J Supercond Nov Magn (2013) 26:1805–1810 DOI 10.1007/s10948-012-2056-5 ORIGINAL PAPER Electromagnetic Devices Applications of EBG for Systems Communications Humberto Fernandes · Humberto Andrade · Anderson Silva Received: 7 November 2012 / Accepted: 4 December 2012 / Published online: 29 December 2012 © Springer Science+Business Media New York 2012 Abstract This paper presents the study and applications of EBG (Electromagnetic Band Gap)/PBG (Photonic Band Gap) substrates, of planar microstrip structures, including quadrature directional couplers, rat-race (ring coupler) and impedance transformers. Through specific programs devel- oped in FORTRAN PowerStation, the frequencies and cou- plings for each structure are obtained. Also are used the PACMO—Computer Aided Design in Microwave program developed by H.C.C. Fernandes. Results of the dimensions and coupling of these devices, varying the frequency band (cellular communication and Wimax systems) and permit- tivity of the substrate, are obtained, comparing the results of conventional materials with EBG/PBG materials in the s and p polarizations. Keywords Quadrature coupler · Rat-race coupler · Impedance transformer · EBG · PBG · Wimax 1 Planar Microstrip Structures Planar microstrip structures have been widely used owing to practicality of construction, ease of installation and the pos- sibility of using a less congested part of the spectrum than, for example, the RF range [1]. There are several types of pla- nar structures, including impedance transformers and direc- tional couplers, which will be the object of the present study H. Fernandes ( ) · H. Andrade · A. Silva Department of Electrical Engineering, Federal University Rio Grande do Norte, Natal RN, Brazil e-mail: humbeccf@ct.ufrn.br H. Andrade e-mail: humbertodionisio@yahoo.com.br A. Silva e-mail: cmaxander@hotmail.com Fig. 1 Schematic of a microstrip structure the goal of which is to present the process of calculating the dimensions of a microstrip for subsequent uses in these de- vices. In this paper, a new EBG substrate is used in these devices. A microstrip is shown in Fig. 1, where w is mi- crostrip width, h the thickness of the substrate, l the length of the microstrip, ε r the relative permittivity substrate, t the thickness of the microstrip and the ground plane is shown in the figure. 2 EBG/PBG Structures Dielectric constant of the substrate is usually in the range 2.2 ≤ ε r ≤ 12. Depending on the characteristics of the sub- strate, the device performance can be optimized. Materials such as EBG (Electromagnetic Band Gap) and PBG (Photonic Band Gap) comprise a new class of periodic substrates. Optical waves behave in photonic substrates as electromagnetic waves behave in low microwave frequency substrates [2]. The EBG/PBG material is a periodic struc- ture in which the spread in bands of certain frequencies is prohibited. The EBG/PBG is a periodic dielectric structure which can exhibit a forbidden band of frequencies (band gap) in its electromagnetic dispersion relation [3], where the signal is blocked. Numerous studies related to photonic crystals were