表皮効果

Multi tool use表皮効果(ひょうひこうか)は交流電流が導体を流れるとき、電流密度が導体の表面で高く、表面から離れると低くなる現象のことである。周波数が高くなるほど電流が表面へ集中するので、導体の交流抵抗は高くなる。
一般に高周波における影響が論じられることが多いが、電力系統など大電流を扱う際にも重要で、直流送電が有利とされる理由の一つでもある。
表皮効果は多くの科学者が研究し、ウィリアム・トムソン(ケルヴィン卿)によって1887年に説明された。導体の電流密度Jは 深さδに対して、次式のように減少する。
- J=J0e−δ/ddisplaystyle J=J_0e^-delta /d

ここで d は表皮深さで、電流が 表面電流の1/e (約 0.37)になる深さであり次のように計算される。
- d=2ρωμdisplaystyle d=sqrt 2rho over omega mu

- ρ = 導体の電気抵抗率
- ω = 電流の角周波数 = 2π × 周波数
- μ = 導体の絶対透磁率
dの厚さの平板が直流電流に対して生じる抵抗と、厚さがdよりもっと厚い平板の交流電流に対する抵抗は同じである。交流電流に対して電線は直流電流に対する厚さdのパイプのような抵抗を示す。. 例として、円形断面の電線の抵抗は概略以下のようになる。
- R=ρd(Lπ(D−d))≈ρd(LπD)displaystyle R=rho over dleft(L over pi (D-d)right)approx rho over dleft(L over pi Dright)

- L = 導体の長さ
- D = 導体の径
D >> dの場合に上の式は成り立つ。
例
銅線の場合、周波数に対する表皮深さd;は表のようになる。
周波数 | 表皮深さd;
|
---|
60 Hz | 8.57 mm
|
10 kHz | 0.66 mm
|
10 MHz | 21 μm
|
関連項目
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