Advanced Eigenvalue Tracking of Characteristic Modes

Safin, Eugen; Manteuffel, Dirk

doi:10.1109/tap.2016.2556698

Cited by 41 publications

(53 citation statements)

References 20 publications

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“…2) Mode Degeneracy: Degeneracy can be traced back to the geometrical symmetries of the Ω region [37], [58], [59] and it poses complications with mode tracking [22], [38], [42]. A spherical shell has a degeneracy [50] of…”

Section: A Known Numerical Issuesmentioning

confidence: 99%

“…As a testing object we propose a perfectly electrically conducting (PEC) sphere for which the characteristic eigenvalues and characteristic eigencurrents are known analytically [1]. The symmetry of the spherical shell also introduces eigenspace degeneration [37] which, together with the null-space of the impedance operator at internal resonances of the shell [34], introduces serious problems with modal tracking [38]- [42].…”

Section: Introductionmentioning

confidence: 99%

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Validating the Characteristic Modes Solvers

Čapek

Losenicky

Jelínek

et al. 2017

IEEE Trans. Antennas Propagat.

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Abstract-Characteristic modes of a spherical shell are found analytically as spherical harmonics normalized to radiate unitary power and to fulfill specific boundary conditions. The presented closed-form formulas lead to a proposal of precise synthetic benchmarks which can be utilized to validate the method of moments matrix or performance of characteristic mode decomposition. Dependence on the mesh size, electrical size and other parameters can systematically be studied, including the performance of various mode tracking algorithms. A noticeable advantage is the independence on feeding models. Both theoretical and numerical aspects of characteristic mode decomposition are discussed and illustrated by examples. The performance of state-of-the-art commercial simulators and academic packages having been investigated, we can conclude that all contemporary implementations are capable of identifying the first dominant modes while having severe difficulties with higher-order modes. Surprisingly poor performance of the tracking routines is observed notwithstanding the recent ambitious development.Index Terms-Eigenvalues and eigenfunctions, convergence of numerical methods, numerical analysis, numerical stability.

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Section: A Known Numerical Issuesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Validating the Characteristic Modes Solvers

Čapek

Losenicky

Jelínek

et al. 2017

IEEE Trans. Antennas Propagat.

View full text Add to dashboard Cite

show abstract

“…The results presented in Fig. 1 demonstrate the impact of modal tracking as well as some of the shortcomings of current and field correlation based tracking algorithms previously discussed in the literature [3], [5], [6]. Specifically, it is observed that tracking problems commonly occur in regions where modal eigenvalue traces cross or come very near one another.…”

Section: A Characteristic Modesmentioning

confidence: 61%

“…In such a case, it must be stated that the solution presented in Fig. 12 is the only correct solution 6 for both arrangements irrespective of how close in appearance (how small ∆ is) the structures are to each other.…”

Section: A On the Physical Importance Of Modal Trackingmentioning

confidence: 99%

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Modal Tracking Based on Group Theory

Mášek

Čapek

Jelínek

et al. 2020

IEEE Trans. Antennas Propagat.

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Issues in modal tracking in the presence of crossings and crossing avoidances between eigenvalue traces are solved via the theory of point groups. The von Neumann-Wigner theorem is used as a key factor in predictively determining mode behavior over arbitrary frequency ranges. The implementation and capabilities of the proposed procedure are demonstrated using characteristic mode decomposition as a motivating example. The procedure is, nevertheless, general and can be applied to an arbitrarily parametrized eigenvalue problems. A treatment of modal degeneracies is included and several examples are presented to illustrate modal tracking improvements and the immediate consequences of improper modal tracking. An approach leveraging a symmetry-adapted basis to accelerate computation is also discussed. A relationship between geometrical and physical symmetries is demonstrated on a practical example.

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Preprocessing for characteristic mode tracking based on the correlation

Liu

Yang

et al. 2020

Int J Numerical Modelling

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Mode swapping in characteristic mode analysis (CMA) affects consistent interpretation of the modal data. Mode tracking based on the eigenvector correlation can effectively determine the correct ordering of modes at each sampling frequency. However, there has been a lack of corresponding preprocessing for this mode-tracking algorithm. For example, the applicable frequency band cannot be determined in advance. In this paper, cosine similarity is used to calculate the correlation between modes of adjacent frequencies. It is then proposed that the 3/2 proportional relationship between the maximum size of the structure and the minimum operating wavelength can be used to choose the reliable operating band range of the algorithm. Meanwhile, it is recommended that the meshing side length should be less than one-tenth of a wavelength, and the adjacent sampling frequency interval should be less than the relative bandwidth of 10%. Through this preprocessing, correlation-based algorithms can efficiently implement mode tracking for open conductors.

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Advanced Eigenvalue Tracking of Characteristic Modes

Cited by 41 publications

References 20 publications

Validating the Characteristic Modes Solvers

Validating the Characteristic Modes Solvers

Modal Tracking Based on Group Theory

Preprocessing for characteristic mode tracking based on the correlation

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