Formulas for the Skin Effect
01 Sep 1942-Vol. 30, Iss: 9, pp 412-424
TL;DR: In this article, the skin effect is used to determine the surface resistivity of conductors at a wide range of frequency bands, including those of wires, transmission lines, and coils.
Abstract: At radio frequencies, the penetration of currents and magnetic fields into the surface of conductors is governed by the skin effect. Many formulas are simplified if expressed in terms of the "depth of penetration," which has merely the dimension of length but involves the frequency and the conductivity and permeability of the conductive material. Another useful parameter is the "surface resistivity" determined by the skin effect, which has simply the dimension of resistance. These parameters are given for representative metals by a convenient chart covering a wide range of frequency. The "incremental-inductance rule" is given for determining not only the effective resistance of a circuit but also the added resistance caused by conductors in the neighborhood of the circuit. Simple formulas are given for the resistance of wires, transmission lines, and coils; for the shielding effect of sheet metal; for the resistance caused by a plane or cylindrical shield near a coil; and for the properties of a transformer with a laminated iron core.
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JDSU1
TL;DR: The lithium-niobate external-modulator technology meets the performance and reliability requirements of current 2.5-, 10-Gb/s digital communication systems, as well as CATV analog systems, and multiple high-speed modulation functions have been achieved in a single device.
Abstract: The current status of lithium-niobate external-modulator technology is reviewed with emphasis on design, fabrication, system requirements, performance, and reliability. The technology meets the performance and reliability requirements of current 2.5-, 10-, and 40-Gb/s digital communication systems, as well as CATV analog systems. The current trend in device topology is toward higher data rates and increased levels of integration. In particular, multiple high-speed modulation functions, such as 10-Gb/s return-to-zero pulse generation plus data modulation, have been achieved in a single device.
1,221 citations
Cites background from "Formulas for the Skin Effect"
...RF loss can also be adequately determined at high frequencies (>2 GHz) with Wheeler’s inductance rule [29]....
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TL;DR: In this paper, a patterned ground shield is inserted between an on-chip spiral inductor and silicon substrate to increase the quality of a 2 GHz LC tank by up to 33% and reduce substrate coupling between two adjacent inductors.
Abstract: This paper presents a patterned ground shield inserted between an on-chip spiral inductor and silicon substrate. The patterned ground shield can be realized in standard silicon technologies without additional processing steps. The impacts of shield resistance and pattern on inductance, parasitic resistances and capacitances, and quality factor are studied extensively. Experimental results show that a polysilicon patterned ground shield achieves the most improvement. At 1-2 GHz, the addition of the shield increases the inductor quality factor up to 33% and reduces the substrate coupling between two adjacent inductors by as much as 25 dB. We also demonstrate that the quality factor of a 2-GHz LC tank can be nearly doubled with a shielded inductor.
1,197 citations
Cites background from "Formulas for the Skin Effect"
...As the magnetic field passes through the patterned ground shield, its intensity is weakened due to the skin effect [14]....
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...To extract , , and from the real and imaginary parts of the measured series impedance, some assumptions about and need to be made. and are subject to skin effect, which governs the magnetic field intensity and current density in the conductor at high frequencies [14] ....
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TL;DR: In this article, the authors present a physical model for planar spiral inductors on silicon, which accounts for eddy current effect in the conductor, crossover capacitance between the spiral and center-tap, capacitance in the spiral, substrate ohmic loss, and substrate capacitance.
Abstract: This paper presents a physical model for planar spiral inductors on silicon, which accounts for eddy current effect in the conductor, crossover capacitance between the spiral and center-tap, capacitance between the spiral and substrate, substrate ohmic loss, and substrate capacitance. The model has been confirmed with measured results of inductors having a wide range of layout and process parameters. This scalable inductor model enables the prediction and optimization of inductor performance.
867 citations
Cites background from "Formulas for the Skin Effect"
...It is difficult to analytically determine the significance of the mutual eddy current and resistance caused by the proximity effect [19]....
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...The eddy current effect occurs when a conductor is subjected to time-varying magnetic fields and is governed by Faraday’s law [19], [20]....
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12 Jun 1997
TL;DR: In this paper, a patterned ground shield is proposed to reduce the unwanted substrate effects by shielding the electric field of an on-chip spiral inductor from the silicon substrate, which can be realized in standard silicon technologies without additional processing steps.
Abstract: This paper presents a patterned ground shield in- serted between an on-chip spiral inductor and silicon substrate. The patterned ground shield can be realized in standard silicon technologies without additional processing steps. The impacts of shield resistance and pattern on inductance, parasitic resistances and capacitances, and quality factor are studied extensively. Experimental results show that a polysilicon patterned ground shield achieves the most improvement. At 1-2 GHz, the addition of the shield increases the inductor quality factor up to 33% and reduces the substrate coupling between two adjacent inductors by as much as 25 dB. We also demonstrate that the quality factor of a 2-GHz tank can be nearly doubled with a shielded inductor. In this paper, we present a patterned ground shield, which is compatible with standard silicon technologies, to reduce the unwanted substrate effects. To provide some background, Section II presents a discussion on the fundamental definitions of an inductor and an tank . Next, a physical model for spiral inductors on silicon is described. The magnetic energy storage and loss mechanisms in an on-chip inductor are discussed. Based on this insight, it is shown that energy loss can be reduced by shielding the electric field of the inductor from the silicon substrate. Then, the drawbacks of a solid ground shield are analyzed. This leads to the design of a patterned ground shield. Design guidelines for parameters such as shield pattern and resistance are given. In Section III, experiment design, on-wafer testing technique, and parasitic extraction procedure are presented. Experimental results are then reported to study the effects of shield resistance and pattern on inductance, parasitic resistances and capacitances, and inductor . Next, the improvement in of a 2-GHz tank using a shielded inductor is illustrated. A study of the noise coupling between two adjacent inductors and the efficiency of the ground shield for isolation are also presented. Lastly, Section IV gives some conclusions.
736 citations
Cites background from "Formulas for the Skin Effect"
...As the magnetic field passes through the patterned ground shield, its intensity is weakened due to the skin effect [14]....
[...]
...and are subject to skin effect, which governs the magnetic field intensity and current density in the conductor at high frequencies [14]....
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TL;DR: This work outlined the theoretical foundation of optimal power transmission efficiency in an inductive link, and combined it with semi-empirical models to predict parasitic components in PSCs to devise an iterative PSC design methodology that starts with a set of realistic design constraints and ends with the optimal PSC pair geometries.
Abstract: The next generation of implantable high-power neuroprosthetic devices such as visual prostheses and brain computer interfaces are going to be powered by transcutaneous inductive power links formed between a pair of printed spiral coils (PSC) that are batch-fabricated using micromachining technology. Optimizing the power efficiency of the wireless link is imperative to minimize the size of the external energy source, heating dissipation in the tissue, and interference with other devices. Previous design methodologies for coils made of 1-D filaments are not comprehensive and accurate enough to consider all geometrical aspects of PSCs with planar 3-D conductors as well as design constraints imposed by implantable device application and fabrication technology. We have outlined the theoretical foundation of optimal power transmission efficiency in an inductive link, and combined it with semi-empirical models to predict parasitic components in PSCs. We have used this foundation to devise an iterative PSC design methodology that starts with a set of realistic design constraints and ends with the optimal PSC pair geometries. We have executed this procedure on two design examples at 1 and 5 MHz achieving power transmission efficiencies of 41.2% and 85.8%, respectively, at 10-mm spacing. All results are verified with simulations using a commercial field solver (HFSS) as well as measurements using PSCs fabricated on printed circuit boards.
616 citations
Additional excerpts
...INDUCTIVE COUPLING AND POWER EFFICIENCY THEORY...
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References
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TL;DR: In this article, the theory of transmission over a coaxial circuit and of the shielding against inductive effects which is afforded by the outer conductor has been discussed and extended beyond the range of present application both as regards structure and frequency.
Abstract: A form of circuit which is of considerable interest for the transmission of high frequency currents is one consisting of a cylindrical conducting tube within which a smaller conductor is coaxially placed. Such tubes have found application in radio stations to connect transmitting and receiving apparatus to antennae. As a part of the development work on such coaxial systems, it has been necessary to formulate the theory of transmission over a coaxial circuit and of the shielding against inductive effects which is afforded by the outer conductor. This paper deals generally with the transmission theory of coaxial circuits and extends the theory beyond the range of present application both as regards structure and frequency.
520 citations
TL;DR: This paper calls attention to the practical value of a more extended use of the impedance concept, which brings out a certain underlying unity in what otherwise appear diverse physical phenomena.
Abstract: This paper calls attention to the practical value of a more extended use of the impedance concept. It brings out a certain underlying unity in what otherwise appear diverse physical phenomena. Although an attempt has been made to trace the history of the concept of “impedance” and many interesting early suggestions have been found, reference to these lies beyond the scope of this paper. Apparently, Sir Oliver Lodge was the first to use the word “impedance,” but the concept has been developed gradually as circumstances demanded through the efforts of countless workers. The main body of the paper is divided into three parts: Part I, dealing with the exposition of the impedance idea as applied to different types of physical phenomena; Part II, in which the general formulae are deduced for reflection and transmission coefficients; Part III, presenting some special applications illustrating the practical utility of the foregoing manner of thought.
184 citations
127 citations
TL;DR: In this article, the proximity effect of wave propagation over parallel wires has been studied in the context of parallel wireless networks, and the authors propose a solution to the problem of proximity effect.
Abstract: (1921). LIV. Wave propagation over parallel wires: The proximity effect. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science: Vol. 41, No. 244, pp. 607-633.
42 citations