The Near-Zone Magnetic Field of a Small Circular-Loop Antenna

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 frequency range 30 Hz to 30 MHz. This formula inc ludes correction terms for fr equency (d ue to the finite time of propagation), as well as corrections for the finite radii of both the transmitting and receiving loops. Other formulas appearing in the literature often fail to include such correc tions whic h can result in errors of up to 20 pe rcent and more in computing standard-fie ld values. The NBS formula is de rived by ex panding the integrand of the re tarded vector potentia l into an infinite se ri es of sphe rica l Ha nkel fun c tions of in creasing o rde r. The resulting series express ion is in e rror by less than 0.2 pe rcent , is rap idl y co nverging and si mple to use without recourse to a table of fun c tions or a compute r.