Efficient Switching Window Computation for CrossTalk Noise

1
Efficient Switching Window Computation for
Cross-Talk Noise

• Bhavana Thudi
• David Blaauw
• University of Michigan, Ann Arbor

2
Traditional Delay Noise Analysis
Aggressor 1
Cc1
K1Cc1
K2Cc2
Victim
Cc2
Aggressor 2

• Delay Noise Increases/Decreases Delay
• Switch factor based noise model
• Iterative Timing Window Propagation

3
Outline

• Introduction
• Delay Model
• Time Sort Algorithm
• Results
• Conclusion

4
Introduction
Motivation
1
1
n
l
l
nx
1
2Cc
2Cc
Cc
m
m
k
0Cc
0Cc

• Iterative solution overall run time of O(n2)
• Multiple solutions

5
Introduction
Motivation
1
3
n
l
l
nx
2
4
2Cc
2Cc
Cc
m
k
m
2Cc
2Cc

• Iterative solution overall run time of O(n2)
• Multiple solutions

6
Introduction
Motivation
1
n
l
l
nx
2Cc
2Cc
Cc
1
m
k
0Cc
m
0Cc

• Iterative solution overall run time of O(n2)
• Multiple solutions

7
Introduction

• Issues with iterative Approaches
• Overall run time of O(n2).
• Multiple solutions
• Switch factor based delay model

• Proposed Approach
• Run time of O(n).
• No multiple solutions
• Superposition based delay model

8
Introduction

• Superposition based model
• Linear driver models Driver gate modeled with
  Thevenin resistance and Ramped voltage source

9
Introduction

• Superposition based model
• Linear driver models Driver gate modeled with
  Thevenin resistance and Ramped voltage source

10
Introduction

• Superposition based model
• Linear driver models Driver gate modeled with
  Thevenin resistance and Ramped voltage source

11
Introduction

• Delay noise is a function of timing windows at
  victim and aggressor node inputs
• Removes cyclical dependency between victim and
  aggressor net.

Switch factor based model
Superposition based model
12
Introduction

• Delay noise is a function of timing windows at
  victim and aggressor node inputs
• Removes cyclical dependency between victim and
  aggressor net.

Switch factor based model
Superposition based model
13
Outline

• Introduction
• Delay Model
• Time Sort Algorithm
• Results
• Conclusion

14
Delay Model

• Event (t, s)
• t event time time when waveform crosses
  switching voltage
• s transition time

vsw,r Vt,n
s
Vdd
vsw,f Vdd Vt,p
0.8Vdd
Early event (te, se)
vsw,r
t
Late event (tl, sl)
0.2Vdd
Timing window (te, tl)
15
Computing Noisy waveforms

• Late event Noise pulse placed at (vsw,r vn)
  point

• Early event Noise pulse placed at (vsw,r - vn)
  point

Noiseless event time tvl
Noisy event time tvne
Noiseless event time tve
Noisy event time tvnl
vn
vsw,r
vsw,r
vn
16
Delay Model Properties

• Property 1 tvi lt tv

Victim input (vi)
Victim (v)
Driver input time is earlier than output event
time
17
Delay Model Properties

• Property 2 tai lt tn

n
l
Victim
k
m
Aggressor input
Aggressor
Aggressor input time earlier than the start of
the noise pulse
18
Delay Model Properties

• Property 3 tai lt tvn

Noisy victim time later than the aggressor input
time
Aggressor input transition
Vdd
vsw,f
Victim noiseless transition
Victim noisy transition
vsw,r
tvn
tv
tai
19
Outline

• Introduction
• Delay Model
• Time Sort Algorithm
• Results
• Conclusion

20
Time Sort Algorithm

• Uses Linear Superposition and Time Sorting

n
l
t
t
t
Condition 1 Arrival time of new event being
scheduled tvn gt t Condition 2 When scheduling
new event vn, no existing event of this type has
already been processed
n
m
k
k
l
m
t
21
Victim Early Event
n
l

• Case 1 taiopt lt t

k
m
tvie t
n
l
tv
tvp
tvn
k
taie
taiopt
22
Victim Early Event
n
l

• Case 1 taiopt lt t

k
m
tvie t
n
l
tv
tvp
tvn
k
taie
tail
taiopt
23
Victim Early Event
n
l

• Case 2 taiopt gt t

k
m
tvie t
n
l
tv
tvp
tvn
k
taie
tail
taiopt
24
Victim Early Event
n
l

• Case 2 taiopt gt t

k
m
tvie t
n
l
tv
tvp
tcp
k
taie
taiopt
25
Properties

• Time progresses forward
• Time roll back may be required in two scenarios
• Roll back for a net can occur only once
• Linear run time is preserved
• Time roll back very rare
• Early and late edge of a node processed only once

26
Outline

• Introduction
• Delay Model
• Time Sort Algorithm
• Results
• Conclusion

27
Results for ISCAS85 circuits
Iterative Approach
Proposed Time Sort Algorithm
28
Conclusion

• Method to compute the switching windows in the
  presence of crosstalk
• Run time linear with circuit size
• Eliminates Multiple solution problem
• Significant Speed up