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Write a short note on Interconnect Delay Model

Subject :- VLSI Design

Topic :- Semiconductor Memories

Difficulty :- Medium

1 Answer
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  • R= driver resistance
  • C= total interconnect capacitance + loading capacitance.
  • Sink Delay: td=R*C
  • 50% delay under step input=0.7 RC.
  • Valid when driver resistance >> interconnect resistance.
  • All sinks have equal delay.

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Lumped RC Delay Model

  • Minimize delay <=> minimize wire length
    tD=RdCload=Rd(Cint+Cg)
    =Rd(C0L+Cg)

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Delay of Distributed RC Lines:

Output Potential range Time elapsed (Distributed RC Network) Time elapsed (Lumped RC Network)
0 to 90% 1.0 RC 2.3 RC
10% to 90% (rise time) 0.9 RC 2.2 RC
0 to 63% 0.5 RC 1.0 RC
0 to 50% (delay) 0.4 RC 0.7 RC
0 to 10% 0.1 RC 0.1 RC

Distributed Interconnect Models

• Distributed RC circuit model – L,T or π circuits
• Distributed RCL circuit model
• Tree of transmission lines

Why Elmore Delay ?

1) Elmore delay is easier to compute analytically in most cases:

  • Elmore's insight [Elmore, J. App. Phy 1948]
  • Verified later on by many other researchers, e.g.
    Elmore delay for RC trees []Penfield- Rubinstein, DAC'18]
    Elmore delay for RC networks with ramp input[Chan, T-CAS'86]

2) for RC trees: [krauter- Tatuianu-Willis-Pileggi, DAC'95]

3) Note: Elmore delah is not 50% value delay in general !

Elmore Delay for RC Trees

  • Defination : h(t)=impuseresponse
    TD=meanofh(t)
    =0h(t)tdt
  • Interpretation
    H(t)=output response (step process)
    h(t)= rate of change of H(t)
    T50 =median of h(t)
    Elmore delay approximates the median of h(t) by the mean of h(t)

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Elmore Delay Model

Advantages

  • Simple closed-form expression
  • Useful for interconnect optimization
  • Upper bound of 50% delay [Gupta et al., DAC’95, TCAD’97]
  • Actual delay asymptotically approaches Elmore delay as input signal rise time increases
  • High fidelity [Boese et al., ICCD’93],[Cong-He, TODAES’96]
  • Good solutions under Elmore delay are good solutions under actual (SPICE) delay

Disadvantages

  • Low accuracy, especially poor for slope computation
  • Inherently cannot handle inductance effect
  • Elmore delay is first moment of impulse response
  • Need higher order moments
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