Proximity Effect in Wires and Thin Tubes

Dwight, H. B.

doi:10.1109/t-aiee.1923.5060915

Cited by 51 publications

(13 citation statements)

References 13 publications

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“…Equation (9) is well known in transmission line theory; its general solution can be written in the form (11) where A and B are arbitrary constants. The solutions of (10) are Bessel functions.…”

Section: Exponential Propagationmentioning

confidence: 99%

“…16 Our standard practice of neglecting the longitudinal displacement currents has given us the general rule that 27rpH., = I is independent of p. On the other hand, r is very small; if air is the dielectric between the conductors, r is of the order of (1/3)iw to-10 • Hence, even at high frequencies r 2 is negligibly small by comparison with 0-2 and we can rewrite (54) as follows: (55) This is Bessel's equation and its solution can be written down at once 16 as (56) where the functions 1, (11) and K,(u) are the modified Bessel junctions oj the first order and respectively oj the first and second kind. For large values of the argument we have approximately…”

Section: Current Distribution In Cylindrical Conductorsmentioning

confidence: 99%

“…This field is impressed upon the inner surface of the outer conductor 33 and the resulting power loss equals, by equation (136), the real part of (140) where at high frequencies 11 aa The radius of this surface is designated by 4. M At low frequencies '1 has to be replaced by the radial impedance looking into the shield.…”

Section: Power Losses In Shieldsmentioning

confidence: 99%

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The Electromagnetic Theory of Coaxial Transmission Lines and Cylindrical Shields

Schelkunoff¹

1934

Bell System Technical Journal

480

166

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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 antennre. 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.

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Section: Exponential Propagationmentioning

confidence: 99%

Section: Current Distribution In Cylindrical Conductorsmentioning

confidence: 99%

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The Electromagnetic Theory of Coaxial Transmission Lines and Cylindrical Shields

Schelkunoff¹

1934

Bell System Technical Journal

480

166

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“…Dwight proposed several ac loss models for tubes and other shapes mainly based on the solution of the current density in the conductor. In general, his works described approximate solutions mainly based on asymptotic tendencies at both low and high frequencies [1][2][3][4][5] . 20 Similarly, Arnold developed an approximate solution based on Dwight's results [6].…”

Section: Introductionmentioning

confidence: 99%

Analytical solution of the induced currents in multilayer cylindrical conductors under external electromagnetic sources

Acero

Carretero

Lope³

et al. 2016

Applied Mathematical Modelling

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We present a closed-form solution for the induced losses in round conductors consisting of several concentric layers. The geometry under study corresponds to an infinitely-long and isolated multilayer cylinder where layers can have different electromagnetic properties and the number of layers is not restricted. The multilayer conductor is under an external time-varying magnetic field which induces currents and, accordingly, generates Joule dissipation. Total induced losses are obtained by integrating the losses of each layer. Mathematical expressions of the current distribution in each layer are derived from the solution of Maxwells equations. These expressions consist of a combination of Bessel functions of different kinds and orders. The current distribution in a particular layer not only depends on the properties of the layer but also on the properties of the rest of layers. Consequently, matrix formalism is adopted for describing current distribution of layers. Matrix description is numerically solved and results are compared with finite element simulations for different arrangements and cases.

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“…. The coefficients fcj to k n are progressively less important in determining the values of R'/R as n increases, and it is proposed in this paper to solve equation (2) only as far as fc 6 .…”

mentioning

confidence: 99%

The alternating-current resistance of parallel conductors of circular cross-section

Arnold¹

1935

Journal of the Institution of Electrical Engineers

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Proximity Effect in Wires and Thin Tubes

Cited by 51 publications

References 13 publications

The Electromagnetic Theory of Coaxial Transmission Lines and Cylindrical Shields

The Electromagnetic Theory of Coaxial Transmission Lines and Cylindrical Shields

Analytical solution of the induced currents in multilayer cylindrical conductors under external electromagnetic sources

The alternating-current resistance of parallel conductors of circular cross-section

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