This document presents a method for estimating bandwidth and delay in VLSI global interconnects considering crosstalk noise. It models crosstalk using a 2-π model for two partially coupled interconnects. It derives analytic expressions for the aggressor and victim waveforms. It then estimates bandwidth by equating the victim noise waveform to 0.5Vdd and estimates delay by solving when the victim noise is equal to the aggressor waveform. The method is shown to estimate bandwidth and delay for different resistance values and is concluded to provide accurate modeling of crosstalk-aware VLSI global interconnects.

1. CROSSTALK AWARE BANDWIDTH
MODELLING FOR VLSI RC GLOBAL
INTERCONNECTS USING 2-Π MODEL
Presented By
Santosh Kumar Chhotray
National Institute of Technology, Durgapur

2. CONTENTS
 Introduction
 Crosstalk noise
 Crosstalk noise effects
 Crosstalk noise model
 Proposed estimation method
 Result
 References
 Conclusion

3. INTRODUCTION
 DSM Technology

4. CROSSTALK NOISE
-Unwanted coupling voltages
-No. of metal layers
-Density of integration
-Reduction of spacing between lines

5. CROSSTALK NOISE EFFECTS
-Noise on non-switching wires
-Increased delay on switching
wires
-Limited bandwidth

6. CROSSTALK NOISE MODEL
Two partially coupled interconnects

7. PROPOSED ESTIMATION METHOD
 Aggressor Waveform
0
( )
dd a
aagg
dd a
t
V t
V t
V t




 
 
 
2
1
( )agg dd
a
V s V
s 

In S-domain
In Elmore delay model, the delay time between node na1 and
node na2, D1→2 is represented as
   1 2 1 1 2 3 2 2 3a a a c a a a c aD R C C C C R C C C       

8. CONT..
 Aggressor Waveform
Where
Now becomes
   1 1 2 3 2 2 3a a a a c a a a c aR C C C C R C C C       
Effective capacitance
   1 1 2 3 2 2 3a a a c a a a c aT R C C C C R C C C      
3 3dj a aT R C
   1 1 2 3 2 2 3a a a a c a eff a a c a effR C C C C R C C C       
a
3 3 1 dj
T
T
a eff aC C e

 
  
 

9. PROPOSED ESTIMATION METHOD
 Analytic Waveform of Victim Interconnect
 1 2 1 1 2
3 2
( ) ( )
1
v v v v v c
noise agg
R R C s R R C s
V s V s
as bs ds
 

  
 1 2 3 1 1 3v v v v v c va R R R C C C C 
    1 1 2 2 3 3 3 3 3 2 1 2v v v v C v v v v v v c v vb R C R C C C R C R C C C R R        
   1 1 2 3 2 2 3 3 3v v v c v v v c v v vd R C C C C R C C C R C       

10. CONT..
Now Vnoise(S) can be written as
where poles s1, s2 and s3 are roots are of . When
relationship of s1< s2<< s3 is satisfied, the most
dominant pole s3 is represented as 1/d. Replacing d by
Vnoise (S) obtained as
31 2
1 2 3
( ) ( )noise agg
KK K
V s V s
s s s s s s
 
   
   
v
 
 
1 2
( )
1
v v c
noise dd
v a
R R C
V s V
s s 




11. CONT..
After solving with partial fraction
Now taking ILT
 1 2 1
( )
1
v v v
noise c dd
a v
R R
V s C V
s s

 
  
  
 
 1 2
( ) 1 v
t
tv v
noise c dd
a
R R
V t C V e


 
  
  

12. DELAY ESTIMATION
Simplifying above equation
 1 2
0.5 1 v
t
tv v
dd c dd
a
R R
V C V e


 
  
  
50%
1 2
1
(1/ )
2
v a
c
v v
t C
R R
 


For delay estimation equating
Vnoise(S)=0.5 Vdd

13. BANDWIDTH ESTIMATION
Rearranging above equation
Now replacing S by
 
 
1 2( )
( )
( ) 1
v vnoise
c
agg v a
R RV s
H s sC
V s s 

 

 
 
1 2
( )
1
v v
c
a v
R R s
H s C
s 
 
  
 
  
 
1 2
2 2
( )
1
c v v v
a v
C R R j
H j
 

  
 


j

14. CONT..
Now to get 3db bandwidth
 
 
1 2
2 2
1
2 1
c v v
v v
C R R 
  
 
  
  
 
   
3 2 22
1 22 2
a
dB
c v v a v
f
C R R

  
 
 

15. RESULTS
Bandwidth for different value of R

16. CONT..
50% delay for different value of Rs

17. CONT..

18. CONCLUSION
For delay estimation
For bandwidth estimation
   
3 2 22
1 22 2
a
dB
c v v a v
f
C R R

  
 
 
50%
1 2
1
(1/ )
2
v a
c
v v
t C
R R
 



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20. CONT..
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21. THANK YOU