Fresnel region fields produced by circular loops and annular slots antennas

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 q₁(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.