Chapter 3b Static Noise Analysis

1
Chapter 3bStatic Noise Analysis

• Prof. Lei He
• Electrical Engineering Department
• University of California, Los Angeles
• URL eda.ee.ucla.edu
• Email lhe_at_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 1275
  - 1283

3
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

4
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 1275
  - 1283

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
2- p Model

• Victim net is modeled as 2-p -RC circuits
• Rd Victim drive resistance
• Cx is assumed to be in middle of Lc

victim / aggressor coupling capacitance
7
2- p Model Parameters
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
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 lt ReCL
• Sizing up victim driver will reduce peak noise
• If RsC1 gt ReCL and tr ltlt tv
• Driver sizing will not reduce peak noise
• Rule 2
• Noise-sensitive victims should avoid
  near-receiver coupling

19
Optimization Rules part 2

• Rule 3
• 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

• Devgans 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 1275
  - 1283

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
• Each noise output is obtained with only one
  aggressor switching
• back-annotates use output noise to determine
  the aggressor input skews, and estimate the
  coupling stage again.

26
Noise Models

• Devgans 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 1275
  - 1283

27
Problem Formulation

• Assume coplanar parallel interconnect structures
  (termed a placement),

Vdd
Gnd
s1
s2
s3
s4

• 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

28
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

29
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
30
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

31
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

32
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 1275
  - 1283

33
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?
34
WCN under the RCL model

• Shielding
• Dedicated shields can reduce crosstalk noise.
• Assume there are shields at both edges of the bus
  structure.

Vdd
Gnd
s1
s2
s3
s4
35
WCN under the RCL model

• Switching Pattern
• 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
36
WCN under the RCL model

• Routing Direction
• 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.

37
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.

38
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
• all aggressors switch in the same direction
• 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.