A NoiseDriven Effective Capacitance Method with Fast Embedded Noise Rule Calculation for Functional

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A Noise-Driven Effective Capacitance Method with
Fast Embedded Noise Rule Calculation for
Functional Noise Analysis
Haihua Su David Widiger Chandramouli
Kashyap Frank Liu Byron Krauter IBM
Corp. Austin, Texas 78758
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Motivation

• To predict noise propagated through gates
  oncombinational paths before reaching latches
• To eliminate driver pre-characterization for
  glitchpropagation and dependency on
• Input waveform shape
• Output load capacitance
• To separate the linear/nonlinear
  analysis,similar to the idea in timing
• To linearize the victim driver so the worst-case
  noisepeak can be quickly found by superposition
• To work efficiently for both RC and RLC
  interconnect loads

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Outline

• Motivation
• Prior art
• Basic idea
• Victim driver dependent current source model
• Linearize victim driver using Ceff
• Noise-driven Ceff flow with embedded noise rule
  evaluation
• Victim driver linear Thevenin model
• Convergence scenarios
• Experimental results
• Conclusion and future work

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Prior Art
CM


Vi
Vo
Vo
Vi
Cg
-
-
Io(Vi, Vo)

• Circuit includes a single voltage controlled
  current source model driving a reduced order
  interconnect model
• Works well when gate internal parasitic
  capacitance is much smaller than the gate
  external parasitic capacitance including the
  interconnect loading
• Simple nonlinear solver (e.g. secant iteration)
  with numerical integration is employed
• Worst-case aggressor/victim alignment becomes
  complicated
• References
• Vladimir Zolotov, David Blaauw, Rajendran Panda
  and Chanhee Oh from Motorola, Noise Injection
  and Propagation in High Performance Designs,
  ISQED 2002
• John Croix from Silicon Metrics and D. F. Wong
  from UIUC, Blade and Razor Cell and
  Interconnect Delay Analysis Using Current-Based
  Models, DAC 2003
• Igor Keller, Ken Tseng and Nishath Verghese from
  Cadence, A Robust Cell-Level Crosstalk Delay
  Change Analysis, TAU 2004

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Outline

• Motivation
• Prior art
• Basic idea
• Victim driver dependent current source model
• Linearize victim driver using Ceff
• Noise-driven Ceff flow with embedded noise rule
  evaluation
• Victim driver linear Thevenin model
• Convergence scenarios
• Experimental results
• Conclusion and future work

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Basic Idea

• Re-use the idea in timing Ceff
• A linear Thevenin model of the victim driver is
  derived through an iterative Ceff procedure
• Load dependent noise rules come from fast
  numerical simulation of the dependent source
  model driving a capacitor
• Compute propagation noise and crosstalk noise at
  sinks using the obtained linearThevenin model

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Outline

• Motivation
• Prior art
• Basic idea
• Victim driver dependent current source model
• Linearize victim driver using Ceff
• Noise-driven Ceff flow with embedded noise rule
  evaluation
• Victim driver linear Thevenin model
• Convergence scenarios
• Experimental results
• Conclusion and future work

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Overall Noise-driven Ceff Flow
PAo
Ao
PWi
Ao
PAo
To
Iactual
Rd
Rd
Iout
?to
PAi
PWo
Ceff
CL

• Given an input noise and start Ceff from total
  interconnect capacitance
• Choose driver resistance (we fix its value for
  simplicity)
• Find output noise characteristics from the
  numerical simulation waveform
• Calculate parameters of a triangular voltage
  source to match the output noise characteristics
  for simple RC circuit in the middle
• Update Ceff to match the average current flowing
  into the actual interconnect load (pi-model or
  higher reduced order model)

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Victim Driver Thevenin Model Parameters

• Driver resistance Rd
• Triangular voltage source with intrinsic delay
  t0, rise time tr, fall time tf and peak Pk
• For simplicity, set t0 To

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Victim Driver Voltage Source Parameters
Calculation

• Three Equations with regard to tr, tf and Pk
• Vo(?to) PAo (to match output noise peak)
• Vo(?to) 0 (to match output noise time to peak)
• Ao ? ?t8 Vo(t) dt (to match post peak noise
  area)
• Result in
• Set Tc 2Ao/PAo ?to-2RdCeff
• Solve f(tr) (1-e ?to/RdCeff) tr Tc (e
  tr/RdCeff 1) 0 for tr (Newton Raphson)
• tf Tc tr
• Pk PAo tf / (Tc - ?to)

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Victim Driver Resistance Calculation

• From sensitivity information in the noise rule
• Tc (2Ao/PAo) ?to-2RdCeff tr tf
• Differentiate to Ceff to get
• Rd 0.5 x (2Ao/PAo?to)/ ?Ceff 0.5 ?PWo/ ?Ceff
  
• Valid and useful when output noise is
  non-negligible
• From the dependent current source model of the
  driver(single-CCC or last-stage CCC)
• Heuristically choose Rd according to the
  input/output noise height
• Expect to have higher Rd than the quiet holding
  resistance
• Useful when output noise is negligible
• Fix Rd throughout the Ceff iterative procedure to
  simplifythe computation
• Same Rd can be used for crosstalk noise analysis

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Three Scenarios of Driver Model Parameters and
Ceff Convergence

• Case 1
• General triangular Thevenin voltage source trgt0,
  tfgt0, Pkgt0
• Nonzero Ceff, 0ltCeffltCtotal
• Case 2
• Very sharp rising transition tr0
• Solve tfgt0 and Pkgt0 to match output noise peak
  and total noise area (another Newton Raphson)
• Nonzero Ceff, 0ltCeffltCtotal
• Case 3
• Effective capacitance Ceff converges to zero
  Ceff0
• Current flowing through the victim driver is
  close to zero
• Set Pk0

Note Considering the switching aggressor driver
induced currents to the victim driver, Ceff can
converge to some negative value
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Outline

• Motivation
• Prior art
• Basic idea
• Victim driver dependent current source model
• Linearize victim driver using Ceff
• Noise-driven Ceff flow with embedded noise rule
  evaluation
• Victim driver linear Thevenin model
• Convergence scenarios
• Experimental results
• Conclusion and future work

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Experiments

• Drivers are under 130nm technology, Vdd1.2
• Different sized inverters drive RC/RLC lines with
  different lengths
• One aggressor and one victim
• Use Linear aggressor driver with the fastest
  transition for the technology
• Superposition is used for the combined
  propagation and crosstalk noise
• Compare with PowerSPICE nonlinearly aligned
  results (true worst-case)

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Sensitivity-based Driver Resistance vs. Input
Noise Pulse

• 130nm inverter driving CL1pF

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Inverter Driving RC Line (1mm) Propagation Noise
Only
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Inverter Driving RC Line (1mm) Propagation
Crosstalk Noise
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Inverter Driving RLC Line (5mm) Propagation Noise
Only
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Inverter Driving RLC Line (5mm) Propagation
Crosstalk Noise
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Effective Capacitance And Its Convergence
Inverters driving 1mm RC lines and 5mm RLC lines
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Conclusion and Future Work

• Presented a noise-driven effective capacitance
  method to linearize the victim driver
• Both the propagation and combined noise results
  match closely to PowerSPICE results
• Can handle both RC and RLC interconnects
  efficiently
• The same idea can be applied in timing analysis
• Noise/timing waveforms with respect to a pi-model
  can be obtained through fast numerical simulation
  can be used to better predict the driving point
  waveform

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• Thank you!