Characterization of group delay in linearly and circularly polarized lossless stacked patch antennas

Abstract

[1] In this study, we investigate the group delay characteristics of linearly and circularly polarized lossless stacked patch antennas. A new closed-form analytic expression for group delay was derived for both polarizations to obtain physical insight and have an efficient technique for conducting parametric studies of the antenna group delay characteristics. The analytical model was constructed by employing an equivalent circuit, consisting of resonant RLC sections that model the lossless patches. The group delay is calculated via the frequency derivative of the input phase function (disregarding the far-field phase contribution, a second-order effect), which is obtained in closed form. The group delay is a function of the circuit parameters (Rl,u, Ll,u, Cl,u) , the values of which must be determined for a particular antenna. We employ a reduced-order Pade approximation to extract the parameter values by making use of sampled data obtained from either a full-wave simulation or alternatively via measured data. A circuit synthesis methodology is then employed to map the extracted Pade expansion coefficients onto a known impedance function. Comparison of the analytical results with the full-wave numerical calculations of the impedance, phase, and group delay quantities show very good agreement. The reduced-order approximation is a balanced compromise between the fidelity of the equivalent circuit model and the ability to obtain the group delay in an analytically exact fashion. Results shown herein establish that the group delay of a stacked patch antenna is proportional to the patch Q and the patch capacitance. The peak group delay of the antenna approaches an asymptotic value as the input resistance increases without bound, and the rate at which this occurs is inversely proportional to the patch Q. Results also illustrate that the peak group delay of the stacked patch approaches infinity as the inductance decreases, and approaches an asymptotic value as the inductance increases. Interestingly, all of these characteristics are independent of antenna polarization.