Full-wave analysis of a wide class of microstrip resonators fabricated on magnetized ferrites with arbitrarily oriented bias magnetic field

A numerical code has. been developed for the full-wave determination of the resonant frequencies and quality factors of microstrip patches with right-angle corners of arbitrary shape in the case in which the substrate of the patches is a magnetized ferrite with arbitrarily oriented bias magnetic field. The code is based on the solution of an electric-field integral equation by means of Galerkin's method in the spectral domain. The evaluation of the infinite integrals arising from the application of the numerical method is efficiently carried out by means of a technique based on the interpolation of the spectral dyadic Green's function. The numerical results obtained indicate that microstrip patches fabricated on ferrite substrates present cutoff frequency regions in which resonances cannot occur owing to the excitation of magnetostatic modes. The limits of these cutoff regions are shown to be dependent on the orientation and the magnitude of the bias magnetic field, on the shape of the patches, and even on the nature of every particular resonant mode. The numerical results also show that the resonant frequencies of microstrip patches. on magnetized ferrites can always be tuned over a wide frequency range provided the orientation of the bias magnetic field is suitably chosen.

I. Introduction

Resonant microstrip patches can be used either as antennas or as components of oscillators and filters in microwave integrated circuits. Although the most conventional microstrip patches are the rectangular and circular patches, other geometries such as the rectangular ring [1], the H-shaped patch [1], and the meander-shaped patch [2] have proven to be useful because of their size reduction capabilities (e.g., in the design of antenna arrays, antennas for personal communication systems, …). This means that the algorithms developed for the analysis of resonant microstrip patches should cover a spectrum of geometries as wide as possible. Apart from their shape, the nature of the substrate of microstrip patches is another interesting degree of freedom for the designer of circuits and antennas. Although the most commonly used substrate materials are dielectrics, magnetized ferrites have proven to have potential application as substrates of microstrip patches. For instance, several researchers have reported that resonant microstrip patches printed on ferrite substrates can be used in the fabrication of tunable band rejection filters [3] and tunable bandpass filters [4], [5]. Also, measurements have shown that the operating resonant frequency of microstrip antennas printed on ferrite substrates can be varied over a wide frequency range by adjusting the bias magnetic field [6]. Apart from that, ferrite substrates can be used for reducing the radar cross section of microstrip antennas under certain conditions [7]–[9] and for achieving linearly, as well as circularly polarized microstrip antennas with a single feed [10]–[12]. Finally, it should be pointed out that when ferrite materials are used as substrates of microstrip phased arrays, wide-angle impedance matching can be obtained by dynamically adjusting the bias magnetic field with scan angle [11], [13].