1. EE 201A Modeling and Optimization for VLSI LayoutJeff Wong and Dan Vasquez EE 201A Noise Modeling Jeff Wong and Dan Vasquez Electrical Engineering Department University of California, Los Angeles

2. MEMS Research LaboratoryJoe Zendejas and Jack W. Judy Efficient Coupled Noise Estimation for On-Chip Interconnects Anirudh Devgan Austin Research Laboratory IBM Research Division, Austin TX

3. EE 201A Modeling and Optimization for VLSI LayoutJeff Wong and Dan Vasquez Motivation Noise failure can be more severe than timing failure –Difficult to control from chip terminals –Expensive to correct (refabrication) Circuit or timing simulation (like SPICE) can be used –Linear reduction techniques can be applied for linearly modeled circuits i.e. moment matching methods –Inefficient for noise verification and avoidance applications

4. EE 201A Modeling and Optimization for VLSI LayoutJeff Wong and Dan Vasquez Noise Estimation The paper presents an electrical metric for efficiently estimating coupled noise for on-chip interconnects 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

5. EE 201A Modeling and Optimization for VLSI LayoutJeff Wong and Dan Vasquez Circuit Schematic Switching signal V s (t) Coupling capacitors C C = [C C,ii ] C 1 = [C 1,ii ] C 2 = [C 2,ii ] Let’s analyze the case for one aggressor net and one victim net V 2,1 V 2,n V 1,1 V 1,n

6. EE 201A Modeling and Optimization for VLSI LayoutJeff Wong and Dan Vasquez Circuit Equations Coupled equation for circuit: In Laplace domain:

7. EE 201A Modeling and Optimization for VLSI LayoutJeff Wong and Dan Vasquez Circuit Equations Aggressor net: Victim net:

8. EE 201A Modeling and Optimization for VLSI LayoutJeff Wong and Dan Vasquez Transfer Function Transfer function: Simplifications (details later): Simplified transfer function:

9. EE 201A Modeling and Optimization for VLSI LayoutJeff Wong and Dan Vasquez Simplifications A 12 = 0 –No resistive (or DC) path exists from the aggressor net to the victim net A 21 = 0 –No resistive (or DC) path exists from the victim net to the aggressor net B 2 = 0 –No resistive (or DC) path exists from the voltage/noise source to the victim net

10. EE 201A Modeling and Optimization for VLSI LayoutJeff Wong and Dan Vasquez Maximum Induced Noise H(s=0) = 0 –Coupling between aggressor and victim net is purely capacitive –Maximum induced noise can be computed Assume V s is a finite or infinite ramp –

11. EE 201A Modeling and Optimization for VLSI LayoutJeff Wong and Dan Vasquez Final value theorem: – Ramp input u(s) : – Maximum Induced Noise

12. EE 201A Modeling and Optimization for VLSI LayoutJeff Wong and Dan Vasquez Circuit Interpretation Switching slope

13. EE 201A Modeling and Optimization for VLSI LayoutJeff Wong and Dan Vasquez Circuit Computations (matrix method) Step 1: Compute –Requires circuit analysis of the aggressor net Step 2: Compute –Requires a matrix multiplication Step 3: Compute –Requires circuit analysis of the victim net

14. EE 201A Modeling and Optimization for VLSI LayoutJeff Wong and Dan Vasquez Circuit Computations (by inspection) Step 1: Compute –Aggressor circuit transformation: Replace input source with it’s derivative Replace aggressor net’s capacitors with open circuits

15. EE 201A Modeling and Optimization for VLSI LayoutJeff Wong and Dan Vasquez Circuit Computations (by inspection) Step 1: Compute –Typical interconnects: Negligible loss: no resistive path to ground

16. EE 201A Modeling and Optimization for VLSI LayoutJeff Wong and Dan Vasquez Circuit Computations (by inspection) Step 2: Compute –Convert steady state derivative on the aggressor net to a current on the victim net – –i : index of node on the victim net –j : index of node on the aggressor net

17. EE 201A Modeling and Optimization for VLSI LayoutJeff Wong and Dan Vasquez Circuit Computations (by inspection) Step 3: Compute –Victim circuit transformation: Replace capacitors with coupling currents The voltage at each node corresponds to that node’s maximum induced noise

18. EE 201A Modeling and Optimization for VLSI LayoutJeff Wong and Dan Vasquez Circuit Computations (by inspection) Step 3: Compute –Typical interconnects: Compute by inspection in linear time

19. EE 201A Modeling and Optimization for VLSI LayoutJeff Wong and Dan Vasquez Circuit Computations (by inspection) Step 3: Compute –3RC Circuit example:

20. EE 201A Modeling and Optimization for VLSI LayoutJeff Wong and Dan Vasquez Computation Costs Step 1: –No computation required Step 2: –Simple multiplications Step 3: –Simple multiplications Multiple aggressor nets: –Coupling currents from step 2 determined from a linear superposition

21. EE 201A Modeling and Optimization for VLSI LayoutJeff Wong and Dan Vasquez Experiment Typical small RC interconnect structure –Rise time of 200 ps or 100 ps –Power supply voltage of 1.8 V –Conventional circuit simulation vs. proposed metric –Run-time comparisons for various circuit sizes

22. EE 201A Modeling and Optimization for VLSI LayoutJeff Wong and Dan Vasquez Accuracy Results 10 nodes, 200 ps rise time

23. EE 201A Modeling and Optimization for VLSI LayoutJeff Wong and Dan Vasquez Accuracy Results 10 nodes, 100 ps rise time

24. EE 201A Modeling and Optimization for VLSI LayoutJeff Wong and Dan Vasquez Accuracy Results Metric accuracy degrades with reduction in rise times Metric estimation is more conservative than circuit model’s –Fast rise times don’t allow circuit to reach ramp steady state noise Loading of interconnect normally does not allow for very small rise times –Metric accuracy should be acceptable for many applications

25. EE 201A Modeling and Optimization for VLSI LayoutJeff Wong and Dan Vasquez Run-time Results Arnoldi-based model reduction used a matrix solution to compute circuit response –Requires repeated factorizations, eigenvalue calculations, and time exponential evaluations

26. EE 201A Modeling and Optimization for VLSI LayoutJeff Wong and Dan Vasquez Conclusions The proposed metric determines an upper bound on coupled noise for RC and over-damped RLC interconnects –Metric becomes less accurate as rise time decreases The proposed metric is much more run-time efficient than circuit modeling methods

27. MEMS Research LaboratoryJoe Zendejas and Jack W. Judy Improved Crosstalk Modeling for Noise Constrained Interconnect Optimization Jason Cong, David Zhigang Pan & Prasanna V. Srinivas Department of Computer Science, UCLA Magma Design Automation, Inc. 2 Results Way, Cupertino, CA 95014

28. EE 201A Modeling and Optimization for VLSI LayoutJeff Wong and Dan Vasquez Motivation Deep sub-micron net designs have higher aspect ratio (h/w) –Increased coupling capacitance between nets Longer propagation delay Increased logic errors --- Noise Reduced noise margins –Lower supply voltages –Dynamic Logic Crosstalk cannot be ignored

29. EE 201A Modeling and Optimization for VLSI LayoutJeff Wong and Dan Vasquez Aggressor Victim Aggressor / Victim Network Assuming idle victim net –L s : Interconnect length before coupling –L c : Interconnect length of coupling –L e : Interconnect length after coupling Aggressor has clock slew t r

30. EE 201A Modeling and Optimization for VLSI LayoutJeff Wong and Dan Vasquez 2-  Model Victim net is modeled as 2  -RC circuits R d : Victim drive resistance C x is assumed to be in middle of L c Rise time victim / aggressor coupling capacitance

31. EE 201A Modeling and Optimization for VLSI LayoutJeff Wong and Dan Vasquez Aggressor Victim 2-  Model Parameters

32. EE 201A Modeling and Optimization for VLSI LayoutJeff Wong and Dan Vasquez Analytical Solution

33. EE 201A Modeling and Optimization for VLSI LayoutJeff Wong and Dan Vasquez Analytical Solution part 2 s-domain output voltage Transform function H(s)

34. EE 201A Modeling and Optimization for VLSI LayoutJeff Wong and Dan Vasquez Analytical Solution part 3 Aggressor input signal Output voltage

35. EE 201A Modeling and Optimization for VLSI LayoutJeff Wong and Dan Vasquez Simplification of Closed Form Solution Closed form solution complicated Non-intuitive –Noise peak amplitude, noise width? Dominant-pole simplification

36. EE 201A Modeling and Optimization for VLSI LayoutJeff Wong and Dan Vasquez Dominant-Pole Simplification RC delay from upstream resistance of coupling element Elmore delay of victim net

37. EE 201A Modeling and Optimization for VLSI LayoutJeff Wong and Dan Vasquez Intuition of Dominant Pole Simplification v out rises until t r and decays after v max evaluated at t r

38. EE 201A Modeling and Optimization for VLSI LayoutJeff Wong and Dan Vasquez Extension to RC Trees Similar to previous model with addition of lumped capacitances

39. EE 201A Modeling and Optimization for VLSI LayoutJeff Wong and Dan Vasquez Results Average errors of 4% 95% of nets have errors less than 10%

40. EE 201A Modeling and Optimization for VLSI LayoutJeff Wong and Dan Vasquez Spice Comparison peak noisenoise width

41. EE 201A Modeling and Optimization for VLSI LayoutJeff Wong and Dan Vasquez Effect of Aggressor Location As aggressor is moved close to receiver, peak noise is increased L s varies from 0 to 1mm L c has length of 1mm L e varies from 1mm to 0

42. EE 201A Modeling and Optimization for VLSI LayoutJeff Wong and Dan Vasquez Optimization Rules Rule 1: –If R s C 1 < R e C L Sizing up victim driver will reduce peak noise –If R s C 1 > R e C L and t r << t v Driver sizing will not reduce peak noise Rule 2: –Noise-sensitive victims should avoid near-receiver coupling

43. EE 201A Modeling and Optimization for VLSI LayoutJeff Wong and Dan Vasquez 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

44. EE 201A Modeling and Optimization for VLSI LayoutJeff Wong and Dan Vasquez Conclusions 2-  model achieves results within 6% error of HSPICE simulation Dominant node simplification gives intuition to important parameters Design rules established to reduce noise

45. EE 201A Modeling and Optimization for VLSI LayoutJeff Wong and Dan Vasquez References Anirudh Devgan, “Efficient Coupled Noise Estimation for On-chip Interconnects”, ICCAD, 1997. J. Cong, Z. Pan and P. V. Srinivas, “Improved Crosstalk Modeling for Noise Constrained Interconnect Optimization”, Proc. Asia South Pacific Design Automation Conference (ASPDAC), Jan. 30 - Feb. 2, 2001, Pacifico Yokohama, Japan.