Topics

1. Topics • Interconnect design. • Crosstalk. • Power optimization.

2. Interconnect • Even assuming logic structure is fixed, we can: • change wire topology; • resize wires; • add buffers; • size transistors.

3. Multipoint nets • Two-point nets are easy to design. • Multipoint nets are harder: • How do we connect all the pins using two-point connections?

4. Spanning tree Steiner tree Steiner point Styles of wiring trees source sink 1 sink 2

5. Sized Steiner tree source Feeds both branches sink 1 Smaller currents in each branch sink 2

6. Buffer insertion in wiring trees • More complex than placing buffers along a transmission line: • complex topology; • unbalanced trees; • differing timing requirements at the leaves.

7. Van Ginneken algorithm • Given: • placements of sources and sinks; • routing of wiring tree. • Place buffers within tree to minimize the departure time at the source to meet all the sink arrival times: • Tsource = min i (T i -D i) • T i = arrival time at node i, D i = delay to node I.

8. Delay calculation • Use Elmore model to compute delay along path from source to sink.

9. Recursive delay calculation • Recursively compute Elmore delay through the tree. • Start at sinks, work back to source. • r, c are unit resistance/capacitance of wire. • Lk is total capacitive load of subtree rooted at node k.

10. Modifying the tree • Add a wire of length l at node k: • Tk’ = Tk - r/Lk - 0.5rcl. • Lk’ = Lk + cl. • Buffer node k: • Tk’ = Tk - Dbuf - Rbuf Lk. • Lk’ = Cbuf. • Join two subtrees m and n at node k: • Tk’ = (Tm , Tn). • Lk’ = Lm + Ln.

11. Crosstalk • Capacitive coupling introduces crosstalk. • Crosstalk slows down signals to static gates, can cause hard errors in storage nodes. • Crosstalk can be controlled by methodological and optimization techniques.

12. Interleaved power/ground VDD VSS VDD VSS VDD VSS

13. Twizzled wires a b a b d b c a c d c d

14. Coupling and crosstalk • Crosstalk current depends on capacitance, voltage ramp. ic w1 w2 t Cc

15. Crosstalk analysis • Assume worst-case voltage swings, signal slopes. • Measure coupling capacitance based on geometrical alignment/overlap. • Some nodes are particularly sensitive to crosstalk: • dynamic; • asynchronous.

16. Coupling situations bus[0] a x r bus[1] sig1 bus[2] better worse

17. Layer-to-layer coupling • Long parallel runs on adjacent layers are also bad. siga bus[0] SiO2

18. Methodological solutions • Add ground wires between signal wires: • coupling to VSS, a stable signal, dominates; • can use VSS to distribute power, so long as power line is relatively stable. • Extreme case—add ground plane. Costs an entire layer, may be overkill.

19. Ground wires VSS sig1 VSS sig2 VSS

20. Crosstalk and signal routing • Can route wires to minimize required adjacency regions. • Take advantage of natural holes in routing areas to decouple signals. • Minimizes need for ground signals.

21. Assumptions • Take into account coupling only to wires in adjacent tracks. • Ignore coupling of vertical wires. • Assume that coupling/crosstalk is proportional to adjacency length.

22. Crosstalk example

23. Crosstalk analysis • Want to estimate delays induced by crosstalk. • Effect of coupling capacitance Cc depends on relative transitions. • Aggressor changes, victim does not: Cc. • Aggressor, victim move in opposite directions: 2Cc. • Aggressor, victim move in same direction: 0.

24. Crosstalk analysis, cont’d. • Coupling effects depend on relative switching time of nets. • Must use iterative algorithm to solve for coupling capacitances and delays.

25. Power optimization • Glitches cause unnecessary power consumption. • Logic network design helps control power consumption: • minimizing capacitance; • eliminating unnecessary glitches.

26. Glitching example • Gate network:

27. Glitching example behavior • NOR gate produces 0 output at beginning and end: • beginning: bottom input is 1; • end: NAND output is 1; • Difference in delay between application of primary inputs and generation of new NAND output causes glitch.

28. Adder chain glitching bad good

29. Explanation • Unbalanced chain has signals arriving at different times at each adder. • A glitch downstream propagates all the way upstream. • Balanced tree introduces multiple glitches simultaneously, reducing total glitch activity.

30. Signal probabilities • Glitching behavior can be characterized by signal probabilities. • Transition probabilities can be computed from signal probabilities if clock cycles are assumed to be independent. • Some primary inputs may have non-standard signal probabilities— control signal may be activated only occasionally.

31. Delay-independent probabilities • Compute output probabilities of primitive functions: • PNOT = 1 - Pin • POR = 1 -  Pi) • PAND = Pi • Can compute output probabilities of reconvergent fanout-free networks by traversing tree.

32. Delay-dependent probabilities • More accurate estimation of glitching. Glitch accuracy depends on accuracy of delay model. • Can use simulation-style algorithms to propagate glitches. • Can use statistical models coupled with delay models.

33. Power estimation tools • Power estimator approximates power consumption from: • gate network; • primary input transition probabilities; • capacitive loading. • May be switch/logic simulation based or use statistical models.

34. Factorization for low power • Proper factorization reduces glitching. bad good

35. Factorization techniques • In example, a has high transition probability, b and c low probabilities. • Reduce number of logic levels through which high-probability signals must travel in order to reduce propagation of glitches.

36. Layout for low power • Place and route to minimize capacitance of nodes with high glitching activity. • Feed back wiring capacitance values to power analysis for better estimates.