An Analytical Approach to Diagnose Coupling Matrix, Extract Circuit Model, and Predict Radiation for Filtering Patch Antennas

In this article, an analytical approach to diagnose coupling matrix, extract circuit model, and predict radiation for linearly polarized Nth-order filtering patch antennas from the $S_{11}$ measurement is proposed and developed. In contrast to existing reported approaches, the proposed method does not require extra EM-simulation ports on the radiator or radiation measurement data. All coupling values and circuit parameters of an Nth-order filtering patch antenna can be extracted with a single round of full-wave simulation or measurement. The proposed analytical approach can rigorously support lossless cases and is also effective for practical filtering patch antennas designed with commonly used copper conductors and low-loss substrates. It is suitable for both filtering patch antennas consisting of single/multiple single-mode radiators (SMRs) and the multimode radiator (MMR). An analytical method based on the diagnosed coupling matrix is proposed to predict the radiation performance of the filtering patch antenna, including the radiation pattern and the absolute value of the realized gain. In this context, the extraction procedure and closed-form formulas are presented in detail. To validate the proposed approach, three practical examples are provided: a stacked filtering patch antenna consisting of two SMRs, a filtering patch antenna with a dual-mode MMR, and a filtering patch antenna with a triple-mode MMR. The simulated and measured results demonstrate the effectiveness of the proposed approach.