Development of a Non-Iterative Macromodeling Technique by Data Integration and Least Square Method

Document Type : Original Article

Authors

1 Department of Electrical and Computer Engineering, Isfahan University of Technology, Isfahan, Iran

2 Department of Electrical Engineering, KN Toosi University of Technology, Tehran, Iran

Abstract

In this paper, a new method is introduced to synthesize the original data obtained from simulation or measurement results in the form of a rational function. The integration of the available data is vital to the performance of the proposed method. The values of poles and residues of the rational model are determined by solving the system of linear equations using the conventional Least Square Method (LSM). To ensure the stability condition of the provided model, a controller coefficient is considered. Also, using this parameter, the designer can increase the stability margin of a system with poor stability conditions. The introduced method has the potential to be used for a wide range of practical applications since there is no specific restriction on the use of this method. The only requirement that should be considered is the Dirichlet condition for the original data, usually the case for physical systems. To verify the performances of the proposed method, several application test cases are investigated and the obtained results are compared with those gathered by the well-known vector fitting algorithm. Also, the examinations show that the method is efficient in the presence of noisy data.

Keywords


  1. Grivet-Talocia S, Gustavsen B, Passive Macromodeling: Theory and Applications. New York, NY, USA: Wiley, 2016.
  2. Alijani M, G, H, Sheikh. S, Kishk. Ahmed, “Development of Closed-Form Formula for Quick Estimation of Antenna Factor”, 15th European Conference on Antennas and Propagation (EuCAP), (2021), 1-5. doi: 10.23919/EuCAP51087.2021.9411008
  3. A, “Objective Functions for the Optimization of an Ultra Wideband Antenna”, International Journal of Engineering, Transaction A: Basics, Vol. 34, No. 7, (2021), 1743-1749. doi: 10.5829/ije.2021.34.07a.19
  4. P, Pandey. R, “Dual Output Voltage Differencing Buffered Amplifier Based Active -C Multiphase Sinusoidal Oscillator”, International Journal of Engineering Transaction C: Aspects, Vol. 34, No. 6, (2021), 1438-1444. doi: 10.5829/ije.2021.34.06c.07
  5. M, M, Molaei. M, J, Aghaei. A, “Electromagnetic Wave Absorption Properties of Barium Ferrite/Reduced Graphene Oxide Nanocomposites”, International Journal of Engineering, Transaction C: Aspects, Vol. 34, No. 6, (2021), 1503-1511. doi: 10.5829/ije.2021.34.06c.14
  6. C, Bruns. H, D, Liu. P, Schuster. C, “Impulse response optimization of band-limited frequency data for hybrid field-circuit simulation of large-scale energy-selective diode grids”, IEEE Transaction Electromagnetic Compatibility, Vol. 58, No. 4, (2016), 1072–1080. doi: 10.1109/TEMC.2016.2540921
  7. A, Time-domain macromodeling of high speed distributed networks. Ph.D. dissertation, The University of Western Ontario, 2011.
  8. M, G, H, Neshati. M, H, “A new non-iterative method for pattern synthesis of unequally spaced linear arrays”, International Journal of RF and Microwave Computer-Aided Engineering, Vol. 29, No. 11, (2019), 740-771. doi: 10.1002/mmce.21921
  9. A, Achar. R, Nakhla. M, S, “Addressing transient errors in passive macromodels of distributed transmission-line networks”, IEEE Transaction Microwave Theory Technique, Vol. 50, No. 12, (2002), 2759-2768. doi: 10.1109/TMTT.2002.805130
  10. Grivet-Talocia. S, Acquadro. S, Bandinu. M, Canavero. F, G, Kelander. I, Rouvala. M, “A parameterization scheme for lossy transmission line macromodels with application to high speed interconnects in mobile devices”, IEEE Transaction Electromagnetic Compatibility, 49, No. 1, (2007), 18-24. doi: 10.1109/TEMC.2006.888179
  11. F, Knockaert. L, Dhaene. T, “Guaranteed passive parameterized admittance-based macromodeling”, IEEE Transaction on Advanced Packaging, Vol. 33, No. 3, (2010), 623-629. doi: 10.1109/TADVP.2009.2029242
  12. B, Semlyen. A, “Rational approximation of frequency domain responses by vector fitting”, IEEE Transactions on Power Delivery, Vol. 14, No. 3, (1999), 1052-1061. doi: 10.1109/61.772353
  13. D, Mrozowski. M, Dhaene. T, De-Zutter. D, “Macromodeling of multiport systems using a fast implementation of the vector fitting method”, IEEE Microwave Wireless Component Letter, Vol. 18, No. 6, (2008), 383-385. doi: 10.1109/LMWC.2008.922585
  14. T, De-Zutter. D, “Selection of lumped element models for coupled lossy transmission lines”, IEEE Transaction Computer-Aided Design Integrated Circuits System, Vol. 11, No. 7, (1992), 805-815. doi: 10.1109/43.144845
  15. M, Khazaka. R, “Macromodeling of distributed networks from frequency domain data using the Loewner matrix approach”, IEEE Transaction Microwave Theory Technique, Vol. 60, No. 12, (2012), 3927-3938. doi: 10.1109/TMTT.2012.2222915
  16. C, M, Kamwa. I, Khazaka. R, Messina. A, R, “A Loewner Interpolation Method for Power System Identification and Order Reduction”, IEEE Transactions on Power Systems, Vol. 34, No. 3, (2019), 1834-1844. doi: 10.1109/TPWRS.2018.2884655
  17. A, Celik. M, Pileggi. L, T, “PRIMA: passive reduced-order interconnect macromodeling algorithm”, IEEE Transaction Computer-Aided Design Integrated Circuits System, Vol. 17, No. 8, (1998), 645-654. doi: 10.1109/43.712097
  18. A, Achar. R, Nakhla. M, S, “Efficient passive circuit models for distributed networks with frequency-dependent parameters”, IEEE Transaction Advanced Packaging, Vol. 23, No. 3, (2000), 382-392. doi: 10.1109/6040.861551
  19. A, Achar. R, Nakhla. M, “A general class of passive macromodels for lossy multi-conductor transmission lines”, IEEE Transaction Microwave Theory Technique, Vol. 49, No. 10, (2001), 1686-1696. doi: 10.1109/22.954772
  20. A, C, Pasha. S, Prince. J, L, Celik. M, “A new discrete transmission line model for passive model order reduction and macromodeling of high-speed interconnections”, IEEE Transaction Advanced Packaging, Vol. 22, No. 3, (1999), 356-364. doi: 10.1109/6040.784485
  21. Q, Wang. J, M, L, Kuh. E, S, “Passive multipoint moment matching model order reduction algorithm on multiport distributed interconnect networks”, IEEE Transaction Circuits System I: Fundamental Theory and Applications, Vol. 46, No. 1, (1999), 140-160. doi: 10.1109/81.739262
  22. E Nakhla. M, “Efficient simulation of non-uniform transmission lines using integrated congruence transform”, IEEE Transactions on Very Large Scale Integration (VLSI) Systems, Vol. 12, No. 12, (2004), 1307-1320. doi: 10.1109/TVLSI.2004.837988
  23. S, Antoulas. A, C, “A new approach to modelling multiport systems from frequency-domain data”, IEEE Transactions Computed-Aided Design Integrated Circuits System, Vol. 29, No. 1, (2010), 14-27. doi: 10.1109/TCAD.2009.2034500
  24. M, G, H, Neshati. M, H, “A New Closed-Form Expression for Dispersion Characteristics of Fundamental Mode of SIW by Least Squares Method”, Journal of Applied Computational Electromagnetic Society, Vol. 30, No. 8, (2015), 930-933.
  25. J, M, Lessons in Estimation Theory for Signal Processing, Communications, and Control. Prentice Hall PTR, 1995.
  26. M, G, H, Neshati. M, H, “Development a New Technique Based on Least Square Method to Synthesize the Pattern of Equally Space Linear”, International Journal of Engineering, Transaction B: Applications, Vol. 32, No. 11, (2019), 1620-1626. doi: 10.5829/ije.2019.32.11b.13
  27. M, G, H, Neshati. M, H, “Development A New Array Factor Synthesizing Technique by Pattern Integration and Least Square Method”, IEEE Transaction Antennas and Propagation, Vol. 66, No. 12, (2018), 6869-6874. doi: 10.1109/TAP.2018.2871715
  28. R, Hilbert. D, Methods of Mathematical Physics. John Wiley & Sons, 1989.
  29. V, Y, “Solving a Polynomial Equation: Some History and Recent Progress”, SIAM Review, Vol. 39, No. 2, (1997), 187-220. doi: 10.1137/S0036144595288554
  30. A, Dounavis. A, “An instrumental variable vector-fitting approach for noisy frequency responses”, IEEE Transaction Microwave Theory Technique, Vol. 60, No. 9, (2012), 2702-2712. doi: 10.1109/TMTT.2012.2206399
  31. http://www.energy.sintef.no/Produkt/VECTFIT/index.asp.
  32. M, Vafapour. M, “Gain Boosted Folded Cascade Op-Amp with Capacitor Coupled Auxiliary Amplifiers”, International Journal of Engineering, Transaction B: Applications, Vol. 34, No. 5, (2021), 1233-1238. doi: 10.5829/ije.2021.34.05b.16
  33. M, A, Azizian. D, Bigdeli. M, Gharehpetian. G, B, “Multi-Conductor Transmission Line Model of Split-Winding Transformer for Frequency Response and Disk-to-Disk Fault Analysis”, International Journal of Engineering, Transaction C: Aspects Vol. 34, No. 6, (2021), 1486-1492. doi: 10.5829/ije.2021.34.06c.12
  34. N, Alijani. M, G, H, Neshati. M, H, “Crosstalk Analysis of Multi-Microstrip Coupled Lines Using Transmission Line Modeling”, International Journal of RF and Microwave Computer-Aided Engineering, Vol. 22, No. 6, (2019), 1-7. doi: 10.1002/mmce.21677