Chapter 3b Static Noise Analysis Cx Victim net Aggressor net Prof. Lei He Electrical Engineering Department University of California, Los Angeles URL: eda.ee.ucla.edu Email: lhe@ee.ucla.edu

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

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

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: 1275 - 1283

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

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

2- π Model Parameters Aggressor Victim

Analytical Solution

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

Analytical Solution part 3 Aggressor input signal Output voltage

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

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

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

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

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%

Spice Comparison peak noise noise width

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

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

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

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: 1275 - 1283

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.

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.

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

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

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.

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

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.

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: 1275 - 1283

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

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

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

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

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

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

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: 1275 - 1283

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?

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

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

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.

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.

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.

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.

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%.