Series expansions for the mutual coupling in microstrip patch arrays

Efficient and Effective Full-Wave Analysis of the Instantaneous and Average Behaviors of Time-Modulated Arrays

“…3 shows that the mutual impedance between two patches from using the closed-form (10) and those from commercial software IE3D are in good agreement. Using the constructed mutual-impedance formula together with the correcting procedure [23], the in-array mutual impedance (11) is obtained to perform the optimization design of TMAs in the following examples. The modified artificial bee colony algorithm [29], [30] is adopted as an optimization strategy.…”

“…Based on formula (10), a first approximation of the array impedance matrix, termed as an isolated impedance matrix [Z iso ], which is the mutual impedance between two isolated elements, is obtained. The effect of the parasitic elements is ignored, thus, to obtain the in-array impedance matrix which involves the interactions between the elements in the array configuration, a correcting procedure proposed in [23] is adopted. The correcting procedure that only requires the knowledge of the input impedance of an isolated element and mutual impedance of two isolated elements, resulting in a corrected matrix termed as an in-array impedance matrix [Z inar ], which is a good approximation of the real one.…”

“…The theory of the in-array mutual impedance based on a closed-form mutual impedance expression [22] and a correcting procedure [23] is introduced in order to obtain the scattering matrix [S] in (5) and (7). The mutual impedance expression between two arbitrary antenna elements proposed in [22] …”

“…In this paper, the full-wave analysis based on a closed-form mutual impedance expression [22] and a correcting procedure [23], focusing on the optimization design of practical uniformly and non-uniformly spaced time-modulated patch arrays, is proposed. The instantaneous and average behaviors of TMAs with mutual coupling effect take into consideration are investigated through using the in-array mutual impedance.…”

Nature-Based Design of Aperiodic Linear Arrays with Broadband Elements Using a Combination of Rapid Neural-Network Estimation Techniques and Genetic Algorithms

“…In general, Z parameters are functions of the positions of every element in an array, as well as of its operating frequency, and hence require simulations or measurements of a full array to determine. However, the isolated Z-parameter matrix, Z 1 , is often used as an approximation of the exact parameters [19,20]. This approximate impedance matrix is generated by ignoring the effects of neighboring array elements in the calculation of the self-and mutual -impedance terms.…”