Chapter 3b Static Noise Analysis

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

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

7. Aggressor Victim 2- π 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 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 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 • 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

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 • 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

27. Vdd s1 s2 G s3 s4 Gnd Problem Formulation • 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 • Assume coplanar parallel interconnect structures (termed a “placement”), Vdd s1 s2 s3 s4 Gnd

28. Characteristics of Lx Coupling (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 s1 s2 s3 s4 Gnd

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.