04 Sep 2018
| 04 Sep 2018
Modeling and Simulation of stochastically deformed Waveguides using Schelkunoff's Method
Hoang Duc Pham
CORRESPONDING AUTHOR
Institute of Theoretical Electrical Engineering, Leibniz Universitaet
Hannover, 30167 Hannover, Appelstrasse 9A, Germany
Soeren Ploennigs
LUIS, Leibniz Universitaet Hannover, 30159 Hannover, Schlosswender Strasse 5, Germany
Wolfgang Mathis
Institute of Theoretical Electrical Engineering, Leibniz Universitaet
Hannover, 30167 Hannover, Appelstrasse 9A, Germany
Related authors
Hoang Duc Pham, Katja Tüting, and Heyno Garbe
Adv. Radio Sci., 19, 49–57, https://doi.org/10.5194/ars-19-49-2021, https://doi.org/10.5194/ars-19-49-2021, 2021
Short summary
Short summary
According to the Guide to the Expression of Uncertaintyin Measurement (GUM), uncertainties must be specified for each measurement. Therefore, this work's primary objective is to examine the effect of irregular deformed boundaries on the electromagnetic field and the resonance frequencies of a field generator (TEM-cell). Using a semi-analytical approach, the wave characteristics can be determined and the uncertainty contribution of the field generator can be estimated.
Wolfgang Mathis
Adv. Radio Sci., 21, 65–75, https://doi.org/10.5194/ars-21-65-2023, https://doi.org/10.5194/ars-21-65-2023, 2023
Short summary
Short summary
Based on new archive sources, it is shown that Egbert von Lepel is one of the pioneers of early radio technology, which has not been adequately dealt with in the history of radio science. In particular, the significance of his 1907 patent of the spark-gap transmitter ("Löschfunkensender") is unknown, although it was granted as a key patent by the Imperial Patent Office in 1911. Therefore, Telefunken paid licenses to von Lepel, but this was the subject of a secret treaty of 1919.
Hoang Duc Pham, Katja Tüting, and Heyno Garbe
Adv. Radio Sci., 19, 49–57, https://doi.org/10.5194/ars-19-49-2021, https://doi.org/10.5194/ars-19-49-2021, 2021
Short summary
Short summary
According to the Guide to the Expression of Uncertaintyin Measurement (GUM), uncertainties must be specified for each measurement. Therefore, this work's primary objective is to examine the effect of irregular deformed boundaries on the electromagnetic field and the resonance frequencies of a field generator (TEM-cell). Using a semi-analytical approach, the wave characteristics can be determined and the uncertainty contribution of the field generator can be estimated.
Wolfgang Mathis and Anja Titze
Adv. Radio Sci., 19, 93–104, https://doi.org/10.5194/ars-19-93-2021, https://doi.org/10.5194/ars-19-93-2021, 2021
Short summary
Short summary
In this article, we examined the emergence of the new broadcast medium
Radioin Germany shortly after World War I which is called
Rundfunkin this country and consider the early radio transmitter stations in Eberswalde and Königs Wusterhausen.
Michael Popp and Wolfgang Mathis
Adv. Radio Sci., 16, 89–97, https://doi.org/10.5194/ars-16-89-2018, https://doi.org/10.5194/ars-16-89-2018, 2018
Short summary
Short summary
The simulation of large scale nonlinear dynamical interconnected systems is a usual task. Due to the high complexity of the considered systems, the principle of thinking in hierarchical structures is common among engineers. This contribution proposes an approach for the numerical simulation of large systems, which keeps the hierarchical system structure alive during the entire simulation and order reduction process, which results in several benefits compared with the state of the art.
Harry Weber and Wolfgang Mathis
Adv. Radio Sci., 15, 223–230, https://doi.org/10.5194/ars-15-223-2017, https://doi.org/10.5194/ars-15-223-2017, 2017
Short summary
Short summary
In diesem Beitrag wird eine selbstkonsistente Carleman Linearisierung zur Untersuchung von Oszillatoren vorgestellt. Anstelle einer linearen Näherung um einen Arbeitspunkt, erfolgt mit Hilfe der selbstkonsistenten Carleman Linearisierung eine Approximation auf einem vorgegebenen Gebiet. Um in Anschluss das stationäre Verhalten von Oszillatoren zu beschreiben, wird die Berechnung einer Poincaré-Abbildung durchgeführt. Mit dieser ist eine anschließende Analyse des Oszillators möglich.
Michał Mika, Mirjam Dannert, Felix Mett, Harry Weber, Wolfgang Mathis, and Udo Nackenhorst
Adv. Radio Sci., 15, 55–60, https://doi.org/10.5194/ars-15-55-2017, https://doi.org/10.5194/ars-15-55-2017, 2017
Sven Feldkord, Marco Reit, and Wolfgang Mathis
Adv. Radio Sci., 15, 43–47, https://doi.org/10.5194/ars-15-43-2017, https://doi.org/10.5194/ars-15-43-2017, 2017
Short summary
Short summary
Recently, for modeling biological amplification processes, nonlinear amplifiers based on the Andronov–Hopf bifurcation have become a focus of attention.
In this contribution, we analyze discrete-time implementations of this type of amplifiers. The effects of the time-discretization by explicit integration methods are discussed. A novel discrete-time system based on the Neimark–Sacker bifurcation is introduced, that outstandingly approximates the behavior of a particular Hopf-type amplifier.
Seyed Mohammadamin Moosavi, Christian Widemann, and Wolfgang Mathis
Adv. Radio Sci., 15, 37–41, https://doi.org/10.5194/ars-15-37-2017, https://doi.org/10.5194/ars-15-37-2017, 2017
Harry Weber and Wolfgang Mathis
Adv. Radio Sci., 14, 51–54, https://doi.org/10.5194/ars-14-51-2016, https://doi.org/10.5194/ars-14-51-2016, 2016
Short summary
Short summary
In this contribution, the limitations of the Carleman linearization approach are presented and discussed. The Carleman linearization transforms an ordinary nonlinear differential equation into an infinite system of linear differential equations which cannot be solved in general. Therefore, the infinite dimensional system has to be approximated by a finite one. The idea of this contribution is to use a Taylor series for the approximation of the infinite system.
Sven Feldkord, Marco Reit, and Wolfgang Mathis
Adv. Radio Sci., 14, 47–50, https://doi.org/10.5194/ars-14-47-2016, https://doi.org/10.5194/ars-14-47-2016, 2016
Short summary
Short summary
Recently, nonlinear amplifiers based on the Andronov–Hopf bifurcation have become a focus of attention in modeling of the mammalian hearing organ. We present a flexible framework implemented on a DSP to analyze various bifurcation based amplifiers to get deeper insights in their nonlinear input-output behavior. A comparison shows the Neimark–Sacker amplifier remarkably outperforms the Andronov–Hopf amplifier regarding the CPU usage.
T. Vennemann, T. Frye, Z. Liu, M. Kahmann, and W. Mathis
Adv. Radio Sci., 13, 1–8, https://doi.org/10.5194/ars-13-1-2015, https://doi.org/10.5194/ars-13-1-2015, 2015
E. Hintzen, T. Vennemann, and W. Mathis
Adv. Radio Sci., 12, 49–52, https://doi.org/10.5194/ars-12-49-2014, https://doi.org/10.5194/ars-12-49-2014, 2014
M. Weber, T. Vennemann, and W. Mathis
Adv. Radio Sci., 12, 91–94, https://doi.org/10.5194/ars-12-91-2014, https://doi.org/10.5194/ars-12-91-2014, 2014
Cited articles
Carson, J. R., Mead, S. P., and Schelkunoff, S.: Hyper-frequency wave guides
– mathematical theory, Bell Labs Tech. J., 15, 310–333, 1936. a
Hertz, H.: Die Kräfte electrischer Schwingungen, behandelt nach der
Maxwell'schen Theorie, Ann. Phys., 272, 1–22, 1889. a
Hung-Chia, H.: General theory of nonconventional waveguides for long-distance
transmission, Scientia Sinica, 11, 761–784, 1962. a
Katsenelenbaum, B. Z.: Theory of nonuniform waveguides: the cross-section
method, The Institution of Electrical Engineers, London, UK, 44, 1998. a
Mathis, W. and Mathis, R.: On the derivation of generalized transmission
line
equations of cylindrical waveguides with irregular deformed surfaces, in:
2015 IEEE International Symposium on Electromagnetic Compatibility (EMC),
Vol. 2015-September, 830–833, IEEE, Dresden, Germany 2015. a
Miller, S. and Beck, A.: Low-loss waveguide transmission, P. IRE, 41,
348–358, 1953. a
Miller, S. E.: Coupled wave theory and waveguide applications, Bell Labs
Tech. J., 33, 661–719, 1954a. a
Miller, S. E.: Waveguide as a communication medium, Bell Labs Tech.
J., 33, 1209–1265, 1954b. a
Moon, P. and Spencer, D. E.: Separability conditions for the Laplace and
Helmholtz equations, J. Frankl. Inst., 253, 585–600, 1952. a
Rayleigh, L.: XVIII. On the passage of electric waves through tubes, or the
vibrations of dielectric cylinders, The London, Edinburgh, and Dublin
Philosophical Magazine and Journal of Science, 43, 125–132, 1897. a
Saad, S. M.: Review of numerical methods for the analysis of
arbitrarily-shaped
microwave and optical dielectric waveguides, IEEE T. Microw.
Theory, 33, 894–899, 1985. a
Schelkunoff, S. A.: Transmission theory of plane electromagnetic waves,
P. IRE, 25, 1457–1492, 1937. a
Schelkunoff, S. A.: Applied mathematics for engineers and scientists, van
Nostrand, Princeton, New Jersey, 1951. a
Southworth, G. C.: Principles and applications of waveguide transmission,
Bell
Labs Tech. J., 29, 295–342, 1950. a
Spencer, D. E.: Separation of variables in electromagnetic theory, J.
Appl. Phys., 22, 386–389, 1951. a
Unger, H.-G.: Helix waveguide theory and application, Bell Labs Tech.
J., 37, 1599–1647, 1958. a
Unger, H.-G.: Mode conversion in metallic and helix waveguide, Bell Labs
Tech. J., 40, 613–626, 1961b. a
Unger, H.-G.: Regellose Störungen in Wellenleitern, Arch. Elektr.
Übertrag., 393–401, 1961c. a
Vlasov, A. N. and Antonsen, T. M.: Numerical solution of fields in lossy
structures using MAGY, IEEE T. Electron Dev., 48, 45–55,
https://doi.org/10.1109/16.892166, 2001. a
Weiss, L. and Mathis, W.: Generalized telegraphist's equations for deformed
waveguides, Electromagnetics, 18, 353–365, https://doi.org/10.1080/02726349808908594,
1998. a
Zaginaylov, G. I. and Shcherbinin, V. I.: Analysis and improvement of
convergence of transverse expansions in excitation problems of irregular
impedance waveguides, in: 2016 IEEE International Conference on Mathematical
Methods in Electromagnetic Theory (MMET), 228–231,
https://doi.org/10.1109/MMET.2016.7544039, IEEE, Lviv, Ukraine, 2016. a
Zaginaylov, G. I., Shcherbinin, V. I., and Glyavin, M. Y.: New approach to
the
theory of irregular lossy waveguides and its application to design of
teraherz gyrotrons, in: 2013 European Microwave Conference, 971–974,
IEEE, Nuremberg, Germany,
2013. a
Short summary
This paper deals with the propagation of electromagnetic waves in cylindrical waveguides with irregularly deformed cross-sections. Waveguides are of high interest because of its practical use as a transmission medium. Schelkunoff's method, is a semi-analytical method for computing electromagnetic waves in hollow and cylindrical waveguides bounded by PEC walls. The aim of this paper is to derive the so-called GTE's for irregular deformed waveguides.
This paper deals with the propagation of electromagnetic waves in cylindrical waveguides with...
