Analysis of crossed dipole to obtain circular polarization applying Characteristic Modes techniques Juan Pablo Ciafardini (1), Eva Antonino Daviu (2), Marta Cabedo Fabrés (2), Nora Mohamed Mohamed-Hicho (2), José Alberto Bava (1), Miguel Ferrando Bataller (2). (1) Dpto. de Electrotecnia. Facultad de Ingeniería, Universidad Nacional de La Plata. Calle 48 y 116 - La Plata (1900), Argentina. [email protected] (2) Instituto de Telecomunicaciones y Aplicaciones Multimedia. Edificio 8G. Planta 4ª, acceso D. Universidad Politécnica Valencia. Camino de Vera, s/n46022 Valencia. España. [email protected] Abstract— The crossed dipole is a common type of antenna developed to achieve wider bandwidth impedance compared that is used to generate circularly polarized radiation in a wide to the original design. In 1961 a new type of crossed dipole frequency range. This antenna was originally developed in the antenna, which used a single feed, was developed for 1930s and today is used in many wireless communication circular polarization radiation [5], Bolster demonstrated systems, including broadcast services, satellite theoretically and experimentally that single-feed crossed communications, mobile communications, global navigation systems satellite system (GNSS), radio frequency identification dipoles connected in parallel if the lengths of the dipoles (RFID), wireless local area networks (WLANs) and global were such that the real parts of their input admittances were interoperability for microwave access (WiMAX). equal and the phase angles of their input admittances This paper shows that it is possible to obtain circular differed by 90º. Based on these conditions, numerous polarization with two cross dipoles with different lengths and single-feed circularly polarized crossed dipole antennas connected in parallel by applying the Theory of Characteristic have been designed [5] - [25]. Modes. The results obtained using this new approach is Along the eight decades since the first crossed dipole was consistent with those obtained using the normal method of proposed, there has been a lot of literature on these antennas, analysis of input admittances. however, this paper presents a new approach using the Theory of Characteristic Modes. Resumen— El dipolo cruzado es un tipo común de antena The Theory of Characteristic Modes was first developed que se emplea para generar radiación con polarización by Garbacz [26] and was later refined by Harrington and circular en un amplio rango de frecuencias. Esta antena fue desarrollada originalmente en la década de 1930 y hoy en día Mautz in the seventies [27], [28]. Initially it was applied to se utiliza en un gran número sistemas de comunicación some cases and then fell in disuse. Recently the theory of inalámbrica, incluyendo los servicios de radiodifusión, las Characteristic Modes reemerged in designing antennas for comunicaciones por satélite, las comunicaciones móviles, los modern applications [29], [34], in the last years the number sistemas globales de navegación por satélite (GNSS), la of publications related to the application of this theory in the identificación de radiofrecuencia (RFID), las redes de área analysis and design of antennas has increased exponentially. local inalámbricas (WLANs), y la interoperabilidad mundial The success of Characteristic Modes lies in the clear para acceso por microondas (WiMAX). physical vision that provide of the phenomena that En este trabajó se demuestra que es posible obtener contribute to radiation from the antenna, allowing a better polarización circular con dos dipolos cruzados de distinta longitud y conectados en paralelo aplicando la Teoría de los understanding of its operation, so that the design of it can be Modos Característicos. Los resultados obtenidos mediante este done in a justified and consistent way. nuevo enfoque son consistentes con los obtenidos mediante el planteo clásico de análisis de admitancias de entrada. II. CHARACTERISTIC MODES THEORY I. INTRODUCTION The characteristic modes or characteristic currents can be The crossed dipole is a common type of antenna used in obtained as the eigenfunctions of the following particular the frequency range from the RF to millimeter waves. The weighted eigenvalue equation [28]: first crossed dipole antenna was developed in the 1930s under the name of "Turnstile Antenna", by Brown [1]. In the = (1) 1940s the antennas "super turnstile" [2] - [4] were where the are the eigenvalues, are the eigenfunctions mode contributes to storing magnetic energy ( > 0) or or the eigencurrents, and and are the real and imaginary electric energy ( <0). part of the impedance operator: As discussed above, an analysis of the variation of = + (2) eigenvalues is often very useful for the design of the antenna as information is obtained about the resonance This impedance operator is obtained after formulating an frequency of the modes. However, in practice other integro-differential equation. It is known from the alternative representations of the eigenvalues are preferred. reciprocity theorem that if Z is a linear symmetric operator, Since the current modal expansion described in Equation then, its Hermitian parts, R and X, will be real and (4) depends inversely on the eigenvalues, it seems more symmetric operators. From this, it follows that all convenient to analyze the variation of the expression: eigenvalues in Equation (1) are real, and all the eigenfunctions, , can be chosen real or equiphasal (a = (6) complex constant times a real function) over the surface on which they are defined [27]. The term presented in (6) is known as modal significance Consistent with the Equation (1), the characteristic modes (MS ) and represents the normalized amplitude of the n can be defined as the real currents on the surface of a current modes [37]. This normalized amplitude only conducting body that only depend on its shape and size, and depends on the shape and size of the conducting object, and are independent of any specific source or excitation. In it does not account for excitation. practice, to compute characteristic modes of a particular However, there exists another even more intuitive conducting body, Equation (1) needs to be reduced to representation of the eigenvalues, which is based on the use matrix form, as explained in [28], using a Galerkin of characteristic angles. Characteristic angles are defined in formulation [35]: [38] as: = 180° − () (7) = (3) From a physical point of view, the characteristic angle models the phase difference between a characteristic current Next, eigenvectors, , and eigenvalues, , of the object Jn , and the associated characteristic field, En. are obtained by solving the generalized eigenproblem of As previously set a mode resonates when λn = 0 that Equation (3) with standard algorithms [36]. means, when its characteristic angle (αn) is 180º. Therefore, As the characteristic modes form a set of orthogonal when the characteristic angle is close to 180º the mode is a functions they can be used to expand the total current J at good radiator. When the characteristic angle is near 90º or the surface of the antenna as follows: 270º the mode mainly stores energy. Thus, the radiating bandwidth of a mode can be obtained from the slope at 180º VJi of the curve described by the characteristic angles. J = nn (4) + λ n 1 j n III. MODAL ANALYSIS OF THE CROSSED DIPOLE ANTENNA where are the eigencurrents, are the eigenvalues and are the modal excitation coefficient. The modal After reviewing the basic concepts of the theory of excitation coefficient can be obtained as: characteristic modes we will perform a modal analysis of the structure of crossed dipole antenna shown in Fig. 1. = 〈 , 〉 = ∯ . (5) The product in the Equation (4) models the coupling between excitation and -th mode, and determines which mode will be excited by the feed of the antenna or the incident field. It should be noted that the total current in equation (4) also depends on , which is the eigenvalue associated with the -th mode. The eigenvalues are very important because their magnitude gives information on the frequency of resonance and radiation properties of different currents modes. If the variation with frequency of the eigenvalues are analyzed it is often observed that these take values ranging from -∞ to + .Considering a mode is at resonance when its associated eigenvalue is zero it is inferred that the smaller the magnitude of the eigenvalue, the more efficiently the mode radiates when excited. In addition, the sign of the eigenvalue determines whether the Fig. 1. Crossed Dipole Antenna. In this figure you can see two dipoles located in the same are observed can be seen that are the same and are plane and at an angle of 90°, the length of each dipole is superposed (MS1 with MS1’ and MS3 with MS3’). Note that L1=L2=L=0.5 meters, and each has a diameter d = 1 the J2 and J2’ modes are not degenerated modes. millimeter. To perform the modal analysis of the structure shown in Fig. 3 shows the variation with frequency of the Fig.1 we worked with the software for electromagnetic characteristic angles (αn), associated with current modes Jn simulations FEKO [39] using Characteristic Modes request. of the crossed dipoles. In this case the resonance of the The Fig. 2 shows the variation with frequency of the modes occurs when the characteristic angle (αn) is equal to modal significance (MSn) related to current modes Jn of the 180°. It is also noted that curves corresponding to the crossed dipole shown Fig. 1. The resonance of each mode degenerate modes are equal and are superimposed (α1 with can be identified by the maximum value of each modal α1’ and α3 with α3’). significance curve. This means that the closer the curve to Although the information given by Fig. 3 could also have its maximum value, the more effectively the associated been taken from Fig. 2 often characteristic angle mode contributes to radiation The radiating bandwidth of a representation is preferred as it is more intuitive. mode can then be established according to the width of its modal-significance curve near the maximum point Finally, Fig.