Internal and External Inductance

Internal and External Inductance - Internal Inductance of...

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Internal Inductance of Conductor in H/m: L int 4 π 10 7 8 π H m = 1 2 10 7 H m = Internal Inductance of Conductor in H/m: L int λ int I = 1 8 µ o π = Result of calculation of internal Flux Linkage per unit length in z direction: λ int 1 8 µ o I π = Integrate internal Flux Linkage (per unit length) over the complete range of the conductor radius. λ int 0 r x µ o I x 3 2 π r 4 d = λ int 1 20000000 henry m I = Flux at radial position x is linked with Current I by a ratio of x 2 / r 2 : d λ int x 2 r 2 d Φ = µ o I x 3 2 π r 4 dx = Calculate Flux per unit length of conductor: d Φ B x dx = Calculate B x from H x : B x µ o H x = µ o I x 2 π r 2 = Substitute I x into Formula for H x : H x I x 2 r 2 2 π x = Ix 2 π r 2 = Solve for I x : I x I x 2 r 2 = I x I π x 2 π r 2 = Calculate Ratio of I x and I considering constant current Density: Solve for H x : H x I x 2 π x = Solution for cylindrical conductor: 2 π x H x I x = Start with Ampere's Law: l H tan dI enclosed = Dr. M. Giesselmann, Feb-27-2008: Internal Inductance of Conductors:

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Complete internal and external Flux Linkage between wire with radius r and return wire at distance D : λ p 1 2 10 7 I 210 7 I ln D r + = unit length in z direction between Distances D 1 and D 2 from reference point: L 12 , 7 ln D 2 D 1 = Result of calculation of external Flux Linkage per unit length in z direction between Distances D 1 and D 2 from reference point: λ , 7 I ln D 2 D 1 =
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Internal and External Inductance - Internal Inductance of...

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