r ice a utomated n anoscale d esign g roup automated design of tunable impedance matching networks...
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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
Antenna Standard 2 at Frequency 2
BPF LNA Mixer
Antenna Standard 3 at Frequency 3
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
|S11
| or
|S22
|
0 dB
Passband
Stopband
Stopband
S11
(Reflection)
2-PortFilter
S22
(Reflection)
Reconfigurable Impedance Matching Networks
Important design considerations Impedance matching in passband
and stopband (|S11| and |S22|)
Insertion loss (|S21|)
Power handling capabilities of the circuit components
Frequency
|S21
|
0 dB
Passband
Stopband
Stopband
2-PortFilter
S21
(Transmission)
Reconfigurable Impedance Matching Networks
Important design considerations Impedance matching in passband
and stopband (|S11| and |S22|)
Insertion loss (|S21|)
Power handling capabilities of the circuit components
Must meet design constraints for each frequency band and load/source impedance
Frequency
Re
spo
nse f1 f2 f3 f4 f5 f6
Reconfigurable IMN Frequency States:
Reconfigurable Impedance Matching Networks
Important design considerations Impedance matching in passband
and stopband (|S11| and |S22|)
Insertion loss (|S21|)
Power handling capabilities of the circuit components
Must meet design constraints for each frequency band and load/source impedance
Implemented with tunable and switchable circuit elementsSwitchable – discrete valuesTunable – continuous values
Frequency
Re
spo
nse f1 f2 f3 f4 f5 f6
Reconfigurable IMN Frequency States:
C1 L1
C2 L2
C3 L3
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
I1
V1
+
-
I2
V2
+
-
S11
(Reflection)
2-PortFilter
S22
(Reflection)
S21
(Transmission)
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 IMN Design Optimization Problem Formulation
General reconfigurable IMN design optimization problem:
|| S21IT ||2
S11IT S11IC, S11OT S11OC
S22IT S22IC, S22OT S22OC
S21IT S11IC, S21OT S21OC
SPT SPC, xmin x xmax
Minimize:
Subject to:
Minimize || S21 ||2 over all bands|| S21IT ||2
S11IT S11IC, S11OT S11OC
S22IT S22IC, S22OT S22OC
S21IT S11IC, S21OT S21OC
SPT SPC, xmin x xmax
Minimize:
Subject to:
Reconfigurable IMN Design Optimization Problem Formulation
S21(ti,fi,ZSi,ZLi) is a vector containing |S21| values in the ith band
Minimize || S21 ||2 over all bands|| S21IT ||2
S11IT S11IC, S11OT S11OC
S22IT S22IC, S22OT S22OC
S21IT S11IC, S21OT S21OC
SPT SPC, xmin x xmax
Minimize:
Subject to:
Reconfigurable IMN Design Optimization Problem Formulation
S21(ti,fi,ZSi,ZLi) is a vector containing |S21| values in the ith band
Frequency
f1 f2 fi fM…
… …
…
Re
spo
nse
Minimize || S21 ||2 over all bands|| S21IT ||2
S11IT S11IC, S11OT S11OC
S22IT S22IC, S22OT S22OC
S21IT S11IC, S21OT S21OC
SPT SPC, xmin x xmax
Minimize:
Subject to:
Reconfigurable IMN Design Optimization Problem Formulation
S21(ti,fi,ZSi,ZLi) is a vector containing |S21| values in the ith band
Frequency
f1 f2 fi fM…
… …
…
Re
spo
nse
Frequency
|S21
|
0 dB
fi
Minimize || S21 ||2 over all bands|| S21IT ||2
S11IT S11IC, S11OT S11OC
S22IT S22IC, S22OT S22OC
S21IT S11IC, S21OT S21OC
SPT SPC, xmin x xmax
Minimize:
Subject to:
Reconfigurable IMN Design Optimization Problem Formulation
S21(ti,fi,ZSi,ZLi) is a vector containing |S21| values in the ith band
Frequency
f1 f2 fi fM…
… …
…
Re
spo
nse
Frequency
|S21
|
0 dB
fi
S21(ti,fi,ZSi,ZLi)
values ()
Minimize || S21 ||2 over all bands|| S21IT ||2
S11IT S11IC, S11OT S11OC
S22IT S22IC, S22OT S22OC
S21IT S11IC, S21OT S21OC
SPT SPC, xmin x xmax
Minimize:
Subject to:
Reconfigurable IMN Design Optimization Problem Formulation
Vector ti contains circuit values mapped to the frequency band fi
ZSi and ZLi are the source and load impedances mapped to fi
Minimize || S21 ||2 over all bands|| S21IT ||2
S11IT S11IC, S11OT S11OC
S22IT S22IC, S22OT S22OC
S21IT S11IC, S21OT S21OC
SPT SPC, xmin x xmax
Minimize:
Subject to:
Reconfigurable IMN Design Optimization Problem Formulation
Vector ti contains circuit values mapped to the frequency band fi
ZSi and ZLi are the source and load impedances mapped to fi
C1 L1
C2 L2
C3 L3
Frequency
f1 f2 fi fM…
… …
…R
esp
on
se
Minimize || S21 ||2 over all bands|| S21IT ||2
S11IT S11IC, S11OT S11OC
S22IT S22IC, S22OT S22OC
S21IT S11IC, S21OT S21OC
SPT SPC, xmin x xmax
Minimize:
Subject to:
Reconfigurable IMN Design Optimization Problem Formulation
Vector ti contains circuit values mapped to the frequency band fi
ZSi and ZLi are the source and load impedances mapped to fi
C1 L1
C2 L2
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
S11IT S11IC, S11OT S11OC
S22IT S22IC, S22OT S22OC
S21IT S11IC, S21OT S21OC
SPT SPC, xmin x xmax
Minimize:
Subject to:
Reconfigurable IMN Design Optimization Problem Formulation
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
Passband and stopband constraints on |S11|, |S21|,
and |S22|
|| S21IT ||2
S11IT S11IC, S11OT S11OC
S22IT S22IC, S22OT S22OC
S21IT S11IC, S21OT S21OC SPT
SPC
xmin x xmax
Minimize:
Subject to:
Circuit element power constraints
Reconfigurable IMN Design Optimization Problem Formulation
Minimize || S21 ||2 over all bands
Passband and stopband constraints on |S11|, |S21|,
and |S22|
|| S21IT ||2
S11IT S11IC, S11OT S11OC
S22IT S22IC, S22OT S22OC
S21IT S11IC, S21OT S21OC SPT
SPC
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
Reconfigurable IMN Design Optimization Problem Formulation
Minimize || S21 ||2 over all bands
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
Zs
Black
Box System
ZinVs
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
-10
-1
-0.1
S11
(dB
)
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
-10
-1
-0.1
S11
(dB
)
Fixed Filter at 2.4 GHz
Normalized Circuit Element Multiplication Factor
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
-10
-1
-0.1
S11
(dB
)
Tunable Filter at 2.4 GHz
Tunable Filter at 5.0 GHz
Normalized Circuit Element Multiplication Factor
2-Band Reconfigurable
Filter |S11| Values
Design Space Characteristics:2-Band Reconfigurable IMN
0.3 1 3 0.3 1 3 10-50
-10
-1
-0.1
S11
(dB
)
Tunable Filter at 2.4 GHz
Tunable Filter at 5.0 GHz
Normalized Circuit Element Multiplication Factor
Region 2Region 1
Cannot utilize standard convex optimization techniques alone to find optimal solution
Local Minima
LocalMinima
31
2-Band Reconfigurable IMN Optimization Algorithm Start Point
0.3 1 3 0.3 1 3 10-50
-10
-1
-0.1
S11
(dB
)
Tunable Filter at 2.4 GHz
Tunable Filter at 5.0 GHz
Fixed Filter at 2.4 GHz
Normalized Circuit Element Multiplication Factor
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
Re
spo
nse f1
Automated Design Methodology:Input: Define design requirements and
circuit parameters
Step 1: Optimize fixed-valued IMN in 1 frequency band
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
Current IMN Configuration:
Frequency
Re
spo
nse f1 f2 f3 f4 f5 f6
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
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
Fre
que
ncy
Re
spo
nse
(|S
21|) f1 f2 f3 f4 f5 f6
Reconfigurable IMN Frequency States:
C1 L1
C2 L2
C3 L3
Reconfigurable IMN Circuit:
Combinatorial Frequency Mapping
Combinatorial mappingEach possible combination of
variable circuit element values is mapped to a reconfigurable frequency state
Frequency
Fre
que
ncy
Re
spo
nse
(|S
21|) f1 f2 f3 f4 f5 f6
Reconfigurable IMN Frequency States:
C1 L1
C2 L2
C3 L3
Reconfigurable IMN Circuit:
C2 has 3 possible values:
[C2(1), C2(2), C2(3)]
C1 has 2 possible values:
[C1(1), C1(2)]
Combinatorial Frequency Mapping
Combinatorial mappingEach possible combination of
variable circuit element values is mapped to a reconfigurable frequency state
Frequency
Fre
que
ncy
Re
spo
nse
(|S
21|) f1 f2 f3 f4 f5 f6
Reconfigurable IMN Frequency States:
C1 L1
C2 L2
C3 L3
Reconfigurable IMN Circuit:C1 has 2 possible values:
[C1(1), C1(2)]C2 has 3 possible values:
[C2(1), C2(2), C2(3)]
Combinatorial Frequency Mapping
Combinatorial mappingEach possible combination of
variable circuit element values is mapped to a reconfigurable frequency state
Frequency
Fre
que
ncy
Re
spo
nse
(|S
21|) f1 f2 f3 f4 f5 f6
Reconfigurable IMN Frequency States:
C1 L1
C2 L2
C3 L3
Reconfigurable IMN Circuit:C1 has 2 possible values:
[C1(1), C1(2)]C2 has 3 possible values:
[C2(1), C2(2), C2(3)]
Combinatorial Frequency Mapping
Combinatorial mappingEach possible combination of
variable circuit element values is mapped to a reconfigurable frequency state
Frequency
Fre
que
ncy
Re
spo
nse
(|S
21|) f1 f2 f3 f4 f5 f6
Reconfigurable IMN Frequency States:
C1 L1
C2 L2
C3 L3
Reconfigurable IMN Circuit:C1 has 2 possible values:
[C1(1), C1(2)]C2 has 3 possible values:
[C2(1), C2(2), C2(3)]
Combinatorial Frequency Mapping
Combinatorial mapping schemeEach possible combination of
variable circuit element values is mapped to a reconfigurable frequency state
Efficiently utilizes available reconfigurable states
Does not balance impact of |S11|, |
S21|, and |S22|
Frequency
Fre
que
ncy
Re
spo
nse
(|S
21|) f1 f2 f3 f4 f5 f6
Reconfigurable IMN Frequency States:
C1 L1
C2 L2
C3 L3
Reconfigurable IMN Circuit:
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
Fre
que
ncy
Re
spo
nse
(|S
21|) f1 f2 f3 f4 f5 f6
Reconfigurable IMN Frequency States:
C1 L1
C2 L2
C3 L3
Reconfigurable IMN Circuit:C1 has 2 possible values:
[C1(1), C1(2)]C2 has 3 possible values:
[C2(1), C2(2), C2(3)]C3 has 2 possible values:
[C3(1), C3(2)]
Automated Design Methodology:Add Reconfigurable Band Constraints
Current IMN Configuration:
Frequency
Re
spo
nse f1 f3
C1 L1
C2 L2
C3 L3
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:
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
Automated Design Methodology:Add Reconfigurable Band Constraints
Current IMN Configuration:
Frequency
Re
spo
nse f1 f3 f5
C2(1) C2(2) C2(3)
f1 f3 f5
C1 L1
C2 L2
C3 L3
C2 has 2 possible values:
[C2(1), C2(2), C2(3)]
C1 and C3 have 1 value each
Reconfigurable Circuit Element Mapping:
Input: Define design requirements and circuit parameters
Step 1: Optimize fixed-valued IMN in 1 frequency band
Step 2: Successively add reconfigurable band constraints
Automated Design Methodology:
Automated Design Methodology:Add Reconfigurable Band Constraints
Current IMN Configuration:
Frequency
Re
spo
nse f1 f2 f3 f4 f5 f6
C2(1) C2(2) C2(3)
C1(1)
C3(1)
C1(2)
C3(2)
C1(1)
C3(1)
C1(2)
C3(2)
C1(1)
C3(1)
C1(2)
C3(2)
f1 f2 f3 f4 f5 f6
C2 has 3 possible values:
[C2(1), C2(2), C2(3)]
C1 has 2 possible values:
[C1(1), C1(2)]
C3 has 2 possible values:
[C3(1), C3(2)]
Reconfigurable Circuit Element Mapping:
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
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
Current IMN Configuration:
Frequency
Re
spo
nse f1 f2 f3 f4 f5 f6
Automated Design Methodology:Add Stopband Rejection Constraints
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
Current IMN Configuration:
Frequency
Re
spo
nse f1 f2 f3 f4 f5 f6
Frequency
|S11
|
0dB |S11|
|S11| frequency response
in band 6Passband Constraint
Automated Design Methodology:Add Stopband Rejection Constraints
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
Current IMN Configuration:
Frequency
Re
spo
nse f1 f2 f3 f4 f5 f6
Frequency
|S11
|
0dB
Stopband Constraints
Stopband Constraints
Add initial relaxed stopband constraints
Passband Constraint
|S11|
Automated Design Methodology:Add Stopband Rejection Constraints
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
Current IMN Configuration:
Frequency
Re
spo
nse f1 f2 f3 f4 f5 f6
Frequency
|S11
|
0dB
Stopband Constraints
Stopband Constraints
Optimize design to meet relaxed stopband constraints
Passband Constraint
|S11|
Automated Design Methodology:Add Stopband Rejection Constraints
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
Current IMN Configuration:
Frequency
Re
spo
nse f1 f2 f3 f4 f5 f6
Frequency
|S11
|
0dB
Stopband Constraints
Stopband Constraints
Passband Constraint
|S11|
Tighten stopband constraints
Automated Design Methodology:Add Stopband Rejection Constraints
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
Current IMN Configuration:
Frequency
Re
spo
nse f1 f2 f3 f4 f5 f6
Frequency
|S11
|
0dB
Stopband Constraints
Stopband Constraints
Passband Constraint
|S11|
Optimize design to meet tightened stopband constraints
Automated Design Methodology:Add Stopband Rejection Constraints
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
Current IMN Configuration:
Frequency
Re
spo
nse f1 f2 f3 f4 f5 f6
Frequency
|S11
|
0dB
Stopband Constraints
Stopband Constraints
Passband Constraint
|S11|
Iteratively continue process until final stopband constraints are added
Automated Design Methodology:Add Stopband Rejection Constraints
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
Current IMN Configuration:
Frequency
Re
spo
nse f1 f2 f3 f4 f5 f6
Frequency
|S11
|
0dB
Stopband Constraints
Stopband Constraints
Passband Constraint
|S11|
Automated Design Methodology:Add Passband Width Constraints
Perform similar iterative process to widen passband constraints
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
Current IMN Configuration:
Frequency
Re
spo
nse f1 f2 f3 f4 f5 f6
Frequency
|S11
|
0dB
Stopband Constraints
Stopband Constraints
Passband Constraints
|S11|
Automated Design Methodology:Add Passband Width Constraints
Optimized design meets widened passband constraints
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
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
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
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:
Pf
S11IT S11IC, S11OT S11OC
S22IT S22IC, S22OT S22OC
S21IT S11IC, S21OT S21OC
SPT SPC, xmin x xmax
Minimize:
Subject to:
Minimize sum of failure probabilities over all bands
Variability-Aware Reconfigurable IMN Design Optimization Formulation
Variability-aware reconfigurable IMN optimization problem:
Pf
S11IT S11IC, S11OT S11OC
S22IT S22IC, S22OT S22OC
S21IT S11IC, S21OT S21OC
SPT SPC, xmin x xmax
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
|S11
| or
|S22
|
0 dB
Frequency
|S21
|
0 dBCritical stopband constraints
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
Constraints on |S11|, |S21|, and |S22| at the edge of the passband
Frequency
|S11
| or
|S22
|
0 dB
Frequency
|S21
|
0 dBCritical passband constraints
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
Constraints on |S11|, |S21|, and |S22| at the edge of the passband
Passband power handling constraints
Frequency
Wor
st-C
ase
Pow
er (
mW
)
Critical passband power handling constraints
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
Constraints on |S11|, |S21|, and |S22| at the edge of the passband
Passband power handling constraints
Other selected active |S11|, |S21|, and |S22| constraints
Frequency
|S11
|
0 dB
Stopband Constraints
Passband Constraints
|S11|
Other selected active critical probabilistic constraints
Calculating Failure Probability
Need to efficiently compute probability of a constraint violation in variability-aware optimization objective function
L1
C1
Joint PDF Space for
L1 and C1:
DesignConstraint
(gc)
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
L1
C1
Joint PDF Space for
L1 and C1:
DesignConstraint
(gc)
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.
L1
C1
Joint PDF Space for
L1 and C1:
DesignConstraint
(gc)
Integrate over approximate failure region
Approximated Constraint
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
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
Fixed
1 2 3 4 5 6 7 8-30
-25
-20
-15
-10
-5
0
Frequency (GHz)
|S11
| (dB
)
Source Impedance: 50
CDMA
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
|S11|
1 2 3 4 5 6 7 8-30
-25
-20
-15
-10
-5
0
Frequency (GHz)
|S11
| (dB
)
Source Impedance: 50
CDMA802.11b/g
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
|S11|
1 2 3 4 5 6 7 8-30
-25
-20
-15
-10
-5
0
Frequency (GHz)
|S11
| (dB
)
Source Impedance: 50
CDMA802.11b/g
802.11a
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
|S11|
1 2 3 4 5 6 7 8-30
-25
-20
-15
-10
-5
0
Frequency (GHz)
|S11
| (dB
)
Source Impedance: 50
CDMA802.11b/g
802.11a 802.11a
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
Results clearly demonstrate the 4 distinct frequency bands when C3 is switched |S11|
1 2 3 4 5 6 7 8-30
-25
-20
-15
-10
-5
0
Frequency (GHz)
|S22
| (dB
)
Source Impedance: 50
CDMA 802.11b/g
802.11a
802.11a
Design Example 1:50 Source Impedance – |S22|
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
Results clearly demonstrate the 4 distinct frequency bands when C3 is switched |S22|
1 2 3 4 5 6 7 8-30
-25
-20
-15
-10
-5
0
Frequency (GHz)
|S21
| (dB
)
Source Impedance: 50
CDMA 802.11b/g
802.11a
802.11a
Design Example 1:50 Source Impedance – |S21|
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
Results clearly demonstrate the 4 distinct frequency bands when C3 is switched |S21|
Design Example 1:35 Source Impedance
Bands maintained as source impedance is varied
1 2 3 4 5 6 7 8-30
-25
-20
-15
-10
-5
0
Frequency (GHz)
S-P
aram
eter
s (d
B)
S11
S22
Source Impedance: 35
1 2 3 4 5 6 7 8-30
-25
-20
-15
-10
-5
0
Frequency (GHz)
S-P
aram
eter
s (d
B)
S21
Source Impedance: 35
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
-30
-25
-20
-15
-10
-5
0
Frequency (GHz)
|S1
1| (
dB)
S11
|S11|
35 GHz Tunable Range
Design Example 2: |S22|
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
-30
-25
-20
-15
-10
-5
0
Frequency (GHz)
|S2
2| (
dB)
S22
|S22|
15 20 25 30 35 40 45 50 55 60 65-35
-30
-25
-20
-15
-10
-5
0
Frequency (GHz)
|S2
1| (
dB)
S21
Design Example 2: |S21|
One continuously tunable element (C3)
Provides narrow-band impedance matching for 20-to-55 GHz
|S21|
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
11| (
dB)
3 4 5 6 7 8 9 10 11-16
-14
-12
-10
-8
-6
-4
-2
0
Frequency (GHz)
S11
3.432GHz
4.488GHz
5.544GHz
7.656GHz
8.712GHz
10.296GHz
9.768GHz
6.600GHz
Design Example 3: |S22|
3 4 5 6 7 8 9 10 11-16
-14
-12
-10
-8
-6
-4
-2
0
Frequency (GHz)
S22
3.432GHz
4.488GHz
5.544GHz
7.656GHz
8.712GHz
10.296GHz
9.768GHz
6.600GHz
|S22
| (dB
)
Design Example 3: |S21|
3 4 5 6 7 8 9 10 11-16
-14
-12
-10
-8
-6
-4
-2
0
Frequency (GHz)
|S21
| (dB
)
S21
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