Skin Effect

Olyslager, Frank; Zutter, D. De

doi:10.1002/0471654507.eme396

Cited by 6 publications

(7 citation statements)

References 3 publications

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“…However, when the conductor is partly contained in one layer and partly in another, the conductor will have to be divided in two separate parts, as correctly remarked by one of the reviewers. Inside , satisfies (1) with (2) On the boundary of , we have that (3) with the index referring to the tangential component of the magnetic field. The expression stands for the limit of the normal derivative of the electric field tending from the inside of the cylinder to .…”

Section: Differential Surface Admittance Conceptmentioning

confidence: 99%

“…Only for the highest frequencies and provided the skin depth becomes much smaller than both and , the well-known skin effect occurs. In this case, the current is flowing in a small surface layer and the behavior of the conductor is usually described in terms of the surface impedance [2]. It is clear that accurate electromagnetic modeling tools need to correctly account for the redistribution of the conductor current.…”

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confidence: 99%

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Skin effect modeling based on a differential surface admittance operator

Zutter

Knockaert

2005

IEEE Trans. Microwave Theory Techn.

133

176

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Abstract-An important issue in high-frequency signal integrity prediction is the modeling of the skin effect of thick conductors. A new differential surface admittance concept is put forward allowing to replace the conductor by equivalent electric surface currents and to replace the material of the conductor by the material of the background medium the conductor is embedded in. This new concept is studied in detail for the two-dimensional TM case starting from the Dirichlet eigenfunctions of the cross section. Detailed expressions are derived for the important practical case of a rectangular cross section. Next, the differential surface admittance operator is exploited to determine the resistance and inductance matrices of a set of multiconductor lines. A first set of numerical results provides the reader with some insight into the behavior of the surface admittance matrix. A second set of results demonstrates the correctness and versatility of the new approach to determine inductance and resistance matrices.

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Section: Differential Surface Admittance Conceptmentioning

confidence: 99%

mentioning

confidence: 99%

Skin effect modeling based on a differential surface admittance operator

Zutter

Knockaert

2005

IEEE Trans. Microwave Theory Techn.

133

176

View full text Add to dashboard Cite

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“…When modeling finite thickness conductors for packaging applications, the full modeling of the interior of the conductor is often avoided by introducing a suitable local surface impedance model [5]- [8]. In that case, only the local thickness of the conductor is taken into account.…”

Section: Local Surface Impedance Approximationmentioning

confidence: 99%

“…In the 1-D approximation, fictitious electric surface currents at the top and bottom of the conductor, both depending on the electric field at the top and at the bottom of the conductor, describe the conductor's behavior over the complete frequency range. This approximation is compared to the usual surface impedance of a conductor of thickness [5]- [8] and illustrated for a conductor above a ground plane.…”

Section: Introductionmentioning

confidence: 99%

Surface Current Modelling of the Skin Effect for On-Chip Interconnections

Zutter

Rogier

Knockaert

et al. 2007

IEEE Trans. Adv. Packag.

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Abstract-In this paper, the skin effect for 2-D on-chip interconnections is predicted using a recently developed differential surface admittance concept. First, the features of the new approach are briefly recapitulated and details are given for a conductor with rectangular cross-section. Next, the 1-D situation is studied as a limiting case of the 2-D situation. The relationship with a local impedance formulation is investigated and illustrated with a numerical example. Finally, the new method is used to determine inductance and resistance matrices of 2-D on-chip interconnect examples with specifications taken from the International Technology Roadmap for Semiconductors. Extra capacitance data are also provided.Index Terms-On-chip interconnect, resistance and inductance matrices, skin effect, surface impedance/admittane.

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“…18 In the realm of MHz time-varying fields, most of the electric current is confined to skin depths on the order of $1-20 lm and is inversely proportional to frequency. It is also highly dependent of the resistivity of the conductor.…”

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confidence: 99%

Unique heating curves generated by radiofrequency electric-field interactions with semi-aqueous solutions

Lara

Haider

Wilson

et al. 2017

Applied Physics Letters

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Aqueous and nanoparticle-based solutions have been reported to heat when exposed to an alternating radiofrequency (RF) electric-field. Although the theoretical models have been developed to accurately model such a behavior given the solution composition as well as the geometrical constraints of the sample holder, these models have not been investigated across a wide-range of solutions where the dielectric properties differ, especially with regard to the real permittivity. In this work, we investigate the RF heating properties of non-aqueous solutions composed of ethanol, propylene glycol, and glycine betaine with and without varying amounts of NaCl and LiCl. This allowed us to modulate the real permittivity across the range 25-132, as well as the imaginary permittivity across the range 37-177. Our results are in excellent agreement with the previously developed theoretical models. We have shown that different materials generate unique RF heating curves that differ from the standard aqueous heating curves. The theoretical model previously described is robust and accounts for the RF heating behavior of materials with a variety of dielectric properties, which may provide applications in non-invasive RF cancer hyperthermia. Published by AIP Publishing.[http://dx.doi.org/10.1063/1.4973218] It has been shown that saline solutions under exposure to radiofrequency (RF) electric fields display peak heating behavior at a certain concentration, 1,2 and this behavior has been generalized to include any aqueous system, regardless of the content or identity, including buffer solutions, blood, and nanoparticle suspensions.3 These studies however, are limited to aqueous systems and until now the theoretical models used to explain this behavior have not been validated for other materials. To fully characterize RF heating, materials representing a wider range of dielectric properties must be studied. Such an understanding may have direct applications in non-invasive RF cancer hyperthermia therapy. [4][5][6][7][8][9] Although most tissues in the human body are made up primarily of water and other tissues, such as fat and bone, have drastically different dielectric properties and are expected to behave differently. Overheating of the subcutaneous fat layer, for example, is a major limiting factor in hyperthermia cancer therapy (especially at 13.56 MHz) and must be overcome if this technology is to be safely implemented in the clinic. 10In this study we probe the dielectric and heating properties of materials with reduced water content and variable conductivity. Experimental RF heating curves similar to those of aqueous solutions are generated for each material, and these are used to confirm the generalization of the theoretical heating model to a wider range of systems. The dielectric properties, such as permittivity, of a material describe its response to electromagnetic (EM) fields. For time-varying alternating electric fields, the permittivity becomes a complex parameter given by the equationwhere e r , e 0 r , e 00 r are the co...

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Skin Effect

Cited by 6 publications

References 3 publications

Skin effect modeling based on a differential surface admittance operator

Skin effect modeling based on a differential surface admittance operator

Surface Current Modelling of the Skin Effect for On-Chip Interconnections

Unique heating curves generated by radiofrequency electric-field interactions with semi-aqueous solutions

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