The near-zone magnetic field of a small circular-loop antenna

Abstract

An improved formula is derived for accurately computing the near-zone magnetic field of a s mall c irc ular transmitting loop an tenna. Such a field can serve as a reference standard for calibrating fi eld-strength meters e mploying small receiving loop anten nas in the fre qu ency range 30 Hz to 30 MHz.This formula in c ludes correction terms for fr equ ency (d ue to the finite tim e of propagation), as well as correction s for the finite radii of both the transmitting and rece iving loop s. Other formula s appearing in the literature often fail to include s uch correc tion s whic h can result in errors of up to 20 pe rcent a nd more in co mputin g standard-fie ld valu es.The N BS formula is de riv ed by ex pandin g th e integran d of the re tard ed vector potentia l into an infinite se ri es of sp he ri ca l Ha nk e l fun c ti ons of in creasing o rde r. Th e res ulting series express ion is in e rror by less than 0.2 pe rce nt , is rap idl y co nverging and si mpl e to use without reco urse to a tabl e of fun c tio ns or a co mpute r.Key Woro s : l."" p-a nl e nn a field s lrc n~I". Illa~neli(" fie ld -s lre n~lh s la nd ard . Illulual indu c la nce IIf ('oaxi a l c ircular filam e nt s . Ilear·zone magne ti c fi e ld , tran s mitting loop antenna.

Numerical simulation of calibrating magnetic field intensity of small circular loop antenna in liquid

“…To do this in the solution, we simply modify the formulation derived by Greene [6] as replacing into = + as explained before. In addition, our formulation requires the field on the central axis of the reference circular loop antenna so that we should summarize some useful expressions below.…”

“…In this paper, first, we extend Greene's formulation for small circular loop antenna located in free space [6] into the homogenous lossy medium. It can be done by replacing into = + , where , , and are propagation, attenuation, and phase constants in the lossy medium.…”

Near-Field and Far-Field Expansions for Traveling-Wave Circular Loop Antennas

“…Several useful mathematically exact representations have been developed for the electromagnetic fields radiated by a uniform current circular loop antenna [1][2][3][4]. A more general methodology for evaluating the complicated near-field integrals associated with circular loop antennas has been recently introduced in [5].…”

“…For example, far-field expressions have been found in [6][7][8] for a single turn traveling-wave loop where the total change in phase over one complete revolution around the loop is an integer multiple of 2π. This analysis was later extended in [9] to include the more general case of a loop with a traveling-wave current distribution of the form (1) where the parameter γ can in general be complex with a negative imaginary part. In this case, the phase changes over one complete revolution by an amount equal to 2π (γ) radians.…”

“…Exact series representations are derived in Section 2 for the nearzone vector potential and corresponding magnetic field components for a traveling-wave loop antenna with a current distribution of the form defined in (1). Convenient far-zone approximations are derived in Section 3 by using the exact near-zone expansions as a starting point.…”