### Abstract

An exact expression for the fields produced by an electrically small loop antenna is obtained in terms of a series involving a new set of functions, namely e_{n}(σ,γ)=(1/2π)∫_{0}^{2π} cos(nΦ)sin[σ(1-2γ cosΦ)^{1/2}]dΦ and f _{n}(σ,γ)=(1/2π)×∫_{0}^{2π} cos(nΦ) cos[σ(1-2γ cosΦ)^{1/2}]dΦ, where - ∞ < σ < ∞ and 0≤γ≤1/2. Series expansion, approximate expressions for γ^{2}σ≪1 and recursion relations for the functions are derived. These functions permit the exact evaluation of the fields in the Fresnel and near-field regions of the loop antenna. In the case that the distance to the point of observation is of the order of a wavelength or greater, but greater than the loop radius, the field expression is given in terms of the function q_{1}(σ,γ) = f_{1}(σ,γ) + ie_{1}(σ,γ). Numerical results describing the behavior of the functions f_{1}(σ,γ) and e_{1}(σ,γ) are given. Field expressions for the electrically large loop antenna are also derived.

Original language | English (US) |
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Pages (from-to) | 3975-3979 |

Number of pages | 5 |

Journal | Journal of Applied Physics |

Volume | 43 |

Issue number | 10 |

DOIs | |

State | Published - Dec 1 1972 |

Externally published | Yes |

### ASJC Scopus subject areas

- Physics and Astronomy(all)

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## Cite this

*Journal of Applied Physics*,

*43*(10), 3975-3979. https://doi.org/10.1063/1.1660858