PRZEGLĄD ELEKTROTECHNICZNY (Electrical Review), ISSN 0033-2097, R. 87 NR 9a/2011 255 Nobby STEVENS, Lieven DESTRYCKER, Werner VERSCHELDE Catholic University College Gent Procedure to Calculate the Inductance of a Circular Loop Near a Metal Plate Abstract. This paper describes the influence of metallic objects on the inductance as a function of the separation distance. We focus our attention on the benchmark configuration of a circular loop antenna near an infinite conducting plate. We consider the quasi-static approach, thus with a constant current distribution over the entire loop. The results are obtained by numerical integration and the accuracy of the numerical integration procedure is verified for a circular loop antenna in free space, for which a closed analytical solution exists. The results are particularly interesting in the domain of low frequency and high frequency Radio Frequency IDentification, where mutual influence of multiple reader antennas is often suppressed by means of a metallic shielding, which results in an important decrease of the readout distance and a detuning of every reader antenna. Abstract. W artykule opisano wpływ obiektów metalowych na indukcyjność jako funkcję dystansu. Analizowano okrągłą antenę w pobliżu nieskończenie długiej metalowej płytki. Badania mają znaczenie w układach RFID gdzie liczne anteny są zakrywane przez metalowe ekrany. (Analiza indukcyjności okrągłej anteny w pobliżu metalowej płyty) Keywords: circular loop, inductance, RFID. Słowa kluczowe: antena RFID, indukcyjność. 1. Introduction The inductance L of a circular loop at low frequencies in free space is well described in the literature [1]. In practice though, objects close to the inductive element can have an important influence. This is especially true for metals and conductive bodies in general, where the induced voltage leads to a current that gives rise to a flux that opposes the change in flux (Lenz’s law, see [2]). For Radio Frequency IDentification (RFID) systems, the modification of the L is crucial, since it is an indicator for the volume in which a tag can be read. Fig. 1. Illustration of a setup with cows in parrallel lines. In certain RFID configurations, it is important that the reader antenna only detects that tag that is meant to be read, and not one that is only slightly further away. An example is an automatic feeding installation in the cattle industry. The goal is to automatically link the amount of food with every individual animal. RFID is an excellent technology for this, since it is an automatic contact-less identification method that supports well possible dirt or moisture. Often, RFID installations are close to each other so there is a chance that not only the animal in that specific feeding box or transfer line is detected, but also the one in the line nearby. This is illustrated in Fig. 1. Processing these data can thus lead to conflicts. This is obviously an electromagnetic compatibility issue: two or more devices hinder the correct operation of one another due to their electromagnetic proximity. A simple solution for this problem is the usage of metallic screens between the boxes. Fig. 1. Illustration of a setup with cows in parrallel lines. This configuration blocks the field of one reader antenna to penetrate a neighboring box, thus avoiding the readout of the tag in that box. Care must be taken when installing these shielding metals, since one still wants the reader antenna to read the tag that is in the box to be read. Another issue is that as the inductance is modified, the circuit of the reader becomes detuned. In this paper, we will develop a numerical procedure to determine the decrease of the inductance L of a circular loop as a function of the distance from a perfectly conducting plate. 2. Inductance of a loop A. Formulation For lower frequencies, the Biot-Savart law may be applied for the calculation of the magnetic field caused by a known current distribution. Fig. 2. Biot-Savart law: Conventions with regard to equation (1). Using the conventions of Fig.2, the equation (1) is valid for a known volume current flowing within an elementary volume dV [2]. We consider non-magnetic materials ( r =1) for the rest of this paper. (1) For surface (in case of perfect electrical conductors) or line currents, respectively equations (2) and (3) can be applied [2]. In equation (2), K(r0) is a surface current, while in equation (3), dI(r0) is an elementary line current. (2)