peri: technique for extending delay/slew metrics for ramps chandramouli v. kashyap charles j. alpert...
TRANSCRIPT
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PERI: Technique For Extending Delay/Slew Metrics For Ramps
Chandramouli V. KashyapCharles J. Alpert
Frank LiuAnirudh Devgan
IBM Corp.11400 Burnet RoadAustin, TX-78758
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A Practical Problem
What are the sink delays and slews?
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scope of this work
Prior Work
step input ramp input
delay
slew
Well studied
Somewhatstudied
Inefficient/inaccurate
Inefficient/inaccurate
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Impulse Response and PDF
V(t)
t
PDF (Probability Density Function)Impulse response of circuit
median mean
median
meanFirst observed by ElmoreGeneralized by Pileggi et al.
circuit delay
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Circuit Response To Input
V(t)
t
input signal derivative of output response(impulse response)
medianmean t
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Circuit Response To Input
t
input signal derivative of output response(impulse response)
V(t)
mean tmedian
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Circuit Response To Input
V(t)
t t
input signal derivative of output response
medianmean
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Circuit Response To Input
V(t)
t t
input signal derivative of output response
medianmean
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Circuit Response To Input
V(t)
t t
input signal derivative of output response
medianmean
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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
stepelmore delaydelaydelay )()1(
delayelmore is the negative of first moment m1
delaystep is the delay for a step input, assumed known
alpha=1 delay =delaystep
alpha=0 delay =delayelmore
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Computing Alpha
2/522
12
212 )
12/2
2(
Tmm
mm
T is 0-100 ramp slew
T=0 alpha=1 delay =delaystep
T=Inf. alpha=0 delay =delayelmore
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Notes On Delay Derivation Distance between mean and
median is proportional to Pearson’s 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
step inputt
V(t)
t
V(t)
step response
timpulse response
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Observations For Slew
ramp inputt
V(t)
t
V(t)
ramp response
t
derivative of response
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Proposed Slew Formula
22stepinout slewslewslew
slewstep is the output slew for a step input: assumed known
slewin is the input slew
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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:
#sinks
1-2 3-4 5-8 9-1314-19
Total
#nets
169 122 46 54 41 432
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Results For Delay
Near-end Far-endMiddle-region
0
0.5
1
1.5
2
2.5
near middle far
AvgMaxMinDesired
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Results For Slew
Near-end Far-endMiddle-region
0
0.25
0.5
0.75
1
1.25
near middle far
AvgMaxMin
Desired
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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