Ueber die Berechnung und Messung kleiner Selbstpotentiale

Wien, Mathias

doi:10.1002/andp.18942891312

Cited by 11 publications

(5 citation statements)

References 3 publications

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“…Wien didn't present it in the general form (7), but with the corresponding DC expressions for the GMD of particular cross-sectional shapes already substituted, like e.g. that for a circular disk, see (our) equation (18), or for an annulus ( [9], p. 938). For a derivation for the case of a round wire at DC see e.g.…”

Section: Deriving the Relationmentioning

confidence: 99%

“…This way Wiens's measurements of the inductance of such coils ( [9], p. 939) can be compared to calculations, see Table 1. A systematic error analysis of Wien's formula (18) in function of the length-to-radius ratio / based on a comparison with exact inductances calculated by numerical integration was presented in [5].…”

Section: Round Wire At DCmentioning

confidence: 99%

“…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: 99%

“…Wien measured the total inductance of three different round tubes of length 0.5 m and various inner and outer radii directly in a Wheatstone bridge at low frequency ( [9], p. 938). In Table 2, his measured results are compared to calculations based on equations (7) and (22).…”

Section: Tubular Conductor At DCmentioning

confidence: 99%

“…In paragraph 6.3.3 we used because this was already predetermined by relation (9) and, luckily, we had the very simple relation = . If in rectangular wires the current at infinite frequency were also uniformly distributed along the circumference of the cross section, as it is in round wires, then could be calculated analytically.…”

Section: Developing the Analytical Approximationmentioning

confidence: 99%

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

Aebischer¹,

Aebischer

2017

AEM

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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 %.

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Section: Deriving the Relationmentioning

confidence: 99%

Section: Round Wire At DCmentioning

confidence: 99%

“…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: 99%

Section: Tubular Conductor At DCmentioning

confidence: 99%

Section: Developing the Analytical Approximationmentioning

confidence: 99%

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

Aebischer¹,

Aebischer

2017

AEM

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Ueber die Verwendung des Electrodynamometers im Nebenschluss

Wien¹

1897

Annalen der Physik

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Um mit demselben Instrument Wechselstriime sehr verschiedener Intensitat messen zu koniien, ist es vielfach wunschenswertli das Electrodyiiamometercbenso wie bei constantem Strom das Galvanometerim i17ebenschZuss zu verwenden. Dabei muss die S'elbstinduction des Dynamometers beriicksichtigt werden. Im Folgenden sind die bezuglichen Formeln abgelei te t.Die Abzweigung (shunt) habe den Widerstand w1 und das Selbstpotential p , ; die entsprechenden Grossen des Dynamometerzweiges seien w, und p , und es fliesse im Hauptzweig der Strom eint.; d a m bestehen nach clen Kirchhoff'schen Regeln fur Wechselstrom zwischen den Intensitaten k, und k, und den Widerstandsoperatoren a, = zul + i n p , und u, = w, + inp, der Verzweigung folgende Gleichungen: 1 = k, + k,, a, k , = a, k,.

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Methode und Instrument zur Messung sehr kleiner Inductionscoefficienten

Martienssen¹

1899

Annalen der Physik

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Ueber die Berechnung und Messung kleiner Selbstpotentiale

Cited by 11 publications

References 3 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

Ueber die Verwendung des Electrodynamometers im Nebenschluss

Methode und Instrument zur Messung sehr kleiner Inductionscoefficienten

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