Dual-Band Bandpass Filters Based on Multilayer Ring Resonators (MRR)

( 210094)

eechenrs@njust.edu.cn kriging krigingOptimize Dual-Band Bandpass Filter Using Space Mapping Algorithm with Response Surface Methodology

XU juan, LUO xuan, CHEN ru shan (School of Electronic and Optical Engineering, Nanjing University of Science and Technology, Nanjing, 210094)Abstract: Generally, the coarse model is mathematical expression or the equivalent circuit mode in space mapping algorithm, but equivalent circuit with low accuracy will lead to poor performance of the space mapping process, and the initial design values obtained by mathematical expression sometimes can not meet the accuracy requirements for the initial response that space mapping algorithm needed. The response surface methodology is a statistical mathematical method, which can construct the relationship between the input (the design variables) and the output (target response) on the basis of observation data. In this paper, the coarse model is constructed by the kriging interpolation based on response surface approximation method, and a multilayer ring resonator based dual-band bandpass filter is optimized through the aggressive space mapping algorithm.Keywords: Space mapping; Filter; Response surface approximation; Kriging interpolation method; Coarse model; Fine model1

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kriging1 S. Koziel, S. Ogurtsov. Rapid Design Optimization of Antennas Using Space Mapping and Response Surface Approximation Models, International Journal of RF and Microwave Computer-Aided Engineering, 20112 J. W. Bandler, R. M. Biernacki, S. H. Chen. Electromagnetic Optimization Exploiting Aggressive Space Mapping, IEEE Transactions on Microwave Theory and Techniques, 19953 S.K. Hashemi. Dual-Band Bandpass Filters Based on Multilayer Ring Resonators , Mediterranean Microwave Symposium (MMS), 2011PAGE 2

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-0.1677465304-14.2160499693

-0.1702320276-14.1532242806

-0.1726212026-14.093706995

-0.1749123921-14.0374132671

-0.1771040291-13.9842641762

-0.179194641-13.9341863682

-0.1811828468-13.8871117299

-0.1830673552-13.8429770929

-0.1848469624-13.8017239635

-0.1865205503-13.7632982775

-0.1880870849-13.7276501764

-0.1895456145-13.694733804

-0.1908952688-13.6645071215

-0.1921352574-13.6369317396

-0.1932648685-13.6119727656

-0.1942834687-13.5895986659

-0.1951905014-13.5697811409

-0.1959854865-13.5524950132

-0.19666802-13.5377181268

-0.1972377732-13.5254312575

-0.1976944928-13.5156180334

-0.1980380003-13.5082648655

-0.1982681921-13.5033608868

-0.1983850397-13.5008979011

-0.1983885895-13.5008703393

-0.1982789631-13.5032752247

-0.1980563576-13.5081121458

-0.1977210462-13.5153832364

-0.1972733783-13.5250931645

-0.1967137803-13.5372491271

-0.1960427562-13.5518608539

-0.1952608883-13.5689406176

-0.1943688381-13.5885032517

-0.1933673467-13.6105661766

-0.1922572365-13.6351494325

-0.1910394115-13.6622757212

-0.1897148586-13.6919704551

-0.1882846488-13.7242618159

-0.1867499382-13.7591808213

-0.1851119693-13.796761401

-0.1833720724-13.8370404834

-0.1815316665-13.8800580919

-0.179592261-13.9258574525

-0.177555457-13.9744851133

-0.1754229486-14.025991077

-0.1731965246-14.0804289461

-0.1708780698-14.1378560842

-0.1684695663-14.1983337921

-0.1659730956-14.2619275019

-0.1633908394-14.3287069899

-0.1607250819-14.3987466103

-0.1579782106-14.4721255515

-0.1551527185-14.5489281171

-0.1522512052-14.6292440349

-0.1492763789-14.7131687959

-0.1462310573-14.8008040272

-0.1431181697-14.8922579018

S11

S21

(GHz)

S(dB)

Sheet1

4.82E-02-3.94E-019.64E-02-4.98E+010-0.0021847505-75.2736600762-0.0045268029-79.1506195977-0.004142669-67.918826903

3.86E-01-3.94E-019.64E-02-4.86E+010.02-0.001745924-44.9182589382-0.0035606688-45.3840452981-0.0032241359-44.7497429809

7.71E-01-3.94E-019.64E-02-4.74E+010.04-0.0016486718-39.0135356748-0.002934696-39.4426155078-0.0026850294-39.0176535414

1.40E+00-3.94E-019.64E-02-4.65E+010.06-0.0018872364-35.5318410994-0.0026442092-35.9480270419-0.0025176314-35.5940120189

1.64E+00-3.94E-019.64E-02-4.57E+010.08-0.0024556093-33.0550393637-0.0026843491-33.4640838386-0.002713975-33.1457166122

1.88E+00-3.94E-019.64E-02-4.47E+010.1-0.0033475419-31.1322565275-0.0030500787-31.5362576116-0.0032658589-31.2395017692

2.17E+00-3.94E-019.64E-02-4.39E+010.12-0.0045565561-29.5613716865-0.0037361896-29.9612038026-0.0041648619-29.6792030472

2.41E+00-3.94E-019.64E-02-4.31E+010.14-0.006075955-28.2341623544-0.0047373089-28.6301745979-0.0054023574-28.3591728651

2.70E+00-3.94E-019.64E-02-4.23E+010.16-0.0078988345-27.08586754-0.0060479054-27.4781465487-0.0069695288-27.2159453816

2.94E+00-3.94E-019.64E-02-4.13E+010.18-0.0100180949-26.0746393538-0.0076622968-26.463126554-0.0088573845-26.208395556

3.18E+00-3.94E-019.64E-02-4.00E+010.2-0.0124264524-25.1718645147-0.009574657-25.5564149901-0.0110567728-25.3083455036

3.47E+00-3.94E-019.64E-02-3.84E+010.22-0.0151164517-24.3571113046-0.0117790226-24.7375260831-0.0135583979-24.4956415471

3.90E+00-3.94E-019.64E-02-3.64E+010.24-0.0180804776-23.6152792607-0.0142693007-23.991324292-0.0163528344-23.7553691948

4.48E+00-3.94E-019.64E-02-3.35E+010.26-0.0213107677-22.9348911931-0.0170392761-23.306309148-0.0194305434-23.0761804145

4.87E+00-5.91E-019.64E-02-3.19E+010.28-0.0247994249-22.307018695-0.0200826188-22.6735366561-0.0227818872-22.4492393371

5.11E+00-9.84E-011.45E-01-2.99E+010.3-0.0285384292-21.7245785606-0.0233928911-22.0859132426-0.0263971444-21.8675308142

5.25E+00-1.77E+001.45E-01-2.80E+010.32-0.0325196513-21.181856346-0.0269635556-21.5377177657-0.0302665252-21.3253915793

5.40E+00-2.95E+001.93E-01-2.62E+010.34-0.0367348637-20.6741743893-0.0307879824-21.0242685298-0.0343801856-20.8181831935

5.49E+00-4.13E+002.41E-01-2.44E+010.36-0.0411757543-20.1976547248-0.0348594568-20.5416855232-0.0387282422-20.3420582469

5.59E+00-5.31E+002.89E-01-2.24E+010.38-0.0458339378-19.749046095-0.0391711868-20.0867169643-0.0433007865-19.8937896242

5.69E+00-6.30E+003.37E-01-2.13E+010.4-0.0507009686-19.3255953313-0.0437163104-19.6566103509-0.0480878984-19.470643463

5.73E+00-7.68E+003.86E-01-2.01E+010.42-0.055768352-18.9249501112-0.0484879032-19.2490149784-0.05307966-19.0702830419

5.78E+00-8.66E+004.34E-01-1.91E+010.44-0.061027557-18.5450843362-0.0534789857-18.8619071384-0.058266169-18.6906949802

5.83E+00-9.84E+004.82E-01-1.83E+010.46-0.0664700271-18.1842400958-0.0586825308-18.4935319482-0.0636375509-18.330131812

5.88E+00-1.10E+015.30E-01-1.73E+010.48-0.072087192-17.8408819838-0.0640914707-18.1423575612-0.0691839721-17.98706676

5.93E+00-1.24E+015.78E-01-1.65E+010.5-0.0778704789-17.5136607413-0.0696987042-17.8070387269-0.0748956513-17.6601577278

5.98E+00-1.36E+016.27E-01-1.59E+010.52-0.0838113231-17.2013840316-0.0754971036-17.4863874986-0.080762871-17.3482183449

6.02E+00-1.48E+016.75E-01-1.56E+010.54-0.0899011788-16.9029927334-0.081479522-17.1793494712-0.086775989-17.0501944697

6.07E+00-1.59E+017.23E-01-1.52E+010.56-0.0961315289-16.6175415477-0.0876387992-16.8849843413-0.0929254485-16.7651449631

6.12E+00-1.73E+017.71E-01-1.46E+010.58-0.1024938955-16.3441830098-0.0939677693-16.6024498801-0.0992017881-16.4922258338

6.12E+00-1.85E+018.19E-01-1.42E+010.6-0.1089798488-16.0821542157-0.1004592664-16.3309886248-0.1055956518-16.2306770706

6.17E+00-1.97E+018.67E-01-1.36E+010.62-0.1155810168-15.8307657265-0.1071061312-16.0699167534-0.1120977976-15.9798116354

6.22E+00-2.09E+019.16E-01-1.32E+010.64-0.1222890939-15.5893922383-0.113901217-15.8186147275-0.118699106-15.7390062034

6.22E+00-2.20E+011.01E+00-1.26E+010.66-0.1290958492-15.35746469-0.120837396-15.5765193757-0.1253905883-15.5076933314

6.22E+00-2.34E+011.11E+00-1.20E+010.68-0.1359931347-15.134463552-0.1279075645-15.3431171612-0.132163394-15.2853547951

6.27E+00-2.46E+011.20E+00-1.16E+010.7-0.1429728929-14.9199130906-0.1351046491-15.1179384251-0.1390088175-15.0715158958

6.27E+00-2.58E+011.35E+00-1.08E+010.72-0.150027164-14.7133764427-0.1424216113-14.9005524439-0.1459183049-14.8657405708

6.31E+00-2.70E+011.49E+00-1.04E+010.74-0.1571480926-14.5144513676-0.1498514537-14.6905631634-0.1528834597-14.667627175

6.31E+00-2.81E+011.64E+00-1.00E+010.76-0.1643279344-14.3227665679-0.1573872242-14.4876055042-0.1598960484-14.4768048282

6.31E+00-2.93E+011.83E+00-9.65E+000.78-0.1715590621-14.1379784903-0.1650220208-14.2913421479-0.1669480055-14.2929302384

6.31E+00-3.07E+012.02E+00-9.45E+000.8-0.1788339707-13.9597685327-0.1727489969-14.1014607304-0.1740314376-14.1156849294

6.36E+00-3.19E+012.22E+00-9.25E+000.82-0.1861452832-13.7878405994-0.1805613648-13.9176713846-0.1811386279-13.9447728123

6.36E+00-3.31E+012.41E+00-9.25E+000.84-0.193485755-13.621918951-0.1884524006-13.7397045782-0.1882620395-13.7799180516

6.36E+00-3.44E+012.60E+00-9.45E+000.86-0.2008482786-13.4617463102-0.1964154475-13.5673092084-0.1953943182-13.6208631842

6.36E+00-3.56E+012.84E+00-9.65E+000.88-0.2082258876-13.3070821857-0.2044439202-13.4002509162-0.2025282956-13.4673674556

6.36E+00-3.68E+012.94E+00-9.84E+000.9-0.2156117599-13.1577013864-0.2125313079-13.2383105902-0.2096569912-13.3192053453

6.36E+00-3.80E+013.04E+00-1.00E+010.92-0.2229992217-13.0133927001-0.2206711781-13.0812830367-0.2167736141-13.1761652546

6.41E+00-3.92E+013.23E+00-1.04E+010.94-0.2303817497-12.8739577149-0.2288571793-12.9289757932-0.2238715641-13.0380483374

6.41E+00-4.06E+013.33E+00-1.08E+010.96-0.2377529743-12.7392097657-0.2370830442-12.7812080671-0.2309444336-12.904667455

6.41E+00-4.17E+013.47E+00-1.12E+010.98-0.2451066813-12.6089729908-0.2453425925-12.6378097852-0.2379860072-12.775846239

6.41E+00-4.29E+013.57E+00-1.18E+011-0.252436814-12.4830814836-0.2536297332-12.4986207396-0.2449902628-12.6514182505

6.41E+00-4.41E+013.66E+00-1.24E+011.02-0.2597374748-12.3613785297-0.2619384672-12.3634898181-0.2519513714-12.5312262232

6.41E+00-4.53E+013.76E+00-1.32E+011.04-0.2670029262-12.2437159182-0.270262889-12.2322743113-0.2588636963-12.4151213798

6.41E+00-4.67E+013.86E+00-1.38E+011.06-0.2742275921-12.1299533194-0.2785971893-12.1048392847-0.2657217931-12.3029628151

6.41E+00-4.80E+013.90E+00-1.44E+011.08-0.2814060581-12.0199577208-0.2869356563-11.9810570107-0.2725204085-12.1946169365

6.41E+00-4.96E+014.00E+00-1.56E+011.1-0.2885330722-11.9136029153-0.2952726776-11.8608064533-0.2792544789-12.0899569567

6.46E+00-4.96E+014.05E+00-1.65E+011.12-0.2956035445-11.810769036-0.3036027411-11.7439727995-0.2859191293-11.988862432

6.46E+00-4.80E+014.10E+00-1.71E+011.14-0.3026125475-11.7113421318-0.311920437-11.6304470317-0.2925096713-11.8912188422

6.46E+00-4.65E+014.14E+00-1.79E+011.16-0.3095553153-11.615213781-0.3202204583-11.5201255391-0.2990216015-11.7969172067

6.46E+00-4.53E+014.19E+00-1.93E+011.18-0.3164272435-11.5222807371-0.3284976021-11.4129097617-0.3054505992-11.7058537342

6.46E+00-4.41E+014.24E+00-2.05E+011.2-0.3232238878-11.4324446053-0.33674677-11.3087058644-0.3117925239-11.6179295013

6.46E+00-4.29E+014.29E+00-2.24E+011.22-0.3299409634-11.3456115452-0.3449629692-11.2074244387-0.3180434133-11.533050158

6.46E+00-4.15E+014.34E+00-2.52E+011.24-0.3365743436-11.2616919977-0.3531413124-11.1089802291-0.3241994803-11.4511256573

6.46E+00-4.04E+014.39E+00-2.76E+011.26-0.3431200583-11.1806004344-0.3612770186-11.0132918807-0.3302571101-11.3720700065

6.51E+00-3.92E+014.39E+00-2.95E+011.28-0.3495742928-11.102255126-0.3693654132-10.920281708-0.3362128577-11.2958010376

6.51E+00-3.80E+014.39E+00-3.15E+011.3-0.3559333857-11.0265779288-0.3774019278-10.829875481-0.3420634444-11.2222401959

6.51E+00-3.66E+014.39E+00-3.43E+011.32-0.3621938272-10.9534940876-0.3853821004-10.742002228-0.3478057549-11.1513123446

6.55E+00-3.54E+014.39E+00-3.86E+011.34-0.368352257-10.8829320533-0.3933015754-10.6565940537-0.3534368338-11.0829455836

6.55E+00-3.43E+014.43E+00-4.04E+011.36-0.3744054623-10.8148233138-0.4011561028-10.5735859705-0.3589538827-11.0170710826

6.55E+00-3.31E+014.43E+00-4.23E+011.38-0.3803503756-10.7491022372-0.4089415381-10.4929157427-0.364354256-10.953622925

6.60E+00-3.17E+014.43E+00-4.53E+011.4-0.3861840723-10.6857059265-0.416653842-10.4145237414-0.3696354584-10.8925379642

6.70E+00-3.23E+014.43E+00-4.70E+011.42-0.3919037679-10.6245740837-0.4242890793-10.3383528104-0.3747951403-10.833755689

6.75E+00-3.35E+014.48E+00-4.96E+011.44-0.3975068162-10.5656488844-0.4318434187-10.2643481414-0.3798310951-10.7772180991

6.80E+00-3.48E+014.53E+00-4.70E+011.46-0.4029907062-10.5088748601-0.4393131317-10.192457158-0.3847412551-10.7228695886

6.80E+00-3.60E+014.53E+00-4.53E+011.48-0.4083530594-10.4541987888-0.4466945918-10.1226294074-0.3895236878-10.6706568374

6.80E+00-3.72E+014.53E+00-4.23E+011.5-0.4135916277-10.4015695927-0.4539842737-10.0548164598-0.3941765925-10.6205287102

6.80E+00-3.84E+014.53E+00-4.04E+011.52-0.4187042896-10.3509382431-0.4611787522-9.9889718147-0.3986982963-10.5724361619

6.80E+00-3.98E+014.53E+00-3.78E+011.54-0.4236890484-10.3022576703-0.4682747009-9.9250508125-0.4030872508-10.5263321488

6.80E+00-4.09E+014.53E+00-3.52E+011.56-0.4285440287-10.2554826808-0.4752688915-9.8630105537-0.4073420281-10.4821715464

6.80E+00-4.21E+014.58E+00-3.37E+011.58-0.433267474-10.2105698785-0.4821581923-9.8028098212-0.4114613171-10.4399110713

6.84E+00-4.33E+014.58E+00-3.11E+011.6-0.4378577433-10.1674775914-0.4889395667-9.7444090093-0.4154439201-10.3995092091

6.84E+00-4.45E+014.58E+00-2.83E+011.62-0.4423133085-10.1261658029-0.4956100725-9.6877700567-0.4192887488-10.3609261463

6.84E+00-4.57E+014.58E+00-2.76E+011.64-0.4466327516-10.086596087-0.50216686-9.632856383-0.4229948211-10.3241237062

6.84E+00-4.70E+014.63E+00-2.56E+011.66-0.4508147613-10.0487315475-0.508607171-9.5796328306-0.4265612573-10.2890652894

6.89E+00-4.65E+014.63E+00-2.40E+011.68-0.4548581306-10.0125367614-0.5149283369-9.528065609-0.4299872763-10.2557158176

6.89E+00-4.53E+014.63E+00-2.13E+011.7-0.4587617536-9.9779777251-0.5211277776-9.4781222431-0.4332721926-10.2240416807

6.89E+00-4.41E+014.67E+00-1.95E+011.72-0.4625246226-9.9450218041-0.527203-9.4297715247-0.4364154126-10.1940106878

6.94E+00-4.27E+014.72E+00-1.73E+011.74-0.4661458251-9.9136376856-0.533151596-9.3829834666-0.439416431-10.1655920204

6.94E+00-4.15E+014.77E+00-1.50E+011.76-0.4696245413-9.8837953342-0.5389712417-9.3377292602-0.4422748277-10.1387561892

6.94E+00-4.04E+014.82E+00-1.40E+011.78-0.4729600408-9.8554659499-0.5446596949-9.2939812348-0.4449902643-10.1134749931

6.94E+00-3.92E+014.87E+00-1.24E+011.8-0.4761516801-9.8286219291-0.5502147944-9.2517128199-0.4475624812-10.0897214813

6.94E+00-3.78E+014.92E+00-1.10E+011.82-0.4791988995-9.8032368272-0.5556344577-9.2108985101-0.4499912939-10.0674699172

6.94E+00-3.66E+014.96E+00-1.02E+011.84-0.4821012206-9.7792853243-0.5609166797-9.1715138314-0.4522765902-10.0466957451

6.94E+00-3.54E+015.01E+00-8.86E+001.86-0.4848582434-9.7567431927-0.5660595311-9.1335353101-0.4544183271-10.0273755592

6.94E+00-3.43E+015.06E+00-7.68E+001.88-0.4874696435-9.7355872658-0.5710611566-9.0969404432-0.4564165278-10.0094870738

6.94E+00-3.31E+015.11E+00-7.09E+001.9-0.4899351699-9.7157954101-0.5759197733-9.0617076714-0.4582712784-9.9930090967

6.99E+00-3.17E+015.16E+00-6.30E+001.92-0.4922546416-9.6973464983-0.5806336689-9.027816353-0.4599827258-9.9779215038

6.99E+00-3.05E+015.20E+00-5.31E+001.94-0.4944279458-9.6802203839-0.5852012005-8.9952467396-0.4615510741-9.9642052158

6.99E+00-2.93E+015.25E+00-4.72E+001.96-0.4964550347-9.6643978781-0.5896207924-8.9639799541-0.4629765823-9.9518421764

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