### Abstract

Exact closed-form expressions for the Fresnel region electric and magnetic fields of circular loop and annular slot antennas are given in terms of the functions e_{n}(σ,γ)=(1/2π)02π cos(nΦ) sin[σ(1-2γ cosΦ)^{1/2}] dΦ and f_{n}(σ ,γ)=(1/2π)02π cos(nΦ) cos[σ(1-2γ cosΦ) ^{1/2}] dΦ, where - ∞ < σ < ∞ and 0 ≤ γ ≤ 1/2. For a circular loope antenna with a constant current distribution the Fresnel region fields are obtained in terms of the functions q_{n} (σ,γ)=f_{n} (σ,γ)+ie _{n}(σ,γ), with n =0,1, and 2, and for a cosine current distribution the Fresnel region fields are obtained in terms of the functions q_{n}(σ,γ), with n =0,1,2,3, and 4. The magnetic field of an annular slot antenna excited by a constant voltage is expressed exactly in terms of an infinite series involving the functions q_{n} (σ,γ). The Fresnel region magnetic field of the annular slot antenna is simply given in terms of q_{1}(σ,γ). The functions q_{n}(σ,γ) permitted a simple evaluation of the electric and magnetic field strength in the Fresnel region. The functions q _{n}(σ,γ) for n =0,1,2,3, and 4 are tabulated for values of σ=0.5, 1, 2, 5, 10, 25, and 50 and values of γ from 0.01 to 0.5.

Original language | English (US) |
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Pages (from-to) | 3500-3504 |

Number of pages | 5 |

Journal | Journal of Applied Physics |

Volume | 44 |

Issue number | 8 |

DOIs | |

State | Published - Dec 1 1973 |

### ASJC Scopus subject areas

- Physics and Astronomy(all)

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## Cite this

*Journal of Applied Physics*,

*44*(8), 3500-3504. https://doi.org/10.1063/1.1662793