High-Frequency Impedance of Rotationally Symmetric Two-Terminal Linear Passive Devices: Application to Parallel Plate Capacitors with a Lossy Dielectric Core and Lossy Thick Plates
Linear passive electrical devices/components are usually characterized in the frequency domain by their impedance, i.e., the ratio of the voltage and current phasors. The use of the impedance concept does not raise particular concerns in low-frequency regimes; however, things become more complicated...
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2025-07-01
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| author | José Brandão Faria |
| author_facet | José Brandão Faria |
| author_sort | José Brandão Faria |
| collection | DOAJ |
| description | Linear passive electrical devices/components are usually characterized in the frequency domain by their impedance, i.e., the ratio of the voltage and current phasors. The use of the impedance concept does not raise particular concerns in low-frequency regimes; however, things become more complicated when it comes to rapid time-varying phenomena, mainly because the voltage depends not only on the position of the points between which it is defined but also on the choice of the integration path that connects them. In this article, based on first principles (Maxwell equations and Poynting vector flow considerations), we discuss the concept of impedance and define it unequivocally for a class of electrical devices/components with rotational symmetry. Two application examples are presented and discussed. One simple example concerns the per-unit-length impedance of a homogeneous cylindrical wire subject to the skin effect. The other, which is more elaborate, concerns a heterogeneous structure that consists of a dielectric disk sandwiched between two metal plates. For the lossless situation, the high-frequency impedance of this device (circular parallel plate capacitor) reaches zero when the frequency reaches a certain critical frequency f<sub>c</sub>; then, it becomes inductive and increases enormously when the frequency reaches another critical frequency at 1.6 f<sub>c</sub>. The influence of losses on the impedance of the device is thoroughly investigated and evaluated. Impedance corrections due to dielectric losses are analyzed using a frequency-dependent Debye permittivity model. The impedance corrections due to plate losses are analyzed by considering radial current distributions on the outer and inner surfaces of the plates, the latter exhibiting significant variations near the critical frequencies of the device. |
| format | Article |
| id | doaj-art-227c8071b905432bb317b0f7ddd2db9b |
| institution | DOAJ |
| issn | 1996-1073 |
| language | English |
| publishDate | 2025-07-01 |
| publisher | MDPI AG |
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| series | Energies |
| spelling | doaj-art-227c8071b905432bb317b0f7ddd2db9b2025-08-20T03:07:58ZengMDPI AGEnergies1996-10732025-07-011814373910.3390/en18143739High-Frequency Impedance of Rotationally Symmetric Two-Terminal Linear Passive Devices: Application to Parallel Plate Capacitors with a Lossy Dielectric Core and Lossy Thick PlatesJosé Brandão Faria0Instituto de Telecomunicações, Instituto Superior Técnico, Universidade de Lisboa, 1049-001 Lisbon, PortugalLinear passive electrical devices/components are usually characterized in the frequency domain by their impedance, i.e., the ratio of the voltage and current phasors. The use of the impedance concept does not raise particular concerns in low-frequency regimes; however, things become more complicated when it comes to rapid time-varying phenomena, mainly because the voltage depends not only on the position of the points between which it is defined but also on the choice of the integration path that connects them. In this article, based on first principles (Maxwell equations and Poynting vector flow considerations), we discuss the concept of impedance and define it unequivocally for a class of electrical devices/components with rotational symmetry. Two application examples are presented and discussed. One simple example concerns the per-unit-length impedance of a homogeneous cylindrical wire subject to the skin effect. The other, which is more elaborate, concerns a heterogeneous structure that consists of a dielectric disk sandwiched between two metal plates. For the lossless situation, the high-frequency impedance of this device (circular parallel plate capacitor) reaches zero when the frequency reaches a certain critical frequency f<sub>c</sub>; then, it becomes inductive and increases enormously when the frequency reaches another critical frequency at 1.6 f<sub>c</sub>. The influence of losses on the impedance of the device is thoroughly investigated and evaluated. Impedance corrections due to dielectric losses are analyzed using a frequency-dependent Debye permittivity model. The impedance corrections due to plate losses are analyzed by considering radial current distributions on the outer and inner surfaces of the plates, the latter exhibiting significant variations near the critical frequencies of the device.https://www.mdpi.com/1996-1073/18/14/3739complex impedancecylindrical geometrydielectric losseselectromagnetic field modelinghigh frequency analysisparallel plate capacitor |
| spellingShingle | José Brandão Faria High-Frequency Impedance of Rotationally Symmetric Two-Terminal Linear Passive Devices: Application to Parallel Plate Capacitors with a Lossy Dielectric Core and Lossy Thick Plates Energies complex impedance cylindrical geometry dielectric losses electromagnetic field modeling high frequency analysis parallel plate capacitor |
| title | High-Frequency Impedance of Rotationally Symmetric Two-Terminal Linear Passive Devices: Application to Parallel Plate Capacitors with a Lossy Dielectric Core and Lossy Thick Plates |
| title_full | High-Frequency Impedance of Rotationally Symmetric Two-Terminal Linear Passive Devices: Application to Parallel Plate Capacitors with a Lossy Dielectric Core and Lossy Thick Plates |
| title_fullStr | High-Frequency Impedance of Rotationally Symmetric Two-Terminal Linear Passive Devices: Application to Parallel Plate Capacitors with a Lossy Dielectric Core and Lossy Thick Plates |
| title_full_unstemmed | High-Frequency Impedance of Rotationally Symmetric Two-Terminal Linear Passive Devices: Application to Parallel Plate Capacitors with a Lossy Dielectric Core and Lossy Thick Plates |
| title_short | High-Frequency Impedance of Rotationally Symmetric Two-Terminal Linear Passive Devices: Application to Parallel Plate Capacitors with a Lossy Dielectric Core and Lossy Thick Plates |
| title_sort | high frequency impedance of rotationally symmetric two terminal linear passive devices application to parallel plate capacitors with a lossy dielectric core and lossy thick plates |
| topic | complex impedance cylindrical geometry dielectric losses electromagnetic field modeling high frequency analysis parallel plate capacitor |
| url | https://www.mdpi.com/1996-1073/18/14/3739 |
| work_keys_str_mv | AT josebrandaofaria highfrequencyimpedanceofrotationallysymmetrictwoterminallinearpassivedevicesapplicationtoparallelplatecapacitorswithalossydielectriccoreandlossythickplates |