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Use of Ritz and Bubnow-Galerkin methods for calculation of inductance and impedance of conductors

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It is shown that the Ritz and Bubnow-Galerkin methods can be applied for the calculation of the inductance and the impedance, respectively. Moreover it is shown that the calculation of the impedance by the Bubnow-Galerkin method is a generalization of the calculation of the inductance by the Ritz method in the case of a nonhomogeneous Neumann boundary problem. For the illustration of these methods the inductance of a rectangular ferromagnetic conductor and the inner impedance of a rectangular conductor placed in a semi-closed slot are calculated.

Übersicht

In der Arbeit wird bewiesen, daß man die Methoden von Ritz und Bubnow-Galerkin zur Berechnung der Induktivität und der Impedanz anwenden kann. Überdies wird gezeigt, daß die Berechnung der Impedanz mit Hilfe der Methode von Bubnow-Galerkin eine Verallgemeinung der Berechnung der Induktivität mit Hilfe der Ritz-Methode für die ungleichartigen Randbedingungen des Neumann-Problems bildet.

Zur Illustration der Methoden werden die Induktivität des rechteckigen ferromagnetischen Leiters und die innere Impedanz des rechteckigen Leiters in der halbgeschlossenen Nut berechnet.

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Abbreviations

A :

Component of the vector potential to thez-axis (complex v. m. s. value)

B t,B n :

Tangential and normal component of magnetic induction (complex r. m. s. values)

C,C 0,K :

Operators in a Hilbert space

H :

Hilbert space

\(H_{C_0 } \) :

Energetic space of a positive definite operator

I=\I\eiψ :

Complex value of the current, |I|=r. m. s. value

\(j = \sqrt { - 1} \) :

Imaginary unit

J :

Current density (complex r. m. s. value)

l :

Conductor length

L, L(ω):

Inductance

Z :

Impedance

z * :

Dimension coupled with complex dimensionz

μ:

Magnetic permeability

ψ:

Conductance

ω:

Pulsation

\(\frac{\partial }{{\partial n}},\frac{\partial }{{\partial t}}\) :

Derivative in normal external direction and tangential direction

Δ:

Scalar Laplacian

1 t,1 n :

Unit vectors, tangential and normal to the curve lying in thex,y-plane

(x/y):

Scalar product of Hilbert space elementsx, y

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Authors and Affiliations

  1. 70/3 Poniatowski St., 71-112, Szczecin, Poland

    J. Purczyński

  2. 3 Szwoleżerów St., 71-062, Szczecin, Poland

    P. Rolicz

  3. 6/4 Podhalańska St., 70-452, Szczecin, Poland

    R. Sikora

Authors
  1. J. Purczyński
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  2. P. Rolicz
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  3. R. Sikora
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Purczyński, J., Rolicz, P. & Sikora, R. Use of Ritz and Bubnow-Galerkin methods for calculation of inductance and impedance of conductors. Archiv f. Elektrotechnik 57, 119–126 (1975). https://doi.org/10.1007/BF01573788

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  • DOI: https://doi.org/10.1007/BF01573788

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