1206 IEEE ANTENNAS AND WIRELESS PROPAGATION LETTERS, VOL. 11, 2012 The Effect of Electromagnetic Waves on Multilayer Orthogonal Microstrip Lines With and Without Defected Microstrip Structure Mohammad Ali Salari, Seyyedpayam Abbasiniazare, and Omid Manoochehri Abstract—A method for analysis of multilayer coupled trans- mission lines with and without defected microstrip structure (DMS) excited by an external electromagnetic wave is presented. The structure is first decomposed into coupled transmission-line sections and crosstalk regions, then a lumped circuit model for the crosstalk region and the DMS section is presented, and the forced terms associated with the incident wave are calculated. Finally, by using the modal decoupling method, the unknown modal coefficients and subsequently voltages and currents are obtained. The validity of the method is verified by comparison between the analytical and the simulated results of HFSS full-wave simulator. Index Terms—Electromagnetic coupling, incident fields, multi- layered media, orthogonal microstrip lines. I. INTRODUCTION O RTHOGONAL interconnections can be seen in many multilayered circuits. This orthogonality decreases the crosstalk between the interconnections of two adjacent layers. There exists a vast amount of papers about the coupling of external electromagnetic waves into transmission lines [1], [2]. A transmission-line method is used in this letter to calculate the effect of external electromagnetic waves on a multilayer coupled microstrip lines. The modeling and analysis of the structure results in practical points that could be exploited in order to reduce the effect of external electromagnetic waves at the terminals, e.g., by adjusting the length of the line or the orientation of the circuit with respect to the source of interfer- ence (when the source is known for us). Moreover, a method of analysis is introduced, when there is a defect on the strip like DMS. The method can be generalized to the other defects like gap or transverse slit in the microstrip line. This letter is organized as follows. In Section II, the forced terms due to an external wave are obtained by primary-sec- ondary field idea. In Section III, a lumped circuit model for the crosstalk region and the defected microstrip structure (DMS) is presented, then the entire structure will be modeled, and the Manuscript received August 16, 2012; accepted September 25, 2012. Date of publication October 02, 2012; date of current version October 25, 2012. M. A. Salari is with the Department of Mathematics, University of Bonn, Bonn 53115, Germany (e-mail: s6mosala@uni-bonn.de). S. Abbasiniazare and O. Manoochehri are with the Department of Electrical and Computer Engineering, Tarbiat Modares University, Tehran, Iran. Color versions of one or more of the figures in this letter are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/LAWP.2012.2221453 Fig. 1. Dimensional parameters of a double-layer structure illuminated by a uniform plane electromagnetic wave. A DMS is placed in the middle of the lower strip. matrix equation that relates the crosstalk region’s voltages and currents is obtained. Finally, the matrix equation that incorpo- rates all the boundary conditions is given. Section IV describes the solution of the obtained matrix equation by modal decou- pling method. In Section V, some examples for normal incidence are presented. II. FORCED TERMS DERIVATION For lossless or low-loss layers, the quasi-TEM assumption can be applied when the distance between the conductors is much smaller than the smallest wavelength of propagating fields. The system in Fig. 1 is assumed to be externally excited by a uniform plane wave of time dependence . For simplicity, we assume the following. 1) The principal propagation mode of the lines is quasi-TEM. 2) The strips and ground plane are perfect electric conductors, the substrate is lossless, and also the thickness of the inter- connections is assumed to be negligible. 3) The incident electromagnetic (EM) field only excites the quasi-TEM dominant mode. 4) The ground plane is infinite. 5) The effect of higher-order modes in discontinuities of the microstrip transmission lines is negligible with respect to the dominant TEM mode. 1536-1225/$31.00 © 2012 IEEE