Low-Cost Optimization of Compact Branch-Line Couplers and Its Application to Miniaturized Butler Matrix Design Slawomir Koziel, Piotr Kurgan Engineering Optimization & Modeling Center, School of Science and Engineering Reykjavik University, Menntavegur 1, 101 Reykjavik, Iceland koziel@ru.is, kurgan@ru.is Abstract—A low-cost technique for simulation-driven design optimization of compact branch-line couplers (BLCs) is presented. In the first stage, the coupler cells are individually optimized using a pattern search algorithm. In the second stage the entire coupler structure undergoes a fast tuning exploiting fast surrogate model, constructed from cascaded local response surface approximations (RSAs) of the cells. Accurate, high- fidelity EM analysis of the entire coupler structure is only needed at the tuning phase. The final design of the compact BLC (87.6% area reduction compared to conventional coupler) is obtained at the cost of less than three full-wave simulations. The optimized coupler is then successfully applied in the design of miniaturized Butler matrix. Keywords—Butler matrix, branch-line coupler, surrogate-based optimization. I. INTRODUCTION Butler matrix is a commonly used beam-forming network that enables the excitation of antenna array radiators with a linear phase and even power distribution [1]. It finds applications in a variety of wireless communication systems involving multi-beam or beam-scanning antennas [1]. A typical Butler matrix is composed of hybrid couplers, phase shifters, and crossovers, and consequently, occupies a considerable area, especially for lower frequency bands. To address this issue, a number of miniaturization schemes have been proposed, e.g., [2-4]. In [2], quasi-lumped artificial transmission lines (ATLs) have been used to design a miniaturized Butler matrix. A lumped-element unit cell has been developed in [3] to obtain a compact size of a Butler matrix. In [4], small footprint has been obtained by integrating the circuit using glass-based thin-film technology. For PCB single-layer applications, one of the most appropriate methods offering a viable chance of circuit miniaturization is the approach of [2]. It is based on replacing conventional TLs with abbreviated ATLs, resulting in a compact, yet much more complex layout. Design of such sophisticated circuits requires vast computational resources and high-fidelity EM simulation tools for a reliable evaluation. This in turn becomes infeasible when design optimization has to be performed. In this work, we propose a two-stage optimization scheme for expedite and reliable simulation-driven design optimization of a miniaturized branch-line coupler. First, a high-fidelity optimization is performed at the level of fundamental building blocks of a coupler. This leads to highly-accurate results obtained at a relatively low cost. Having the coupler assembled from the previously optimized building blocks, surrogate-based optimization scheme is applied to adjust the response of the entire coupler. At this stage, high-fidelity simulation is performed only ones or twice. The optimization procedure proposed here enables a reliable design of a highly miniaturized branch-line coupler as well as a Butler matrix at the cost not exceeding three high fidelity simulations of the compact coupler. II. DESIGN STRATEGY Our overall goal is a computationally efficient design of a planar miniaturized 4×4 Butler matrix. The Butler matrix is designed in a systematic bottom-up fashion. This is done due to practical reasons, as EM-based design optimization of a Butler matrix with a compact footprint is extremely CPU-intensive and exceeds computational capabilities of typical PCs (cf. Section IV). Instead, we solve the problem by separately designing the constitutive elements of a Butler matrix and, subsequently, combining the results using circuit theory. This can be done with a negligible error since the elements of the Butler matrix are spatially distant from each other and parasitic phenomena between them can be neglected. In this work, a Butler matrix in a branch-line coupler (BLC) configuration is used, with crossovers realized by cascading two BLCs with 90° phase shifters between them. We exploit a widely-known concept of artificial transmission lines (ATLs) to obtain compact BLCs and crossovers. In this popular miniaturization approach, conventional transmission lines (TLs) are replaced by ATLs that mimic their electrical properties is a limited frequency range, while exhibiting advantageous properties, such as diminished physical dimensions. In our approach, the overall circuit size reduction is achieved by means of miniaturization of its components. Here, we propose a two-stage low-cost simulation-driven optimization scheme for obtaining highly compressed circuits. 978-2-87487-035-4  2014 EuMA 6 -9 Oct 2014, Rome, Italy Proceedings of the 44th European Microwave Conference 227