V.I. Stepanov1, A.A. Metel2, A.S. Salnikov3, D.V. Bilevich4, I.M. Dobush5, A.A. Kalentyev6, A.Е. Goryainov7

1-7 “50ohm Lab” TUSUR (Tomsk, Russia)

1 vladislav.stepanov@50ohm.tech; 2 aleksandr.metel@50ohm.tech; 3 andrei.salnikov@main.tusur.ru; 4 dmitrii.v.bilevich@tusur.ru; 5 igor.dobush@main.tusur.ru; 6 aleksei.a.kalentev@tusur.ru; 7 aleksandr.goryainov@50ohm.tech

Problem statement. Electromagnetic (EM) simulation is one of the main steps in the microwave monolithic integrated circuits design process. However, this approach is not used for structural and parametric synthesis. This is due to the time-consuming computation, which depends on many parameters of the simulated device. This problem applies to devices such as antennas, inductors, and transformers. Using compact models is the one of the ways to solve the time-consuming problem. However, in many cases, the analytical calculation of circuit elements in compact models is not possible due to the large number of elements, leading to a complex extraction technique. Moreover, depending on the process of the device, it is necessary to use different compact models, and for antennas, they do not exist. Using the surrogate model can be an alternative way to solve this problem. A surrogate model is a model that is comparable in accuracy to EM simulation but with lower computational time. Surrogate models can be building for any device and do not depend on their process, making this approach universal, unlike compact models. Therefore, the use of surrogate models is the most promising approach, and the development of a methodology for constructing surrogate models is an actual task.

Purpose. To research surrogate modeling conditions and methods of the integrated balun, to suggest a surrogate modeling technique and synthesize integrated balun with specified requirements by suggested technique.

Results. An investigation of approaches to building surrogate models was carried out. A universal technique for building a surrogate model was developed using space mapping and Kriging interpolation technique. Using the built surrogate model, the synthesis of an integrated balun was performed based on a commercial 0.25 μm GaAs pHEMT process.

Practical significance. The developed technique allows us to build surrogate models for various microwave devices that require time consuming EM modeling. The obtained by suggested technique surrogate models can be used for parametric synthesis.

Stepanov V.I., Metel A.A., Salnikov A.S., Bilevich D.V., Dobush I.M., Kalentyev A.A., Goryainov A.Е. A research of integrated balun surrogate model  accuracy dependence on modeling conditions and techniques. Radiotekhnika. 2023. V. 87. № 10. P. 107−121.
DOI: https://doi.org/10.18127/j00338486-202310-12 (In Russian)

1. Buzova M.A., Krasil'nikov A.D., Pestovskij K.I. Metodika proektirovaniya antennyh sistem dlya bystrorazvertyvaemyh kompleksov DKMV-diapazona // Radiotekhnika. 2023. V. 87. № 6. S. 92−99. DOI: https://doi.org/10.18127/j00338486-202306-12 (in Russian).
2. Nastos N., Papananos Y. Integrated inductors over MOSFETs - experimental results of a three dimensional integrated structure. Proceedings of the 2003 International Symposium on Circuits and Systems. 2003. V. 1. P. 57–60.
3. Meng C., Teng Y., Lin Y., Jhong J., Yen I. Characteristics of Integrated RF Transformers on GaAs Substrate. 2007 Asia-Pacific Microwave Conference. 2007. P. 1–4.
4. Yu C., Grove, R.A., Xuejue H., Zamdmer N. D., Plouchart J., Wachnik R.A., King T.J., Chenming H. Frequency-independent equivalent-circuit model for on-chip spiral inductors. IEEE J. Solid-State Circuits. 2003. V. 38. № 3. P. 419–426.
5. Watson A., Francis, P., Kyuwoon H., Weisshaar A. Wide-band distributed modeling of spiral inductors in RFICs. IEEE MTT-S International Microwave Symposium Digest. 2003. V. 2. P. 1011–1014.
6. Bandler J.W., Biernacki R.M., Shao H.C., Hemmers R.H., Madsen K. Electromagnetic optimization exploiting aggressive space mapping. IEEE Trans. Microw. Theory Tech. 1995. V. 43. № 12. P. 2874–2882.
7. Kurgan P. Efficient Surrogate Modeling and Design Optimization of Compact Integrated On-Chip Inductors Based on Multi-Fidelity EM Simulation Models. Micromachines. 2021. V. 12. № 11. P. 1341.
8. Rayas-Sanchez J.E., Koziel S., Bandler J.W. Advanced RF and Microwave Design Optimization: A Journey and a Vision of Future Trends. IEEE J. Microwaves. 2021. V. 1. № 1. P. 481–493.
9. Passos F., Gonzalez-Echevarría R., Roca E., Castro-López R., Fernandez F.V. A two-step surrogate modeling strategy for single-objective and multi-objective optimization of radiofrequency circuits. Soft Comput. 2019. V. 23. № 13. P. 4911–4925.
10. Passos F., Kotti, M., Gonzalez-Echevarria R., Fino M.H., Fakhfakh M., Roca E., Castro-Lopez R., Fernandez F.V. Physical vs. surrogate models of passive RF devices. 2015 IEEE International Symposium on Circuits and Systems (ISCAS). 2015. P. 117–120.
11. Bandler J.W., Biernacki R.M., Shao H.C., Grobelny P.A., Hemmers R.H. Space mapping technique for electromagnetic optimization. IEEE Trans. Microw. Theory Tech. 1994. V. 42. № 12. P. 2536–2544.
12. Rayas-Sánchez J.E. Power in simplicity with ASM. IEEE Microw. Mag. 2016. V. 17. № 4. P. 64–76.
13. Passos F., Roca E., Castro-Lopez R., Fernández F.V. An inductor modeling and optimization toolbox for RF circuit design. Integration. 2017. V. 58. P. 463–472.
14. Meng J., Xia L. Support Vector Regression Model for Millimeter Wave Transitions. Int. J. Infrared Millimeter Waves. 2007. V. 28. № 5. P. 413–421.
15. Koziel S., Bandler J.W. Accurate modeling of microwave devices using kriging-corrected space mapping surrogates. Int. J. Numer. Model. Electron. Networks, Devices Fields. 2012. V. 25. № 1. P. 1–14.
16. Bakr M.H., Bandler J.W., Georgieva N., Madsen K. A hybrid aggressive space-mapping algorithm for EM optimization. IEEE Trans. Microw. Theory Tech. 1999. V. 47. № 12. P. 2440–2449.
17. Bakr M.H., Bandler J.W., Ismail M.A., Rayas-Sanchez J.E., Zhang Q. Neural space-mapping optimization for EM-based design. IEEE Trans. Microw. Theory Tech. 2000. V. 48. № 12. P. 2307–2315.
18. Bandler J.W., Cheng Q.S., Nikolova N.K., Ismail M.A. Implicit Space Mapping Optimization Exploiting Preassigned Parameters. IEEE Trans. Microw. Theory Tech. 2004. V. 52. № 1. P. 378–385.
19. Bandler J.W., Ismail M.A., Rayas-Sánchez J.E., Zhang Q. Neural inverse space mapping (NISM) optimization for EM-based microwave design. Int. J. RF Microw. Comput. Eng. 2003. V. 13. № 2. P. 136–147.
20. Koziel S., Bandler J.W., Madsen K. A space-mapping framework for engineering optimization. Theory and implementation. IEEE Trans. Microw. Theory Tech. 2006. V. 54. № 10. P. 3721–3730.
21. Rayas-Sanchez J.E., Vargas-Chavez N. A linear regression inverse space mapping algorithm for EM-based design optimization of microwave circuits. 2011 IEEE MTT-S International Microwave Symposium. 2011. V. 1. № 1. P. 1–4.
22. Koziel S., Echeverra C.D. Reliable simulation-driven design optimization of microwave structures using manifold mapping. Prog. Electromagn. Res. B. 2010. V. 26. P. 361–382.
23. Encica L., Paulides J.J.H., Lomonova E.A., Vandenput A.J.A. Aggressive Output Space-Mapping Optimization for Electromagnetic Actuators. IEEE Trans. Magn. 2008. V. 44. № 6. P. 1106–1109.
24. Bakr M.H., Bandler J.W., Madsen K., Rayas-Sanchez J.E., Sondergaard J. Space-mapping optimization of microwave circuits exploiting surrogate models. IEEE Trans. Microw. Theory Tech. 2000. V. 48. № 12. P. 2297–2306.
25. Couckuyt I., Koziel S., Dhaene T. Kriging, co-kriging and space mapping for microwave circuit modeling. Eur. Microw. Week 2011 "Wave to Futur. EuMW 2011, Conf. Proc. 41st Eur. Microw. Conf. EuMC. 2011. P. 444–447.
26. Koziel S., Bandler J.W. Space-mapping-based modeling utilizing parameter extraction with variable weight coefficients and a data base. 2006 IEEE MTT-S International Microwave Symposium Digest. 2006. № 2. P. 1763–1766.
27. Miraftab V., Mansour R.R. EM-based microwave circuit design using fuzzy logic techniques. IEE Proc. Microwaves, Antennas Propag. 2006. V. 153. № 6. P. 495.
28. Simpson T.W., Poplinski J.D., Koch P.N., Allen J.K. Metamodels for computer-based engineering design: Survey and recommendations. Eng. Comput. 2001. V. 17. № 2. P. 129–150.
29. Bramerdorfer G., Zavoianu A.C. Surrogate-based multi-objective optimization of electrical machine designs facilitating tolerance analysis. IEEE Trans. Magn. 2017. V. 53. № 8. P. 1–11.
30. Bouhlel M.A., Hwang J. T., Bartoli N., Lafage R., Morlier J., Martins J.R.R.A. A Python surrogate modeling framework with derivatives. Adv. Eng. Softw. Elsevier. 2019. V. 135. P. 1–13.
31. Pietrenko‐Dabrowska A., Koziel S. Surrogate modeling of impedance matching transformers by means of variable-fidelity electromagnetic simulations and nested cokriging. International Journal of RF and Microwave Computer-Aided Engineering. 2020. V. 30. № 8. P. 1–10.
32. Forrester A.I.J., Sóbester A., Keane A.J. Engineering design via surrogate modelling. UK: John Wiley & Sons Ltd. 2008. 210 p.
33. Sychjov A.N., Shestakov V.A. Optimal'nyj sintez integral'nyh SVCh-ustrojstv na osnove zameshhajushhego modelirovanija. Obzor. Doklady TUSUR. 2010. V. 2, № 22. S. 81–85 (in Russian).
34. Koziel S., Bandler J.W., Madsen K. Space mapping with adaptive response correction for microwave design optimization. IEEE Transactions on Microwave Theory and Techniques. 2009. V. 57. № 2. P. 478-486.