516 IEEE MICROWAVE AND WIRELESS COMPONENTS LETTERS, VOL. 14, NO. 11, NOVEMBER 2004 Quasi-TEM Model of Magnetostatic-Surface Wave Excitation in Microstrip Lines Jose Aguilera, Manuel J. Freire, Ricardo Marques, Member, IEEE, and Francisco Medina, Senior Member, IEEE Abstract—The per unit length capacitance and inductance of a YIG-loaded microstrip line are computed in the frame of a quasi- transverse electromagnetic approach. The transmission line pa- rameters, i.e., the complex propagation constant and the complex characteristic impedance are computed from them and the inser- tion loss of a finite-length YIG-loaded microstrip line is obtained using the simple transmission line model. In particular, it is shown that this model is suitable even for the magnetostatic regime. Index Terms—Ferrites, magnetostatic waves, quasi-transverse electromagnetic (quasi-TEM) analysis. I. INTRODUCTION Q UASI-TRANSVERSE electromagnetic (TEM) analysis is preferable versus full-wave models for those situations where quasi-TEM results are expected to be accurate enough. The quasi-TEM approach was applied to the analysis of magnetostatic surface wave (MSSW) microstrip transducers many years ago [1], [2]. However, some simplifications such as assuming uniform current density across the strip [1] or other quasi-analytical approximations [2] were used. In this letter, we present an accurate quasi-TEM analysis of the excitation of MSSWs by a microstrip line free from simplifying assumptions. In particular, the surface current distribution is computed rather than imposed. The radiation resistance, the line impedance, and the phase constant can be easily obtained for this quasi-TEM model. Comparisons with full-wave data [3] and experiments are provided to validate the model. II. METHOD OF ANALYSIS Fig. 1 shows the cross section and the side view of a YIG- loaded microstrip line. In our analysis, the vector potential in the spatial domain is written in the form . In the quasi-TEM approach, only the transverse com- ponents of the magnetic field, , are relevant. They are related with the vector potential on the th layer of the structure (1) where is the transverse permeability tensor. From the Maxwell equation for the divergence of , the following equation is obtained: (2) Manuscript received February 20, 2004; revised June 10, 2004. This work was supported by CICYT and FEDER under Project TIC2001-3163. The review of this letter was arranged by Associate Editor A. Weisshaar. The authors are with the Microwave Group, Department of Electronics and Electromagnetism, University of Seville, Seville 41012, Spain (e-mail: josag@us.es). Digital Object Identifier 10.1109/LMWC.2004.837067 Fig. 1. Cross section of the YIG-loaded microstrip line. where the superscript indicates transpose matrix. Equation (2) is solved making use of the magnetic Green’s function which relates the longitudinal component of the surface current density on the strip, , with the vector potential in (3) The magnetic Green’s function is obtained following the guidelines shown in [4] and is related with the magnetostatic Green’s function that appears in [5]. Taking into account the current function in [5], the structure of Fig. 1, this current is (4) and therefore (5) Moreover, in the quasi-TEM approximation , the -component of the magnetic field can be related with the vector potential in the same form (6) Taking into account (5) and (6), and the magnetostatic Green’s function reported in [5], the following equation is obtained: (7) This equation can be written in the spectral domain as (8) 1531-1309/04$20.00 © 2004 IEEE