PERI: Technique For Extending DelaySlew Metrics For Ramps

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PERI Technique For Extending Delay/Slew Metrics
For Ramps

• Chandramouli V. KashyapCharles J. AlpertFrank
  LiuAnirudh Devgan

IBM Corp. 11400 Burnet Road Austin, TX-78758
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A Practical Problem
What are the sink delays and slews?
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Prior Work
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Impulse Response and PDF
V(t)
First observed by Elmore
Generalized by Pileggi et al.
t
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Circuit Response To Input
V(t)
t
t
mean
median
derivative of output response (impulse response)
input signal
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Circuit Response To Input
V(t)
t
t
mean
median
derivative of output response (impulse response)
input signal
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Circuit Response To Input
V(t)
t
t
mean
median
derivative of output response
input signal
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Circuit Response To Input
V(t)
t
t
median
mean
derivative of output response
input signal
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Circuit Response To Input
V(t)
t
t
median
mean
derivative of output response
input signal
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Known Facts

• Time domain signal like a CDF
• Its time derivative is the PDF
• Output response is given by convolution
• Probability moments add in convolution

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Proposed Delay Formula
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Computing Alpha
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Notes On Delay Derivation

• Distance between mean and median is proportional
  to Pearsons coefficient
• Easily computed from circuit moments
• The constant of proportionality is independent of
  input slew
• This is a simplifying assumption we make

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Observations For Slew
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Observations For Slew
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Proposed Slew Formula
slewin is the input slew
slewstep is the output slew for a step input
assumed known
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Notes On Slew Derivation

• Slew is proportional to standard deviation of
  signal PDF
• Observed by Elmore, Pileggi
• Std.-Dev. Easily computed from moments
• Constants of proportionality are identical for
  ramp, impulse and output
• This is a simplifying assumption we make

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Experimental Setup

• 432 routed nets in 0.18um technology
• 4th order RICE used as golden
• Step delay/slew computed using RICE
• Measured delay(formula)/delay(rice)
• Likewise, slew(formula)/slew(rice)
• Distribution of sinks

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Results For Delay
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Results For Slew
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Summary

• Provides a practical and useful method for fast
  delay and slew computation
• Renders prior research on step delay and slew
  metrics usable in a tool flow
• Useful for physical design and optimization