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EE 201A Noise Modeling. Jeff Wong and Dan Vasquez Electrical Engineering Department University of California, Los Angeles. Efficient Coupled Noise Estimation for On-Chip Interconnects. Anirudh Devgan Austin Research Laboratory IBM Research Division, Austin TX. Motivation.

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ee 201a noise modeling
EE 201ANoise Modeling
  • Jeff Wong and Dan Vasquez
  • Electrical Engineering Department
  • University of California, Los Angeles
efficient coupled noise estimation for on chip interconnects

Efficient Coupled Noise Estimation for On-Chip Interconnects

Anirudh Devgan

Austin Research Laboratory

IBM Research Division, Austin TX

  • Noise failure can be more severe than timing failure
    • Difficult to control from chip terminals
    • Expensive to correct (refabrication)
  • Circuit or timing simulation (like SPICE) can be used
    • Linear reduction techniques can be applied for linearly modeled circuits
      • i.e. moment matching methods
    • Inefficient for noise verification and avoidance applications
noise estimation
Noise Estimation
  • The paper presents an electrical metric for efficiently estimating coupled noise for on-chip interconnects
  • Capacitive coupling between an aggressor net and a victim net leads to coupled noise
    • Aggressor net: switches states; source of noise for victim net
    • Victim net: maintains present state; affected by coupled noise from aggressor net
circuit schematic
Circuit Schematic

Coupling capacitors

CC = [CC,ii]



C2 = [C2,ii]



Switching signal


C1 = [C1,ii]

  • Let’s analyze the case for one aggressor net and one victim net
circuit equations
Circuit Equations
  • Coupled equation for circuit:
  • In Laplace domain:
circuit equations1
Circuit Equations
  • Aggressor net:
  • Victim net:
transfer function
Transfer Function
  • Transfer function:
  • Simplifications (details later):
  • Simplified transfer function:
  • A12 = 0
    • No resistive (or DC) path exists from the aggressor net to the victim net
  • A21 = 0
    • No resistive (or DC) path exists from the victim net to the aggressor net
  • B2 = 0
    • No resistive (or DC) path exists from the voltage/noise source to the victim net
maximum induced noise
Maximum Induced Noise
  • H(s=0) = 0
    • Coupling between aggressor and victim net is purely capacitive
    • Maximum induced noise can be computed
  • Assume Vs is a finite or infinite ramp
maximum induced noise1
Maximum Induced Noise
  • Final value theorem:
  • Ramp input u(s):
circuit interpretation
Circuit Interpretation

Switching slope

circuit computations matrix method
Circuit Computations(matrix method)
  • Step 1: Compute
    • Requires circuit analysis of the aggressor net
  • Step 2: Compute
    • Requires a matrix multiplication
  • Step 3: Compute
    • Requires circuit analysis of the victim net
circuit computations by inspection
Circuit Computations(by inspection)
  • Step 1: Compute
    • Aggressor circuit transformation:
      • Replace input source with it’s derivative
      • Replace aggressor net’s capacitors with open circuits
circuit computations by inspection1
Circuit Computations (by inspection)
  • Step 1: Compute
    • Typical interconnects:
      • Negligible loss: no resistive path to ground
circuit computations by inspection2
Circuit Computations (by inspection)
  • Step 2: Compute
    • Convert steady state derivative on the aggressor net to a current on the victim net
    • i: index of node on the victim net
    • j: index of node on the aggressor net
circuit computations by inspection3
Circuit Computations (by inspection)
  • Step 3: Compute
    • Victim circuit transformation:
      • Replace capacitors with coupling currents
      • The voltage at each node corresponds to that node’s maximum induced noise
circuit computations by inspection4
Circuit Computations (by inspection)
  • Step 3: Compute
    • Typical interconnects:
      • Compute by inspection in linear time
circuit computations by inspection5
Circuit Computations (by inspection)
  • Step 3: Compute
    • 3RC Circuit example:
computation costs
Computation Costs
  • Step 1:
    • No computation required
  • Step 2:
    • Simple multiplications
  • Step 3:
    • Simple multiplications
  • Multiple aggressor nets:
    • Coupling currents from step 2 determined from a linear superposition
  • Typical small RC interconnect structure
    • Rise time of 200 ps or 100 ps
    • Power supply voltage of 1.8 V
    • Conventional circuit simulation vs. proposed metric
    • Run-time comparisons for various circuit sizes
accuracy results
Accuracy Results
  • 10 nodes, 200 ps rise time
accuracy results1
Accuracy Results
  • 10 nodes, 100 ps rise time
accuracy results2
Accuracy Results
  • Metric accuracy degrades with reduction in rise times
  • Metric estimation is more conservative than circuit model’s
    • Fast rise times don’t allow circuit to reach ramp steady state noise
  • Loading of interconnect normally does not allow for very small rise times
    • Metric accuracy should be acceptable for many applications
run time results
Run-time Results
  • Arnoldi-based model reduction used a matrix solution to compute circuit response
    • Requires repeated factorizations, eigenvalue calculations, and time exponential evaluations
  • The proposed metric determines an upper bound on coupled noise for RC and over-damped RLC interconnects
    • Metric becomes less accurate as rise time decreases
  • The proposed metric is much more run-time efficient than circuit modeling methods
improved crosstalk modeling for noise constrained interconnect optimization

Improved Crosstalk Modeling for Noise Constrained Interconnect Optimization

Jason Cong, David Zhigang Pan & Prasanna V. Srinivas

Department of Computer Science, UCLA

Magma Design Automation, Inc.

2 Results Way, Cupertino, CA 95014

  • Deep sub-micron net designs have higher aspect ratio (h/w)
    • Increased coupling capacitance between nets
      • Longer propagation delay
      • Increased logic errors --- Noise
  • Reduced noise margins
    • Lower supply voltages
    • Dynamic Logic
  • Crosstalk cannot be ignored
aggressor victim network
Aggressor / Victim Network



  • Assuming idle victim net
    • Ls: Interconnect length before coupling
    • Lc: Interconnect length of coupling
    • Le: Interconnect length after coupling
  • Aggressor has clock slew tr
2 model
2- Model

Rise time

victim / aggressor

coupling capacitance

  • Victim net is modeled as 2 -RC circuits
  • Rd: Victim drive resistance
  • Cx is assumed to be in middle of Lc
2 model parameters
2- Model Parameters



analytical solution part 2
Analytical Solution part 2
  • s-domain output voltage
  • Transform function H(s)
analytical solution part 3
Analytical Solution part 3
  • Aggressor input signal
  • Output voltage
simplification of closed form solution
Simplification of Closed Form Solution
  • Closed form solution complicated
  • Non-intuitive
    • Noise peak amplitude, noise width?
  • Dominant-pole simplification
dominant pole simplification
Dominant-Pole Simplification

RC delay from upstream resistance of coupling element

Elmore delay of victim net

intuition of dominant pole simplification
Intuition of Dominant Pole Simplification
  • vout rises until tr and decays after
  • vmax evaluated at tr
extension to rc trees
Extension to RC Trees
  • Similar to previous model with addition of lumped capacitances
  • Average errors of 4%
  • 95% of nets have errors less than 10%
spice comparison
Spice Comparison

peak noise noise width

effect of aggressor location
Effect of Aggressor Location
  • As aggressor is moved close to receiver, peak noise is increased

Ls varies from 0 to 1mm

Lc has length of 1mm

Le varies from 1mm to 0

optimization rules
Optimization Rules
  • Rule 1:
    • If RsC1 < ReCL
      • Sizing up victim driver will reduce peak noise
    • If RsC1 > ReCL and tr << tv
      • Driver sizing will not reduce peak noise
  • Rule 2:
    • Noise-sensitive victims should avoid near-receiver coupling
optimization rules part 2
Optimization Rules part 2
  • Rule 3:
    • Preferred position for shield insertion is near a noise sensitive receiver
  • Rule 4:
    • Wire spacing is an effective way to reduce noise
  • Rule 5:
    • Noise amplitude-width product has lower bound
    • And upper bound
  • 2- model achieves results within 6% error of HSPICE simulation
  • Dominant node simplification gives intuition to important parameters
  • Design rules established to reduce noise
  • Anirudh Devgan, “Efficient Coupled Noise Estimation for On-chip Interconnects”, ICCAD, 1997.
  • J. Cong, Z. Pan and P. V. Srinivas, “Improved Crosstalk Modeling for Noise Constrained Interconnect Optimization”, Proc. Asia South Pacific Design Automation Conference (ASPDAC), Jan. 30 - Feb. 2, 2001, Pacifico Yokohama, Japan.