Field expressions for a circular loop antenna in terms of a new set of functions

Manuel A. Huerta, Guillermo Gonzalez

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


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 en(σ,γ)=(1/2π)∫0 cos(nΦ)sin[σ(1-2γ cosΦ)1/2]dΦ and f n(σ,γ)=(1/2π)×∫0 cos(nΦ) cos[σ(1-2γ cosΦ)1/2]dΦ, where - ∞ < σ < ∞ and 0≤γ≤1/2. Series expansion, approximate expressions for γ2σ≪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 q1(σ,γ) = f1(σ,γ) + ie1(σ,γ). Numerical results describing the behavior of the functions f1(σ,γ) and e1(σ,γ) are given. Field expressions for the electrically large loop antenna are also derived.

Original languageEnglish (US)
Pages (from-to)3975-3979
Number of pages5
JournalJournal of Applied Physics
Issue number10
StatePublished - 1972
Externally publishedYes

ASJC Scopus subject areas

  • Physics and Astronomy(all)


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