Transmission Line Model for Slot-coupled Microstrip Reflectarray Antennas

A transmission line model is adopted for the analysis of slot-coupled microstrip reflectarrays. The current on the equivalent impedance for the single radiating element is used to obtain the reflectarray phase design curve. Computational costs are drastically reduced with respect to theoretical full-wave analysis. Numerical and experimental validations are presented on the phase curve useful for the design of a 10 GHz slot-coupled reflectarray prototype. INTRODUCTION A fundamental task in microstrip reflectarrays design is the determination of an appropriate phase distribution on the radiating elements giving a field pattern with prescribed features. The required phase curve can be obtained as a function of the element resonant size or using stubs with different lengths [1-2]. A novel structure has been recently proposed by the authors [3] which is based on slot-coupled array elements having the same resonant size. Microstrip lines with different lengths are adopted as coupling elements to introduce the correct phase distribution on the array [3]. This multi-layer structure significantly reduces interference effects on the scattered field due to phase tuning elements usually located on the patches side. As a matter of fact, the prescribed field is obtained without changing the geometry of the reflecting surface. A transmission line model [4] is adopted in this paper for the analysis of slot-coupled microstrip reflectarrays. Patch elements printed on a thin dielectric substrate are represented by a transmission line modeling the fundamental TEM mode propagation. The remaining part of circuit includes two transformers coupling the aperture to the upper patch and the lower microstrip line, respectively. This equivalent transmission line model is used to obtain the reflectarray phase design curve with reduced computational costs when compared to full-wave analysis methods. Numerical validations are presented on the scattered field of a 10 GHz slot-coupled reflectarray element. Results are compared with moment-method analysis and measurements. TRANSMISSION LINE MODEL The analysis is addressed to the structure in fig.1, where a square patch slot-coupled to a phase tuning microstrip line is used as single reflectarray element [3]. Figure 1 Slot-coupled single element geometry. The transmission line approach [4], adopted to model the structure, is reported in fig.2. A fundamental TEM mode propagation is assumed for the L x L square patch, as given by the upper transmission line terminated on the YS admittance loads. Two transformers are used for modeling the coupling of the aperture to the patch and microstrip line, respectively. The transformation ratio n1 is given as [4]: (1) L L n a = 1