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Effects of Inductance on the Propagation Delay and Repeater Insertion in VLSI Circuits

Effects of Inductance on the Propagation Delay and Repeater Insertion in VLSI Circuits. Yehea I. Ismail and Eby G. Friedman , Fellow, IEEE. Agenda. Introduction Propagation Delay Formula Comparison to an RC Model Dependence of Delay on wire Length Repeater Insertion for an RLC Interconnect

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Effects of Inductance on the Propagation Delay and Repeater Insertion in VLSI Circuits

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  1. Effects of Inductance on the Propagation Delayand Repeater Insertion in VLSI Circuits Yehea I. Ismail and Eby G. Friedman, Fellow, IEEE

  2. Agenda • Introduction • Propagation Delay Formula • Comparison to an RC Model • Dependence of Delay on wire Length • Repeater Insertion for an RLC Interconnect • Conclusions

  3. Introduction

  4. Propagation Delay Formula

  5. Close Form

  6. Interconnect Model-RCL

  7. A gate driving an RLC transmission line

  8. The transfer function- a lossy transmission line Zs is source impedance, ZL is load impedance γ is propagation constant, Z0 is characteristic impedance

  9. Laplace transform-1

  10. Laplace transform-2

  11. The parameter ζ Three parameter:ζ,RT,CT

  12. Laplace transform-3 The scaled 50% propagation delay t`pd can be calculated by solving Thus, the propagation delay of an RCL line with a source Resistance Rtr and a load capacitance CL has the form

  13. AS/X [20] simulations the maximum error is 4.6% and the average error is 1.65%

  14. AS/X [20] simulations Eq.(18):

  15. Delay function is more accurate When CT And RT are high and ζ is low Eq(18) suffers high errors This case can only occur for unreasonably high values of the inductance per unit length of the line as compared to the resistance and capacitance per unit length Such a case does not exist in a practical VLSI circuit.

  16. ζ characterize inductance effects

  17. ζ characterize inductance effects

  18. ζ characterize inductance effects

  19. ζ characterize inductance effects

  20. The Factor of Inductance

  21. Comparison to an RC model

  22. Comparison to an RC model

  23. copper interconnect line

  24. copper interconnect line

  25. copper interconnect line

  26. Dependence of Delay on Interconnect Length αasym is the asymptotic value at high frequencies of the attenuation per unit length of the signals L  0 tpd =0.37RCl2 R  0 tpd = l(LC)0.5

  27. Repeater Insertion for an RLC Interconnect The buffer output impedance Rtr is R0/h The input capacitance of the buffer CL is hC0

  28. Curve Fitting Method

  29. highly accurate The error is less than 0.05% If Lt 0 hopt(RLC) = hopt(RC) kopt(RLC) = kopt(RC)

  30. Comparison with RC model

  31. Total delay in RC & RLC When TL/R=3 ,tpdtotal increase by 10% When TL/R=5 ,tpdtotal increase by 20% When TL/R=10 ,tpdtotal increase by 30%

  32. Repeater Insertion in RC & RLC

  33. Area in RC & RLC Amin is the area of a minimum size buffer = When TL/R=3 ,Area increase by 154% When TL/R=5 ,Area increase by 435%

  34. conclusion • Propagation delay --- 35% • propagation delay has linear dependence on the length of the line.

  35. Conclusion for repeater insertion • Insert less buffer • Reduce delay • Reduce buffer area

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