Switch multiple aggressors to find the maximum noise
PP alignment:
align the maximum positive peaks of individual noises
all aggressors switch in the same direction
NN alignment:
align the maximum negative peaks of individual noises
PN alignment:
align the peaks of maximum amplitude
Aggressors have switching directions that all the aligned peaks have the same polarity.
WCN is the maximum noise among the above simulations.

42. Experiment
Noises on a quiet victm from different algorithms for an aligned RLC bus structure
Accurate results
SA+GA  select larger noise from annealing algorithm (SA) and genetic algorithm (GA) as the accurate WCN.
SS + ASWCN is approximated by the larger one between the results
obtained by SS and AS.
SS + AS gives results very close to SA + GA
WCN under the RC model severely underestimates the noise in most cases, especially for strong drivers and larger spacing.

43. Experiment
Noises on a noisy victm from different algorithms for an aligned RLC bus structure
Similarly, SS + AS gives results very close to SA + GA.
SP severely underestimates WCN, witha maximum underestimation
of 39.93% and an average underestimation of 20.53%.