2012APMC Conference Presentation
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This document discusses optimization techniques for designing ultra-wideband planar monopole antennas. It presents two powerful design methodologies: size optimization using design of experiments, and topology optimization using binary particle swarm optimization. Size optimization is a systematic approach that varies geometric parameters to achieve design goals with a small number of simulations. Topology optimization determines the optimal metal distribution within the design area without a predefined shape using an automatic approach. These techniques are demonstrated by designing UWB antennas and band-notched UWB antennas, improving efficiency over trial-and-error approaches.
![Phase 2: Analysis of Experiment
Least square The saturated model:
k −1
estimation k
F = β0 + ∑ βi x i + ∑
ˆ
k
∑β xi x j
The 32 simulations provide the i =1 i =1 j = i +1
ij
coefficient estimations ß +
k − 2 k −1
∑∑ ∑β
k
ijl x i x j x l +... + βij ...k x i x j ...x k
i =1 j = i +1 l = j +1
Repeated Source
Sum of
df
Mean
Fcalc
ANOVA ß2
Squares Square
Not all the ß indeed exist in 157.26 1 157.26 97.50
ß23 38.19 1 38.19 23.67
the response surface model Residual 17.74 11 1.61
Total 459.29 15
Lack-of-fit The quadratic model:
Need quadratic terms?
k
test k k −1 k k
F = β0 + ∑ βi x i + ∑ ∑ β ij x i x j +∑ β ii xi2
∑β
i =1
x 2
ii i
ˆ
i =1 i =1 j = i +1 i =1
Yes Central
composite 1st stage 2nd stage
Perform additional axial points design (CCD)
to fit the 2nd order model
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2012APMC Conference Presentation
- 1. NATIONAL TAIWAN UNIVERSITY Graduate Institute of Communication Engineering Applications of Optimization Techniques to Designs of Ultra-Wideband Planar Monopole Antennas Yen-Sheng Chen*, Wei-Hsiang Chou, and Shih-Yuan Chen
- 2. AGENDA
- 3. Why We Interested in UWB? communication Time-domain pulse Frequency-domain bandwidth Narrowband 1 0 1 0 time Freq. 5.5 (GHz) Sinusoidal waveform Narrowband communication Ultra-wideband 1 0 1 0 time Freq. 3.1 10.6 (GHz) Short pulse Ultra-wideband UWB It has low system complexity characteristics ⎛ P ⎞ It saves power (Shannon formula: C = W log⎜1 + ⎜ ⎟ ⎟ ) ⎝ WN 0 ⎠ It provides higher throughput NTU It penetrates through walls and ground Graduate Institute of Communication Engineering 3 of 22 H. Schantz, The Art and Science of Ultrawideband Antennas, Boston: Artech House, 2005.
- 4. UWB Antenna Designs The first requirement of UWB antennas Emitted signal power UWB spectrum 0.9 1.6 1.9 2.4 3.1 5.1 5.9 10.6 Frequency (GHz) UWB antennas requires a large bandwidth, and sometimes the interference (5.1-5.9 GHz) should be notched out UWB antenna type Helical, spiral, biconical, and planar monopole antennas Planar monopole Design challenge The design procedure will be time-consuming if we trial-and-error tune the antenna shape NTU We need well-organized or automatic design tools! Graduate Institute of Communication Engineering 4 of 22
- 5. Contribution of This Work We use two powerful design methodologies, improving the efficiency of trial-and-error approaches Size optimization Topology optimization Design of experiments Methodology Binary particle swarm (DOE) optimization (BPSO) Variable Continuous Discrete nature A well-organized and Characteristics A labor-saving and systematic approach automatic approach It only costs a small Benefit It may find Innovative number of simulations antenna shapes The two methodologies will be demonstrated to design NTU Graduate Institute of UWB antennas and band-notched UWB antennas Communication Engineering 5 of 22
- 6. AGENDA 1. Overview 3. Topology optimization 4. Summary
- 7. Size Optimization Size optimization It’s a well-planned procedure which changes the length, gap, cross area, or geometric ratio of the antenna so that the design goals can be achieved What’s the requirements? A detailed and predefined initial layout Carefully identifying the geometric parameters as the decision variables Conventional methods used in UWB monopole designs Genetic algorithms (GA) Particle swarm optimization (PSO) Other precise but computationally complex methods NTU Graduate Institute of Communication Engineering 7 of 22
- 8. DOE Operation Procedure Design of Experiments (DOE) is for the first time applied to the design of UWB monopole antennas Solution space Design of experiments Phase 1 Identify the important geometric Predefined parameters and the interested response simulation set Select a proper experimental design Analysis of experiments Phase 2 Estimate how do the parameters affect the interested response Formulate the response surface model Optimization Phase 3 Use response surface model to predict the optimum result Response surface Obtain the setting of the parameters NTU Graduate Institute of Y.-S. Chen, S.-Y. Chen, and H.-J. Li, “A novel dual-antenna structure for UHF RFID tags,” Communication Engineering 8 of 22 IEEE Trans. Antennas Propagat., vol. 59, no. 11, pp. 3950–3960, Nov. 2011
- 9. The First Design: UWB Input Process Output factors response Selected Top view Bottom view geometric Impedance parameters bandwidth W Patch width F = Max(|S11|i) or L Patch length F = Sum(|S11|i) l Feeding segment length (Uniformly Sample w Patch width minus feeding between 3.1-10.6 GHz) segment width G The distance between ground plane and the antenna body Benchmarking structure The design specification: Substrate (Rogers duroid 5880) εr = 2.2 Total area: 36 × 50 mm2 tanδ = 0.0009 Thickness = 0.7874 mm Design goal: To have a wide impedance bandwidth Microstrip feed line throughout 3.1-10.6 GHz Width = 2.3 mm (50 Ω) K.L. Wong, C.H. Wu and S.W. Su, “Ultra-wideband square planar metal-plate monopole NTU antenna with a trident-shaped feeding strip ,” IEEE Trans. Antennas Propagat., vol. 53, pp. Graduate Institute of Communication Engineering 9 of 22 1262-1269, Apr. 2005.
- 10. Phase 1: Design of Experiment Assign proper simulation set so that the response surface can be rebuilt as precise as possible The ranges of the geometric parameters are determined by EM knowledge, experience, and sequential operations The predefined simulation set is according to the “25 full factorial design” HFSS simulation set Parameter Low High No. L W l w G F L 15 25 1 Low Low Low Low Low -5.7 dB W 15 25 2 Low Low Low Low High -2.4 dB l 3 8 3 Low Low Low High Low -9.2 dB 4 Low Low Low High High -2.1 dB w 2.5 5 G 0.7 1.3 32 High High High High High -3.6 dB These treatments give valuable information, and the results will be further analyzed NTU Graduate Institute of Communication Engineering 10 of 22
- 11. Phase 2: Analysis of Experiment Least square The saturated model: k −1 estimation k F = β0 + ∑ βi x i + ∑ ˆ k ∑β xi x j The 32 simulations provide the i =1 i =1 j = i +1 ij coefficient estimations ß + k − 2 k −1 ∑∑ ∑β k ijl x i x j x l +... + βij ...k x i x j ...x k i =1 j = i +1 l = j +1 Repeated Source Sum of df Mean Fcalc ANOVA ß2 Squares Square Not all the ß indeed exist in 157.26 1 157.26 97.50 ß23 38.19 1 38.19 23.67 the response surface model Residual 17.74 11 1.61 Total 459.29 15 Lack-of-fit The quadratic model: Need quadratic terms? k test k k −1 k k F = β0 + ∑ βi x i + ∑ ∑ β ij x i x j +∑ β ii xi2 ∑β i =1 x 2 ii i ˆ i =1 i =1 j = i +1 i =1 Yes Central composite 1st stage 2nd stage Perform additional axial points design (CCD) to fit the 2nd order model 11 of 22 xi is the factor that transform the range of each parameter into [-1. 1]
- 12. Phase 3: Optimizaiton Prediction by the response surface model For the objective function F = Max(|S11|i): ⎛ W − 20 ⎞ ⎛ l − 5.5 ⎞ ⎛ G −1⎞ ⎛ L − 20 ⎞⎛ W − 20 ⎞ F = 0.38 − 0.05⎜ ⎟ + 0.83⎜ ⎟ + 0.016⎜ ⎟ − 0.02⎜ ⎟⎜ ⎟ ⎝ 5 ⎠ ⎝ 2.5 ⎠ ⎝ 0.3 ⎠ ⎝ 5 ⎠⎝ 5 ⎠ 2 ⎛ W − 20 ⎞⎛ w − 3.75 ⎞ ⎛ l − 5.5 ⎞⎛ w − 3.75 ⎞ ⎛ W − 20 ⎞ − 0.04⎜ ⎟⎜ ⎟ + 0.02⎜ ⎟⎜ ⎟ + 0.11⎜ ⎟ ⎝ 5 ⎠⎝ 1.25 ⎠ ⎝ 2.5 ⎠⎝ 1.25 ⎠ ⎝ 5 ⎠ So a non-linear programming problem can be formulated: min. F s.t. -1 ≤ W, L, w, l, G ≤ 1 Solving the problem gives us the setting of the geometric parameters: F = Max(|S11|i): W L w l G 25 24 5 3 0.76 F = Sum(|S11|i) W L w l G The 10-dB-RL requirement is achieved! 22 15 4 3 0.7 12 of 22
- 13. The Second Design: Band-Notched The partial response between 5.15 Its basic topology comes from the and 5.825 GHz must be notched out previous UWB design obtained by the Benchmarking structure objective function of max(|S11|j) A C-shaped thin slot etched near the feed point Input factors: a Side length Top Bottom b Total slot length view view c Slot width d Distance between the lower edge and the feeding junction Parameter Low High Objective function: Maximize F = (d1 × d2)1/2 L 5.3 5.8 W 19 20 l 0.3 0.6 d1: Mapping the |S11|-peak frequency w 1 3 d2: Mapping that associated peak value of |S11| Q.-X. Chu and Y.-Y. Yang, “A compact ultrawideband antenna with 3.4/5.5 GHz dual band-notched characteristics,” IEEE Trans. 13 of 22 Antennas Propagat., vol. 56, no. 12, pp. 3637-3644, Dec. 2008.
- 14. Performance of the Band-Notched Design Following the DOE procedure, we can obtain the optimal design It only costs 16 simulations! a b c d 5.3 19.7 0.48 1 The performances are also confirmed by measurements: Ordinary UWB Band-notched UWB 14 of 22
- 15. AGENDA 1. Overview 2. Size optimization 4. Summary
- 16. Topology Optimization Topology optimization It needs no detailed and predefined shape; the problem is how to determine the best metal distribution within the design area Problem formulation Find : x ∗ = arg min f ( x ) x ⎧ x ∈ {0,1} Subject to : ⎨ ⎩Problem constraints How to solve the associated problem? Genetic algorithms (Kerkhoff etc. in 2004 and 2007) Binary/hybrid particle swarm optimization (Jin etc. in 2010) NTU Graduate Institute of Communication Engineering 16 of 22
- 17. BPSO Operation Procedure Binary particle swarm optimization (BPSO) is implemented as the external topology optimizer of Ansoft HFSS Matlab HFSS Update positions VBScript.vbs Assign the material ( ) ( ) 1 ⎧1 if rand ( ) <S V ( i +1) S V( i +1) ⎪ = X( conditions by *.vbs i +1) =⎨ ) ≥ S (V( ) ) ( i+1) 1 + e− V ⎪0 if rand ( i +1 ⎩ Update velocities Simulate the batch of V ( i +1) (i ) = c0 V + c1r1 P − X ( (i ) (i ) ) + c r (G2 2 (i ) −X (i ) ) predefined configurations No Iteration > Nite? Export the simulated results VBScript.m Compute the Shutdown HFSS performance index NTU Graduate Institute of Communication Engineering 17 of 22
- 18. The First Design: UWB Top view Bottom view The design specification: Total area: 36 × 50 mm2 Design goal: To have a wide bandwidth throughout 3.1-10.6 GHz Substrate (Rogers duroid 5880) εr = 2.2 y tanδ = 0.0009 Thickness = 0.7874 mm Microstrip feed line x Width = 2.3 mm (50 Ω) Decision variable Objective function BPSO parameter Pixel size: 3 × 3 mm2 F = Max(|S11|i) Nite = 30, Npop = 40 Constraint of symmetry Sample frequency: Typical BPSO operators Uniform distribution # of decision variable: 50 throughout the band Total time: 63 hours N. Jin and Y. Rahmat-Samii, “Advances in particle swarm optimization for antenna designs: Real-number, binary, single- 18 of 22 objective and multiobjective implementation,” IEEE Trans. Antennas Propagat., vol. 55, no. 3, pp. 556–567, Mar. 2007.
- 19. The Second Design: Band-Notched Top view Bottom view Problem features The frequencies being notched out: 5.15-5.825 GHz # of decision variable: 54 Objective function: F = f1 + f 2 ⎧ Max( S11 )-0.3 if Max( S11 ) ≥ 0.3 y f1 = ⎨ ⎩0 if Max( S11 ) < 0.3 Metal f 2 = 1 − S11 @ 5.5GHz x Why do we irregularly discretize the whole design domain? To reduce the number of decision variables If we use too elaborate pixels within the whole design space, most of the combination won’t be promising antenna shapes, so the problem complexity will be too difficult! NTU Graduate Institute of Communication Engineering 19 of 22
- 20. Performances of the Two Designs After an automatic search, the optimal designs can be found: Ordinary UWB Band-notched UWB Both designs are well matched throughout the desired band For the band-notched design, the realized gains around 5.5 GHz are all below 0 dBi NTU Graduate Institute of Communication Engineering 20 of 22
- 21. AGENDA 1. Overview 2. Size optimization 3. Topology optimization
- 22. Summary Implementation Significance Performance Spend less Size optimization simulation runs DOE is for the first It’s systematic and time applied to the efficient, avoiding Offer very good design of UWB trial-and-error matching antennas approaches Create a notch band Topology Operate in an automatic manner optimization BPSO algorithm was It’s automatic, Offer very good implemented saving a number of matching development cost Create a notch band Future works We’ll use antenna gain and fidelity factor as the performance indexes We’ll establish multiobjective frameworks to simultaneously optimize all the responses NTU Graduate Institute of Communication Engineering 22 of 22
- 23. Thanks for your attention! Yen-Sheng Chen Graduate Institute of Communication Engineering National Taiwan University, Taipei, Taiwan E-mail: d98942005@ntu.edu.tw