Accuracy of Approximate Formulas for Internal Impedance of Tubular Cylindrical Conductors for Large Parameters

Lovrić, Dino; Boras, Vedran; Vujević, Slavko

doi:10.2528/pierm10121503

Cited by 24 publications

(22 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It can be shown that in the DC limit → 0 the imaginary part of the bracket converges to −1/4, so that log( ) adopts its DC value given by equation (17), as expected. The total inductance of a finitely long round wire at arbitrary frequency can be approximated by equation (7) with log( ) given by equation (30), or by its approximate formula (38) based on elementary functions taken from paragraph 6.3.3.…”

Section: Derivation Of the Gmdsupporting

confidence: 73%

“…In the limit → 0 this reduces to the constant −1/4, thus reproducing the GMD of a circular disk as given by equation (17). Inserting equation (22) into (7) yields Wiens's formula for the DC inductance of a tubular conductor of finite length ( [9], p. 938).…”

Section: Tubular Conductor At DCmentioning

confidence: 90%

“…The total inductance of a finitely long tubular conductor at arbitrary frequency can be approximated with the help of equation (7) with log( ) given by equation (49). Note that for large arguments the numerical evaluation of equations (47) -(49) (and (53)) becomes unstable, also in MATLAB ® [17]. The onset of instability with respect to the magnitude of depends on the radius ratio / .…”

Section: Derivation Of the Gmdmentioning

confidence: 99%

“…The larger this ratio, the earlier the onset. Lovrić et al presented a special formula for the internal inductance of a tubular conductor claimed to be stable under all conditions [17].…”

Section: Derivation Of the Gmdmentioning

confidence: 99%

See 3 more Smart Citations

The GMD Method for Inductance Calculation Applied to Conductors with Skin Effect

Aebischer¹,

Aebischer

2017

AEM

View full text Add to dashboard Cite

The GMD method (geometric mean distance) to calculate inductance offers undoubted advantages over other methods. But so far it seemed to be limited to the case where the current is uniformly distributed over the cross section of the conductor, i.e. to DC (direct current). In this paper, the definition of the GMD is extended to include cases of nonuniform distribution observed at higher frequencies as the result of skin effect. An exact relation between the GMD and the internal inductance per unit length for infinitely long conductors of circularly symmetric cross section is derived. It enables much simpler derivations of Maxwell's analytical expressions for the GMD of circular and annular disks than were known before. Its salient application, however, is the derivation of exact expressions for the GMD of infinitely long round wires and tubular conductors with skin effect. These expressions are then used to verify the consistency of the extended definition of the GMD. Further, approximate formulae for the GMD of round wires with skin effect based on elementary functions are discussed. Total inductances calculated with the help of the derived formulae for the GMD with and without skin effect are compared to measurement results from the literature. For conductors of square cross section, an analytical approximation for the GMD with skin effect based on elementary functions is presented. It is shown that it allows to calculate the total inductance of such conductors for frequencies from DC up to 25 GHz to a precision of better than 1 %.

show abstract

Section: Derivation Of the Gmdsupporting

confidence: 73%

Section: Tubular Conductor At DCmentioning

confidence: 90%

Section: Derivation Of the Gmdmentioning

confidence: 99%

“…The larger this ratio, the earlier the onset. Lovrić et al presented a special formula for the internal inductance of a tubular conductor claimed to be stable under all conditions [17].…”

Section: Derivation Of the Gmdmentioning

confidence: 99%

See 2 more Smart Citations

The GMD Method for Inductance Calculation Applied to Conductors with Skin Effect

Aebischer¹,

Aebischer

2017

AEM

View full text Add to dashboard Cite

show abstract

“…Recently, the interest in circular and tubular geometries has apparently rebirth [10][11][12][13][14][15][16][17][18][19][20][21], however, most of published work has been focused on the development of approximate formulas for internal impedance evaluation of homogeneous structures. Those formulas are basically used to circumvent the troublesome computation of Bessel functions.…”

Section: Introductionmentioning

confidence: 99%

Skin Effect in Inhomogeneous Euler-Cauchy Tubular Conductors

Faria¹

2011

PIER M

View full text Add to dashboard Cite

Abstract-This paper presents a novel contribution to the analysis of skin effect phenomena in inhomogeneous tubular conductors. For homogeneous tubular geometries the skin effect diffusion equation has an analytical solution described by a combination of Bessel functions, but, when the conductivity and magnetic permeability of the tubular conductor arbitrarily depend on the radial coordinate an analytical solution cannot be found. However, this work shows that simple closed form solutions for the electromagnetic field and conductor internal impedance do exist, provided that a specific type of radial variation of medium parameters is properly chosen -these novel structures are coined here Euler-Cauchy Structures. Analytic and computation results concerning general and particular Euler-Cauchy Structures are presented, validated, and discussed. Future research on this seminal topic may lead to new engineering applications.

show abstract

The high‐frequency phenomenon of copper clad aluminum wires which are lower the alternating current resistance than copper solid wires, and the application of copper clad aluminum wires to the electrical equipment

Ueda¹,

Hung²

2023

Electrical Engineering Japan

View full text Add to dashboard Cite

The paper is proposed approximate formulas of the ac resistance of lead wires and coils which made by using copper clad aluminum (CCA) wires. There are the frequency range that the ac resistance of CCA wires is lower than it of cupper solid wires for lead wires and coils of an electrical equipment. It is shown that the application of CCA wires is economical as comparing with copper solid wires, if the design is due to successful calculation in the electrical equipment. The measured resistance is compared with the formula. CCA wires is an example of multiple conductors which shall be expected to apply in future.

show abstract

Accuracy of Approximate Formulas for Internal Impedance of Tubular Cylindrical Conductors for Large Parameters

Cited by 24 publications

References 12 publications

The GMD Method for Inductance Calculation Applied to Conductors with Skin Effect

The GMD Method for Inductance Calculation Applied to Conductors with Skin Effect

Skin Effect in Inhomogeneous Euler-Cauchy Tubular Conductors

The high‐frequency phenomenon of copper clad aluminum wires which are lower the alternating current resistance than copper solid wires, and the application of copper clad aluminum wires to the electrical equipment

Contact Info

Product

Resources

About