R ICE A UTOMATED N ANOSCALE D ESIGN G ROUP Automated Design of Tunable Impedance Matching Networks...

RRICEICE AAUTOMATED UTOMATED

NNANOSCALEANOSCALE D DESIGN ESIGN

GGROUPROUP

Automated Design of Tunable Impedance Matching Networks for

Reconfigurable Wireless Applications

Arthur Nieuwoudt,1 Jamil Kawa,2 and Yehia Massoud1

1 Rice Automated Nanoscale Design Group, Rice University2 Advanced Technology Group, Synopsys, Inc.

6/11/2008

Wireless Applications

Wireless applications have become pervasive 1-4 Cellular telephones (GSM/CDMA)Bluetooth Wireless local area networks

New wireless applications will become mainstream Consumer and vehicular electronics

leveraging ultrawideband systems 5-7

Millimeter wave systems 8

Need to develop multi-standard wireless systems

1 P. Wambacq, G. Vandersteen, W. Eberle, J. Phillips, J. Roychowdhury, D. Long, A. Demir, and B. Yang, DATE, 2001.2 A. Nieuwoudt and Y. Massoud, DAC, 2005.3 A. Nieuwoudt and Y. Massoud, ICCAD, 2005.

4 A. Nieuwoudt, T. Ragheb, and Y. Massoud, DAC, 2006.5 G. Aiello and G. Rogerson, IEEE Micro. Mag., 2003.6 A. Ismail and A. Abidi, IEEE JSSC, 2004.7 A. Nieuwoudt, T. Ragheb, and Y. Massoud, ASP-DAC, 2007.8 B. Razavi, IEEE JSSC, 2006.

Traditional Multi-Standard Wireless Systems

Redundant circuit blocks traditionally needed

Limited by hardware complexity and power consumption

Traditional Multi-StandardRF Front-End

BPF LNA Mixer

Antenna Standard 1 at Frequency 1

BPF LNA Mixer

Reconfigurable Multi-Standard Wireless Systems

Multi-standard RF systems can be implemented with a single front end 1-3

Reduced hardware complexity and power consumption Facilitates the evolution toward system-on-chip designs

Filters and impedance matching networks (IMN) are critical circuits in wireless systems

Reconfigurable Multi-Standard RF Front-End

BPF LNA Mixer

Antenna

Standards 1, 2 and 3 at Frequencies 1, 2 and 3

1 J.-F. Luy, T. Mueller, T. Mack, and A. Terzis, IEEE Micro. Mag., 2004.2 R. Mukhopadhyay, Y. Park, P. Sen, N. Srirattana, J. Lee, C.-H. Lee, S. Nuttinck, A. Joseph, J. D. Cressler, and J. Laskar, IEEE Trans. MTT, 2005.3 J.-H. Kim, Y.-K. Jang, and H.-J. Yoo, Analog Int. Cir. Sig. Proc., 2007.

Impedance Matching Networksand Filters

Filters and IMNs are critical in common RF circuitsLow noise amplifiers Power amplifiersMixersPre-processing filters and

antenna impedance matching

Important implications for critical performance metricsNoisePower consumptionGain Implementation technologyCost

BPF LNA Mixer

Antenna

Filters and IMNs

Impedance Matching Networksand Filters

BPF LNA Mixer

Antenna

Filters and IMNs Previous research has

demonstrated the potential of reconfigurable IMNs 1-5

Implemented using semiconductor, barium-strontium-titanate (BST), and RF MEMS based technologies

Traditionally realized using a manual design process that combines standard filter synthesis with the designer’s knowledge

Limited previous research on automated design techniques for reconfigurable IMNs

Need to create systematic automated design methods for reconfigurable filters and IMNs

1 C. T.-C. Nguyen, DAC, 2005.2 A. R. Brown and G. M. Rebeiz, IEEE Trans. MTT, 2000.3 K. Entesari and G. M. Rebeiz, IEEE Trans. MTT, 2005.

4 G. K. Fedder and T. Mukherjee, ISSCC, 2005.5 J. Nath, D. Ghosh, J.-P. Maria, A. I. Kingon, W. Fathelbab, P. D. Franzon, and M. B. Steer, IEEE Trans. MTT, 2005.

Overview

Reconfigurable impedance matching networksDesign considerationsModeling

Automated design of reconfigurable impedance matching networksFrequency mapping to reconfigurable circuit elementsDesign optimization problem formulationAutomated design methodologyVariability-aware optimization

Results Conclusions

Reconfigurable Impedance Matching Networks

Important design considerations Impedance matching in passband

and stopband (|S11| and |S22|)

Frequency

Passband

Stopband

(Reflection)

2-PortFilter

(Reflection)

Insertion loss (|S21|)

Power handling capabilities of the circuit components

Frequency

Passband

Stopband

2-PortFilter

(Transmission)

Must meet design constraints for each frequency band and load/source impedance

Frequency

nse f1 f2 f3 f4 f5 f6

Reconfigurable IMN Frequency States:

Must meet design constraints for each frequency band and load/source impedance

Implemented with tunable and switchable circuit elementsSwitchable – discrete valuesTunable – continuous values

Frequency

Reconfigurable IMN Circuit:

Canonical Circuit Representations for Reconfigurable IMNs

Microwave filters/IMNs designed using canonical circuit topologies Filter can then be physically synthesized based on canonical circuit

Directly implemented using lumped passive components Microstrip implementation realized by converting lumped elements into

equivalent transmission line representations

To provide a technology-independent solution, we focus on the design of the fixed/variable components in canonical topology

Butterworth/Chebyshev Canonical Bandpass Filter Topology

Modeling of Reconfigurable IMNs

Use 2-port ABCD parameters to model shunt and series cascaded filter stages

Convert filter's ABCD parameters to S-parameters for circuit optimization

Parasitic resistances calculated based on component quality factors

Worst-case power determined using voltage and current from ABCD formulation

2-PortFilter

(Reflection)

2-PortFilter

(Reflection)

(Transmission)

Overview

Results Conclusions

Reconfigurable IMN Design Optimization Problem Formulation

General reconfigurable IMN design optimization problem:

|| S21IT ||2

S11IT S11IC, S11OT S11OC

SPT SPC, xmin x xmax

Minimize:

Subject to:

Minimize || S21 ||2 over all bands|| S21IT ||2

Minimize:

Subject to:

S21(ti,fi,ZSi,ZLi) is a vector containing |S21| values in the ith band

Minimize:

Subject to:

Frequency

f1 f2 fi fM…

… …

Minimize:

Subject to:

Frequency

f1 f2 fi fM…

… …

Frequency

Minimize:

Subject to:

Frequency

f1 f2 fi fM…

… …

Frequency

S21(ti,fi,ZSi,ZLi)

values ()

Minimize:

Subject to:

Vector ti contains circuit values mapped to the frequency band fi

ZSi and ZLi are the source and load impedances mapped to fi

Minimize:

Subject to:

Frequency

f1 f2 fi fM…

… …

Minimize:

Subject to:

C3 L3 Frequency Band fi:

ti = [C1, L1, C2(i), L2, C3, L3]

Source Impedance = ZSiLoad Impedance = ZLi

Minimize || S21 ||2 over all bands

Passband constraints on |S11|:

S11(ti,fi,ZS1,ZL1) is

the |S11| constraint function (S11IT)

S11max is the passband

constraint on |S11| (S11IC)

Passband and stopband constraints on |S11|, |S21|,

and |S22|

|| S21IT ||2

Minimize:

Subject to:

Other constraints defined in a similar manner to S11IT S11IC

S11OT S11OC – |S11| stopband constraints

S22IT S22IC & S22OT S22OC – |S22| passband and stopband constraints

S21IT S21IC & S21OT S21OC – |S21| passband and stopband constraints

SPT SPC – Power handling constraints for circuit elements

Typical design problem can require 100s of nonlinear constraints

and |S22|

|| S21IT ||2

S21IT S11IC, S21OT S21OC SPT

xmin x xmax

Minimize:

Subject to:

Circuit element power constraints

and |S22|

|| S21IT ||2

S21IT S11IC, S21OT S21OC SPT

xmin x xmax

Minimize:

Subject to:

Circuit element power constraints

Design variables:

Fixed components – Li or Ci only contain 1 value

Switchable elements – Li or Ci contain elements corresponding to the discrete IMN states

Tunable elements – Li or Ci contain elements distributed over the continuous range of IMN states

Bound constraints on circuit component values

Design Space Analysis

Need to determine if efficient gradient-based optimization techniques can be employed to solve IMN design problem

Consider a black box system with general input and source (Zs)

impedances

We examine |S11| in dB used in optimization formulation:

General conclusion – |S11| has one minimum value with respect to

Rin and Xin when Rs 0 and either Xs 0 or Xs 0

Box System

Impedance Values:

Design Space Analysis

|S22| and |S21| have similar behavior to |S11|

One set of extrema with respect to Rin and Xin

Minimum/maximum values for |S11|, |S21|, and |S22| typically occur

near to each other in the design space

Narrow-band filter designs will typically have circuit elements that resonate near the narrow-band frequencyS-parameters well-behaved with respect to circuit element values

(one significant local minimum value)Analytical solutions provide good start point for design process

This does not necessarily hold for reconfigurable filters Simulated third-order narrow-band (2.4 GHz) and 2-band

switchable (2.4 and 5.0 GHz) filters to demonstrate these design space characteristics

0.3 1 3 10-50

Fixed Filter at 2.4 GHz

Normalized Circuit Element Multiplication Factor

Design Space Characteristics:Narrow-Band Fixed Valued IMN

Simulated |S11| along an

arbitrary vector of circuit element values

Narrow-Band Filter

|S11| Values

0.3 1 3 10-50

Design Space Characteristics:Narrow-Band Fixed Valued IMN

Minimum |S11| Value

Narrow-band filter has one minimum |S11| value

Simulated |S11| along an

arbitrary vector of circuit element values

Narrow-Band Filter

|S11| Values

Design Space Characteristics:2-Band Reconfigurable IMN

0.3 1 3 0.3 1 3 10-50

Tunable Filter at 2.4 GHz

2-Band Reconfigurable

Filter |S11| Values

Design Space Characteristics:2-Band Reconfigurable IMN

0.3 1 3 0.3 1 3 10-50

Region 2Region 1

Cannot utilize standard convex optimization techniques alone to find optimal solution

Local Minima

LocalMinima

2-Band Reconfigurable IMN Optimization Algorithm Start Point

0.3 1 3 0.3 1 3 10-50

Fixed filter solution can be utilized as a start point for optimizing the reconfigurable filter

Fixed filter solution as start point

Region 2Region 1

Avoids local minima in gradient-based optimization

Local Minima

Constraint Relaxation for Reconfigurable IMN Optimization

Solution to a less complex related IMN optimization problem can provide a suitable start point for the complete problem

Formulate this less complex IMN optimization problem by relaxing the IMN design constraints

Constraint relaxation for the reconfigurable IMN design problem can be achieved in several different waysRemove frequency bands and reconfigurable circuit elements

from considerationRelax the design requirements associated with the filter

Constraint relaxation forms the basis for the proposed design automation methodology

Automated Design Methodology for Reconfigurable IMNs

High-level strategy for the automated design methodLeverage constraint relaxation

and sequential quadratic programming to solve optimization problem

Iteratively add constraints until the full problem is solved

Constraints added in order of complexity (most difficult to least difficult)

Use solution to previous optimization problem as the start point for next iteration

Automated Design Methodology:Input: Define design requirements and

circuit parameters

Step 1: Optimize fixed-valued IMN in 1 frequency band

Step 2: Successively add reconfigurable band constraints

Step 3: Successively tighten stopband rejection constraints

Step 4: Successively widen passband constraints

Step 5: Successively tighten quality factors

Step 6: Add component power constraints

Output: Reconfigurable IMN circuit design

Initially solve a narrow-band fixed-valued IMN design optimization problem

Only consider constraints on S-parameters at the center of the passband

Automated Design Methodology:Solve for Initial Fixed-Valued IMN

Current IMN Configuration:

Frequency

nse f1

circuit parameters

Iteratively solve a series of narrow-band IMN optimization problemsAdd additional frequency bands and reconfigurable

circuit elementsOnly consider constraints on S-parameters at the center

of each passbandDesign variables added in each optimization problem

Automated Design Methodology:Add Reconfigurable Band Constraints

Frequency

circuit parameters

Frequency Mapping to Reconfigurable Circuit Elements

How do we map each set of frequencies and load/source impedances to the reconfigurable circuit elements?

Want an efficient mapping to reduce hardware complexity Frequency

21|) f1 f2 f3 f4 f5 f6

Combinatorial Frequency Mapping

Combinatorial mappingEach possible combination of

variable circuit element values is mapped to a reconfigurable frequency state

Frequency

21|) f1 f2 f3 f4 f5 f6

C2 has 3 possible values:

[C2(1), C2(2), C2(3)]

[C1(1), C1(2)]

Frequency

21|) f1 f2 f3 f4 f5 f6

Reconfigurable IMN Circuit:C1 has 2 possible values:

[C1(1), C1(2)]C2 has 3 possible values:

[C2(1), C2(2), C2(3)]

Frequency

21|) f1 f2 f3 f4 f5 f6

[C2(1), C2(2), C2(3)]

Frequency

21|) f1 f2 f3 f4 f5 f6

[C2(1), C2(2), C2(3)]

Combinatorial mapping schemeEach possible combination of

Efficiently utilizes available reconfigurable states

Does not balance impact of |S11|, |

S21|, and |S22|

Frequency

21|) f1 f2 f3 f4 f5 f6

Symmetric Combinatorial Frequency Mapping

Symmetric combinatorial mappingEach possible combination of

symmetric pairs of variable circuit element values is mapped to a reconfigurable frequency state

Symmetry balances variable circuit element impact on |S11|, |S22|, and |S21|

Still efficiently utilizes available reconfigurable circuit element states

Frequency

21|) f1 f2 f3 f4 f5 f6

[C2(1), C2(2), C2(3)]C3 has 2 possible values:

[C3(1), C3(2)]

Frequency

nse f1 f3

C2(1) C2(2)

f1 f3C2 has 2 possible values:

[C2(1), C2(2)]

C1 and C3 have 1 value each

Reconfigurable Circuit Element Mapping:

circuit parameters

Frequency

nse f1 f3 f5

C2(1) C2(2) C2(3)

f1 f3 f5

[C2(1), C2(2), C2(3)]

C1 and C3 have 1 value each

Input: Define design requirements and circuit parameters

Automated Design Methodology:

Frequency

C2(1) C2(2) C2(3)

f1 f2 f3 f4 f5 f6

[C2(1), C2(2), C2(3)]

[C1(1), C1(2)]

[C3(1), C3(2)]

circuit parameters

Add the stopband rejection constraints associated with each frequency bandStart with relaxed stopband constraints in the frequency

domain for S-parameters Iteratively tighten the stopband constraints in the

frequency domainConsider each frequency band simultaneously

Frequency

Automated Design Methodology:Add Stopband Rejection Constraints

circuit parameters

Frequency

0dB |S11|

|S11| frequency response

in band 6Passband Constraint

circuit parameters

Frequency

Stopband Constraints

Add initial relaxed stopband constraints

Passband Constraint

circuit parameters

Frequency

Optimize design to meet relaxed stopband constraints

Passband Constraint

circuit parameters

Frequency

Passband Constraint

Tighten stopband constraints

circuit parameters

Frequency

Passband Constraint

Optimize design to meet tightened stopband constraints

circuit parameters

Frequency

Passband Constraint

Iteratively continue process until final stopband constraints are added

circuit parameters

Frequency

Passband Constraint

Automated Design Methodology:Add Passband Width Constraints

Perform similar iterative process to widen passband constraints

circuit parameters

Frequency

Passband Constraints

Automated Design Methodology:Add Passband Width Constraints

Optimized design meets widened passband constraints

circuit parameters

Perform a similar iterative process to optimize design with circuit component quality factors

Add circuit component power handling constraints

Design methodology produces reconfigurable IMN design that meets performance constraints

Automated Design Methodology:Quality Factor and Power Constraints

circuit parameters

Step 5: Successively tighten quality factors

Step 6: Add component power constraints

Output: Reconfigurable IMN circuit design

Computational Complexity

Automated design methodology requires the solution to Nopt successive optimization problems

Nte: Number of pair-wise symmetric variable circuit elements

Ni: Number of reconfigurable states for a given set of

pair-wise symmetric variable circuit elements

Nsbr, Npbw, Nqf: Number of iterative optimization problems solved for

stopband, passband and qualify factor constraints Each optimization problem typically requires less than

1000 function evaluations to converge

Variability-Aware ReconfigurableIMN Optimization

Sources of variation and uncertainty are important considerations for reconfigurable IMNsProcess variations during fabricationUncertainty in models for implemented components

Developed variability-aware optimization process for reconfigurable IMNs

Use deterministically optimized design as start point for variability-aware optimization process

Variability-aware reconfigurable IMN optimization problem:

Minimize:

Subject to:

Minimize sum of failure probabilities over all bands

Variability-Aware Reconfigurable IMN Design Optimization Formulation

Variability-aware reconfigurable IMN optimization problem:

Minimize:

Subject to:

Pf = [ Probability[S11crit(ti,fi,ZS1,ZL1) S11const],

Probability[S21crit(ti,fi,ZS1,ZL1) S21const]

Probability[S22crit(ti,fi,ZS1,ZL1) S22const]

Probability[SPcrit(ti,fi,ZS1,ZL1) SPconst] ]

Critical constraints

on |S11|, |S21|, |S22|

and power in passband and stopband

Failure probability objective function vector:

Minimize sum of failure probabilities over all bands

Variability-Aware Reconfigurable IMN Design Optimization Formulation

Critical Failure Probability Constraints

Deterministic IMN optimization problem has a large number of constraints spanning passband and stopband frequenciesProbabilistic constraints more computationally complex to determineNeed to limit the number of probabilistic constraints evaluated in the

objective function Pf to reduce CPU runtime

Probabilistically evaluate critical constraints only during variability-aware optimization process

What are critical constraints?Active constraints at the conclusion of the deterministic optimization

process (i.e. S11(ti,fi,ZS1,ZL1) = S11const)

Constraints with the highest probability of being violated for the IMN design problem

Critical Constraints for IMN Design Optimization Problem

For the IMN optimization, critical constraints includeConstraints on |S11|, |S21|, and |S22| at the edge of the stopband

Frequency

0 dBCritical stopband constraints

Constraints on |S11|, |S21|, and |S22| at the edge of the passband

Frequency

0 dBCritical passband constraints

Passband power handling constraints

Frequency

Critical passband power handling constraints

Passband power handling constraints

Other selected active |S11|, |S21|, and |S22| constraints

Frequency

Passband Constraints

Other selected active critical probabilistic constraints

Calculating Failure Probability

Need to efficiently compute probability of a constraint violation in variability-aware optimization objective function

Joint PDF Space for

L1 and C1:

DesignConstraint

Integrate over failure

region

Calculating Failure Probability Using Random Sampling Methods

Random sampling methods for variability quantificationLarge number of

model evaluations required

Numerical instabilitydue to statistical sampling for finitedifference derivativecalculation during gradient-based optimization process

Joint PDF Space for

L1 and C1:

DesignConstraint

Calculating Failure Probability Using Analytic Variability Quantification

Analytic methods for variability quantificationDetermine failure probability analytically by integrating in the joint

PDF space of the design variable statistical distributionsEfficient techniques

have been developed to approximate integral 1-3

Utilize analytic methods for variability quantification to determine failure probabilities in this study

1 D. Wei and S. Rahman, Prob. Eng. Mech., 2007.2 Y.-G. Zhao and T. Ono, Structural Safety, 1999.

3 M. S. Eldred and B. J. Bichon, Proc. Structures, Structural Dynamics, and Materials Conf., 2006.

Joint PDF Space for

L1 and C1:

DesignConstraint

Integrate over approximate failure region

Approximated Constraint

Overview

Results Conclusions

Design Examples

Designed 3 reconfigurable IMNs using the proposed methodExample 1 – 5th order reconfigurable IMN covering CDMA,

802.11b/g, and 802.11a frequencies 1

Example 2 – 5th order reconfigurable IMN covering mm-wave frequencies (licensed commercial and military applications) 2

Example 3 – 9th order reconfigurable IMN covering the 14 sub-bands in the ultrawideband MB-OFDM standard 3

Average computational complexity: 24 optimization problem solutions requiring 12.9 minutes CPU time compared to several days for exhaustive search methods

1 J.-H. Kim, Y.-K. Jang, and H.-J. Yoo, Analog Int. Cir. Sig. Proc., 2007.2 J.-H. Park, S. Lee, J.-M. Kim, H.-T. Kim, Y. Kwon, and Y.-K. Kim, IEEE J.Microelect. Sys., 2005.3 A. Batra, J. Balakrishnan, G. R. Aiello, J. R. Foerster, and A. Dabak, IEEE Trans. MTT, 2004.

Design Example Constraints

Passband |S11|, |S22| constraints = -10 dB

Stopband |S11|, |S22| constraints = -3 or -5 dB

Quality factors ranging from 100 to 20 Power handing constraints = 300 or 400 mW Constraints on component values for on-chip integration

Filter Order

Frequency Bands Source Impedance

Design 1 5th WCDMA (2.11-2.17 GHz)802.11b/g (2.405-2.484 GHz)

802.11a (5.15-5.35 GHz)802.11a (5.725-5.825 GHz)

Variable

(20 to 50 )

Design 2 5th Continuous Narrow-Band: 20 – 55 GHz Fixed

Design 3 9th Ultrawideband: 14 Bands (528 MHz Width)Centered from 3.4 to 10.3 GHz

1 2 3 4 5 6 7 8-30

Frequency (GHz)

Source Impedance: 50

Design Example 1:50 Source Impedance – |S11|

C3 has 4 discrete values

corresponding to the 4 frequency bands

C2 and C4 have a

continuous range of values corresponding to source impedance changes from 20 to 50

1 2 3 4 5 6 7 8-30

Frequency (GHz)

CDMA802.11b/g

C2 and C4 have a

1 2 3 4 5 6 7 8-30

Frequency (GHz)

CDMA802.11b/g

802.11a

C2 and C4 have a

1 2 3 4 5 6 7 8-30

Frequency (GHz)

CDMA802.11b/g

802.11a 802.11a

C2 and C4 have a

Results clearly demonstrate the 4 distinct frequency bands when C3 is switched |S11|

1 2 3 4 5 6 7 8-30

Frequency (GHz)

CDMA 802.11b/g

802.11a

C2 and C4 have a

1 2 3 4 5 6 7 8-30

Frequency (GHz)

CDMA 802.11b/g

802.11a

C2 and C4 have a

Design Example 1:35 Source Impedance

Bands maintained as source impedance is varied

1 2 3 4 5 6 7 8-30

Frequency (GHz)

1 2 3 4 5 6 7 8-30

Frequency (GHz)

CDMA 802.11b/g

802.11a 802.11a

CDMA 802.11b/g

802.11a 802.11a

|S11| and |S22| |S21|

Design Example 2: |S11|

One continuously tunable element (C3)

Provides narrow-band impedance matching for 20-to-55 GHz

15 20 25 30 35 40 45 50 55 60 65-35

Frequency (GHz)

35 GHz Tunable Range

15 20 25 30 35 40 45 50 55 60 65-35

Frequency (GHz)

15 20 25 30 35 40 45 50 55 60 65-35

Frequency (GHz)

Design Example 3

9th order reconfigurable IMN for ultrawideband (UWB) applications (3.1 to 10.6 GHz)

Reconfigurable IMN selects one of the 14 528 MHz wide sub-bands in the proposed multi-band OFDM UWB standard 1

Only one reconfigurable element required (C5)

C5 has 14 discrete values corresponding to each

frequency band

1 A. Batra, J. Balakrishnan, G. R. Aiello, J. R. Foerster, and A. Dabak, IEEE Trans. MTT, 2004.

Design Example 3: |S11||S

3 4 5 6 7 8 9 10 11-16

Frequency (GHz)

3.432GHz

4.488GHz

5.544GHz

7.656GHz

8.712GHz

10.296GHz

9.768GHz

6.600GHz

3 4 5 6 7 8 9 10 11-16

Frequency (GHz)

3.432GHz

4.488GHz

5.544GHz

7.656GHz

8.712GHz

10.296GHz

9.768GHz

6.600GHz

3 4 5 6 7 8 9 10 11-16

Frequency (GHz)

Variability-Aware Optimization Results

Utilized variability-aware optimization process to reduce the impact of variations on a 3rd order 2-band switchable IMN

Simultaneously consider three design methods for reducing the impact of process variationsVariability-aware optimization processAdditional tunable circuit elements to dynamically adjust frequency

response post-fabricationRelaxation of the design constraints (overdesign during

deterministic optimization)

Considered circuit component values with standard deviations ranging from 0.5% to 5.0% 1,2

64 cases simulated

1 Q. S. I. Lim, A. V. Kordesch, and R. A. Keating, Proc. RF Micro. Conf., 2004. 2 A. Nieuwoudt and Y. Massoud, IEEE Trans. CAD, 2006.

Two-Band Design:Nominal S-Parameters

Variability-Aware Optimization Results for 2-Band Design

Design Specification

Average Percentage Yield Average Absolute

Yield Increase

Maximum Absolute

Yield Increase

Without Variability-Aware

Optimization

Variability-Aware

Optimization

Nominal Design 0.2% 10.2% 10.0% 31.0%

One Tunable Circuit Element

3.2% 23.7% 20.5% 53.7%

Relaxed Design Constraints

70.9% 83.1% 12.2% 25.3%

Relaxed Design Constraints and 1 Tunable Element

87.1% 96.6% 9.5% 34.6%

Method can be utilized to explore trade-off between performance, hardware complexity, and yield

Conclusions

Developed an automated design methodology for reconfigurable IMNs and filters Technology-independent automated design framework for tunable and

switchable filters and IMNsLeverages a multi-step optimization process with constraint relaxation for

deterministic design realizationVariability-aware optimization phase for robust designSuccessfully generated 4 reconfigurable IMNs with variable frequency bands

and source impedances

Proposed method can be utilized to explore the trade-off between performance and yield for reconfigurable IMNs

Provides an invaluable tool for designers developing reconfigurable RF systems for multi-standard wireless applications

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