Precision calculations of the characteristic impedance of complex coaxial waveguides used in wideband thermal converters of AC voltage and current
Abstract
The article presents precision and numerically stable method of calculation of the characteristic impedance of cylindrical multilayer waveguides used in high-precision wideband measuring instruments and standards, especially calculable thermal converters of AC voltage and precision wideband current shunts. Most of currently existing algorithms of characteristic impedance calculation of such waveguides are based upon approximations. Unfortunately, application of such methods is limited to waveguides composed of a specific, usually low number of layers. The accuracy of approximation methods as well as the number of layers is sometimes not sufficient, especially when the coaxial waveguide is a part of precision measurement equipment. The article presents the numerically stable matrix analytical formula using exponentially scaled modified Bessel functions to compute characteristic impedance and its components of the cylindrical coaxial multilayer waveguides. Results obtained with the developed method were compared with results of simulations made using the Finite Element Method (FEM) software simulations. Very good agreement between results of those two methods were achieved.
References
Y. Shan, Y. Meng and P. Filipski, „Evaluation of a Calorimetric Thermal Voltage Converter for RF–DC Difference up to 1 GHz”, IEEE Transactions on Instrumentation and Measurement, vol. 63, no. 2, pp. 467-472, 2014. https://doi.org/10.1109/TIM.2013.2278597
P. Filipski, C. van Mullem, D. Janik, M. Klonz, J. Kinard, T. Lipe and B. Waltrip, „Comparison of high-frequency AC-DC voltage transfer standards at NRC, VSL, PTB, and NIST”, IEEE Transactions on Instrumentation and Measurement, vol. 50, no. 2, pp. 349-352, 2001. http://doi.org/10.1109/TIM.2013.2278597
M. Malinowski, K. Kubiczek and M. Kampik, „A precision coaxial current shunt for current AC-DC transfer”, Measurement, vol. 176, p. 109126, 2021. http://doi.org/10.1016/j.measurement.2021.109126
M. Malinowski et al., „A Precision Coaxial Low-Current Shunt with Improved Mathematical Model”, 2021 13th International Conference on Measurement, 2021.
G. Kyriazis, R. de Souza, E. Yasuda and L. Di Lillo, „Modeling the AC–DC Transfer Difference of Wideband Cage-Type Current Shunts”, IEEE Transactions on Instrumentation and Measurement, vol. 69, no. 7, pp. 4436-4444, 2020.
http://doi.org/10.1109/TIM.2019.2944012
A. Andreychenko, H. Kroeze, D. Klomp, J. Lagendijk, P. Luijten and C. van den Berg, „Coaxial waveguide for travelling wave MRI at ultrahigh fields”, Magnetic Resonance in Medicine, vol. 70, no. 3, pp. 875-884, 2012. https://doi.org/10.1002/mrm.24496
H. Bao, K. Nielsen, O. Bang and P. Jepsen, „Dielectric tube waveguides with absorptive cladding for broadband, low-dispersion and low loss THz guiding”, Scientific Reports, vol. 5, no. 1, 2015. https://doi.org/10.1038/srep07620
J. Melzer, M. Navarro-Cía, O. Mitrofanov and J. Harrington, „Silver-coated Teflon hollow waveguides for the delivery of terahertz radiation”, Optical Fibers and Sensors for Medical Diagnostics and Treatment Applications XIV, 2014.
S. Khalili, M. Botshekanan Dehkordi and E. Carrera, „A nonlinear finite element model using a unified formulation for dynamic analysis of multilayer composite plate embedded with SMA wires”, Composite Structures, vol. 106, pp. 635-645, 2013.
https://doi.org/10.1016/j.compstruct.2013.07.006
Z. Mikno, M. Stepien and B. Grzesik, „Optimization of resistance welding by using electric servo actuator”, Welding in the World, vol. 61, no. 3, pp. 453-462, 2017. http://doi.org/10.1007/s40194-017-0437-x
M. Stepien, S. Krosny and B. Grzesik, „Analysis of quench propagation using coupled electrical-thermal FEM model”, Journal of Physics: Conference Series, vol. 234, no. 2, p. 022036, 2010. https://doi.org/10.1088/1742-6596/234/2/022036
G. Aiello, S. Alfonzetti, E. Dilettoso and N. Salerno, „Eddy Current Computation by the FEM-SDBCI Method”, IEEE Transactions on Magnetics, vol. 52, no. 3, pp. 1-4, 2016.
https://doi.org/10.1109/TMAG.2015.2483367
S. Krosny, M. Woźniak, S. Hopkins, M. Stȩpień, B. Grzesik and B. Glowacki, „Modelling of transient state phenomena of composite superconducting conductors during pulse Ic(B) measurements”, Journal of Physics: Conference Series, vol. 234, no. 2, p. 022019, 2010. https://doi.org/10.1088/1742-6596/234/2/022019
K. Kubiczek and M. Kampik, „Highly accurate and numerically stable computations of double-layer coaxial waveguides", Engineering Computations, 2019. Available: http://doi.org/10.1108/EC-09-2018-0415
C. Paul, Introduction to electromagnetic compatibility. Hoboken, N.J.: Wiley, 2006, pp. 871-900.
J. Jackson, Classical electrodynamics. New Delhi: Wiley India, 2011, pp. 69-75.
H. W. Dommel, “Overhead line parameters from handbook formulasand computer programs”, with discussions by A. Deri and G. Tevan, Adam Semlyen, and F. L. Alvarado, IEEE Trans., Power Appar. Syst., 1985, 104, (2), pp. 366–372
H. W. Dommel, “EMTP Theory Book”, Microtran Power System Analysis Corporation, Vancouver, British Columbia:, 1992, 2nd Edn.
S. Vujević, V. Boras, P. Sarajčev, „A novel algorithm for internal impedance computation of solid and tubular cylindrical conductors”, International Review of Electrical Engineering (IREE). Vol.4, Part B, pp. 1418-1425, 2009.
N. Nahman and D. Holt, „Transient analysis of coaxial cables using the skin effect approximation „, IEEE Transactions on Circuit Theory, vol. 19, no. 5, pp. 443-451, 1972.
A. Semlyen and A. Deri, „Time Domain Modeling of Frequency Dependent Three-Phase Transmission Line Impedance”, IEEE Power Engineering Review, vol. -5, no. 6, pp. 64-65, 1985.
S. Vujevic and D. Lovric, „On the numerical computation of cylindrical conductor internal impedance for complex arguments of large magnitude”, Facta universitatis - series: Electronics and Energetics, vol. 30, no. 1, pp. 81-91, 2017. http://doi.org/10.2298/FUEE1701081V
S. Vujevic, D. Lovric and V. Boras, „High-Accurate Numerical Computation of Internal Impedance of Cylindrical Conductors for Complex Arguments of Arbitrary Magnitude”, IEEE Transactions on Electromagnetic Compatibility, vol. 56, no. 6, pp. 1431-1438, 2014. http://doi.org/10.1109/temc.2014.2352398
J. Carson and J. Gilbert, „Transmission characteristics of the submarine cable”, Journal of the Franklin Institute, vol. 192, no. 6, pp. 705-735, 1921.
J. A. Brandao Faria, „A matrix approach for the evaluation of the internal impedance of multilayered cylindrical structures”, Progress In Electromagnetics Research B, Vol. 28, 351-367, 2011.
K. Kubiczek and M. Kampik, „Highly Accurate and Numerically Stable Matrix Computations of the Internal Impedance of Multilayer Cylindrical Conductors”, IEEE Transactions on Electromagnetic Compatibility, pp. 1-8, 2019. Available:
http://doi.org/10.1109/TEMC.2018.2890447
ANSYS Academic Multiphysics Campus Solution 2017. „Engineering Simulation & 3-D Design Software | ANSYS”, Ansys.com, 2019. [Online]. Available: Available: https://www.ansys.com/.
U. Bakshi and A. Bakshi, Transmission lines and waveguides. 70p.: Ill., pp. 24, ch.1.
P. Peres, C. de Souza and I. Bonatti, „ABCD Matrix: A Unique Tool for Linear Two-Wire Transmission Line Modelling”, International Journal of Electrical Engineering Education, vol. 40, no. 3, pp. 220-229, 2003.
S. Schelkunoff, "The Electromagnetic Theory of Coaxial Transmission Lines and Cylindrical Shields", Bell System Technical Journal, vol. 13, no. 4, pp. 532-579, 1934.
J. H. Poynting, “On the transfer of energy in the electromagnetic field”, Philosophical Transactions of the Royal Society of London. 175: 343–361, 1884.
D. Lovric and S. Vujevic, „Accurate Computation of Internal Impedance of Two-Layer Cylindrical Conductors for Arguments of Arbitrary Magnitude”, IEEE Transactions on Electromagnetic Compatibility, vol. 60, no. 2, pp. 347-353, 2018. http://doi.org/10.1109/TEMC.2017.2715985
A. Gil, J. Segura and N. Temme, „Computing solutions of the modified bessel differential equation for imaginary orders and positive arguments”, ACM Transactions on Mathematical Software, vol. 30, no. 2, pp. 145-158, 2004. http://doi.org/10.1145/992200.992203
N. Marcuvitz, Waveguide handbook. New York: McGraw-Hill, 1951, pp. 72-80.
Downloads
Published
Issue
Section
License
Copyright (c) 2022 International Journal of Electronics and Telecommunications
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
1. License
The non-commercial use of the article will be governed by the Creative Commons Attribution license as currently displayed on https://creativecommons.org/licenses/by/4.0/.
2. Author’s Warranties
The author warrants that the article is original, written by stated author/s, has not been published before, contains no unlawful statements, does not infringe the rights of others, is subject to copyright that is vested exclusively in the author and free of any third party rights, and that any necessary written permissions to quote from other sources have been obtained by the author/s. The undersigned also warrants that the manuscript (or its essential substance) has not been published other than as an abstract or doctorate thesis and has not been submitted for consideration elsewhere, for print, electronic or digital publication.
3. User Rights
Under the Creative Commons Attribution license, the author(s) and users are free to share (copy, distribute and transmit the contribution) under the following conditions: 1. they must attribute the contribution in the manner specified by the author or licensor, 2. they may alter, transform, or build upon this work, 3. they may use this contribution for commercial purposes.
4. Rights of Authors
Authors retain the following rights:
- copyright, and other proprietary rights relating to the article, such as patent rights,
- the right to use the substance of the article in own future works, including lectures and books,
- the right to reproduce the article for own purposes, provided the copies are not offered for sale,
- the right to self-archive the article
- the right to supervision over the integrity of the content of the work and its fair use.
5. Co-Authorship
If the article was prepared jointly with other authors, the signatory of this form warrants that he/she has been authorized by all co-authors to sign this agreement on their behalf, and agrees to inform his/her co-authors of the terms of this agreement.
6. Termination
This agreement can be terminated by the author or the Journal Owner upon two months’ notice where the other party has materially breached this agreement and failed to remedy such breach within a month of being given the terminating party’s notice requesting such breach to be remedied. No breach or violation of this agreement will cause this agreement or any license granted in it to terminate automatically or affect the definition of the Journal Owner. The author and the Journal Owner may agree to terminate this agreement at any time. This agreement or any license granted in it cannot be terminated otherwise than in accordance with this section 6. This License shall remain in effect throughout the term of copyright in the Work and may not be revoked without the express written consent of both parties.
7. Royalties
This agreement entitles the author to no royalties or other fees. To such extent as legally permissible, the author waives his or her right to collect royalties relative to the article in respect of any use of the article by the Journal Owner or its sublicensee.
8. Miscellaneous
The Journal Owner will publish the article (or have it published) in the Journal if the article’s editorial process is successfully completed and the Journal Owner or its sublicensee has become obligated to have the article published. Where such obligation depends on the payment of a fee, it shall not be deemed to exist until such time as that fee is paid. The Journal Owner may conform the article to a style of punctuation, spelling, capitalization and usage that it deems appropriate. The Journal Owner will be allowed to sublicense the rights that are licensed to it under this agreement. This agreement will be governed by the laws of Poland.
By signing this License, Author(s) warrant(s) that they have the full power to enter into this agreement. This License shall remain in effect throughout the term of copyright in the Work and may not be revoked without the express written consent of both parties.