Analog and RF Circuit Macromodels for SystemLevel Analysis

1
Analog and RF Circuit Macromodels for
System-Level Analysis

• X. Li, P. Li, Y. Xu, L. Pileggi
• Carnegie Mellon University
• Pittsburgh, PA 15213, USA

2
Overview

• Introduction
• Previous work
• Proposed methodology
• Simulation results
• Conclusion

3
Overview

• Introduction
• Previous work
• Proposed methodology
• Simulation results
• Conclusion

4
Motivation

• Circuit-level simulation is not affordable for
  entire mixed-signal system
• Build macromodel to simplify internal behavior
  keep external behavior identical

System-Level Performance
Simulation
System-Level Simulation Engine
Modeling
Circuit-Level Design
5
Macromodeling
Ideal Functionality
Nonlinearity
Nonideal Functionality
Noise

• A simplified macromodel must still capture these
  2nd order effects
• We will focus on nonlinearity modeling in this
  work

6
Overview

• Introduction
• Previous work
• Proposed methodology
• Simulation results
• Conclusion

7
Volterra Series Approach

• Symbolic-based Wambacq98, Wambacq02
• Projection-based Phillips98, Roychowdhury99,
  Phillips00, Peng03
• Need high order derivative information for device
  model

Strong
Nonlinearity
Narrow
Valid Input Freq Range
Weak
Wide
Valid Input Amp Range
Narrow
Wide
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Trajectory PWL Approach

• Linearize system at various points in state space
  Rewienski01
• Applicable for strongly nonlinear system
• Accuracy depends on input training signal

Strong
Nonlinearity
Narrow
Valid Input Freq Range
Weak
Wide
Valid Input Amp Range
Narrow
Wide
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Challenge for Macromodeling
Modeling Gap
System-Level Performance
Circuit-Level Design

• Compatibility
• Compatible with commercial device model
• Without depending on high order derivative
  information
• Simplicity
• Low computation cost to speedup system-level
  simulation
• Accuracy
• Capable of capturing 2nd order effects
• Regularity
• Easily incorporated into system-level simulation
  tools

10
Overview

• Introduction
• Previous work
• Proposed methodology
• Simulation results
• Conclusion

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Special Property in RF System
LO Signal
LPF
90O Shift
LNA
RF Filter
IF Filter
Base Band Signal
LPF
RF Signal
IF Signal

• Signals in RF system have limited bandwidth
• SPW (Cadence) COSSAP (Synopsys) use complex
  low-pass representation to simulate the narrow
  band signal flow
• These commercial simulation tools require
  macromodels for specific frequency band

12
Proposed Approach ROMAN

• Unlike NORM, we focus on narrow band model for RF
  circuits
• Narrow band assumption helps us to achieve simple
  macromodel with high accuracy

Strong
ROMAN
Nonlinearity
Narrow
Valid Input Freq Range
Weak
Wide
Valid Input Amp Range
NORM
Narrow
Wide
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ROMAN Reduced-Order Macromodeling of Analog
including Nonlinearities
Start from a given nonlinear circuit
Approximate Volterra kernels by LPTV analysis at
selected freqs
Select user-defined model template
In
Out
In
Out
Out
In
Compact, reduced ordersystem-level
modelincluding parasitics
In
Out
Match Volterra kernels between model template
original circuit
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ROMAN Approximate Volterra Kernels
Nonlinear System
?0
2?
2?0
Out
In
?
??0
?2?0
Volterra Kernel Transfer Function
Relation?
LPTV System
Out
In
?
??0
?2?0
LPTV Transfer Function
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ROMAN Approximate Volterra Kernels

• Approximate 1st Volterra kernel transfer function
• LPTV analysis
• Volterra series analysis
• Therefore

Linear Response
Nonlinear Response
Extract 1st order kernel transfer function under
DC operation point
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ROMAN Approximate Volterra Kernels

• Approximate 2nd Volterra kernel transfer function
• Approximate 3rd Volterra kernel transfer function

Extract 2nd 3rd order kernel transfer functions
under time-varying operation point
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ROMAN Approximate Volterra Kernels

• Algorithm for approximating kernel transfer
  functions

CKT Netlist
Linearize CKT _at_ DC
PRIMA
DC Solver
Linearize CKT _at_ PSS
PTV
PSS Solver
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ROMAN Model Structure Mapping
What we already know?
What we dont know?
User-Defined Model Template
H1(s) H2(s, j?0) H3(s, j?0, j?0)
H1(s) H2(s1,s2) H3(s1,s2,s3)

• From mathematic point of view
• H1(s) H2(s, j?0) H3(s, j?0, j?0) not contain
  sufficient information to completely recover
  H2(s1,s2) H3(s1,s2,s3)
• From circuit point of view
• We only know circuit behaviors around center
  frequency ?0
• Need constraints on model template
• Use block diagram structure to facilitate
  system-level simulation

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ROMAN Model Structure Mapping

• By selecting multiple expansion points, ROMAN can
  map Volterra kernels to a variety of model
  structures
• Here is an example for single-point mapping

20
Overview

• Introduction
• Previous work
• Proposed methodology
• Simulation results
• Conclusion

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Low Noise Amplifier

• Match Volterra kernel transfer function at
  expansion point 900MHz reduce model order
• HB simulation speedup (Circuit / Model) 1.71 /
  0.029 (Sec.)

• Complex nonlinear behavior due to the large
  number of MOSFETs and passive components

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Low Noise Amplifier

• Two tone test for IM3 measurement
• Input frequency range 750MHz 1050MHz

High accuracy at the expansion point
Estimated IM3 by macromodel
IM3 error of macromodel
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Low Noise Amplifier

• Improve accuracy by matching Volterra kernel
  transfer functions at two expansion points
  800MHz, 1000MHz

Estimated IM3 by macromodel
IM3 error of macromodel
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Down-Conversion Mixer

• Convert strongly nonlinear system to time-varying
  forms
• Reduced PTV system to simple block diagram model
  with LPTV transfer functions
• Match Volterra kernel transfer function at 935MHz
• HB simulation speedup (Circuit / Model) 10954 /
  0.076 (Sec.)

• Strong nonlinearity due to the large LO signal
  amplitude

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Down-Conversion Mixer

• Two tone test for IM3 measurement
• Input frequency range 935MHz 960MHz

High accuracy at the expansion point
Estimated IM3 by macromodel
IM3 error of macromodel
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GSM Receiver System

• Incorporate ROMAN models into Simulink run
  system-level simulation
• Transient analysis in 0, 1?s
• Simulation time 28.44 seconds

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Overview

• Introduction
• Previous work
• Proposed methodology
• Simulation results
• Conclusion

28
Conclusion
Approximate Volterra kernel by LPTV analysis w/o
depending on high order derivatives
Simplified macromodel by order reduction
techniques
Block diagram structures are easily incorporated
into system-level simulation tools
High accuracy by exploring narrow-band property