Low-Cost Automated Design of Compact Branch-Line Couplers

Abstract

Branch-line couplers (BLCs) are important components of wireless communication systems. Conventional BLCs are often characterized by large footprints which make miniaturization an important pre-requisite for their application in modern devices. State-of-the-art approaches to design compact BLCs are largely based on the use of high-permittivity substrates and multi-layer topologies. Alternative methods involve replacement of transmission-line sections of the circuit, with their composite counterparts, referred to as compact cells (CCs). Due to the efficient use of available space, CC-based couplers are often characterized by small footprints. The design of compact BLCs is normally conducted based on engineering experience. The process is laborious and requires many adjustments of topology followed by manual or, semi-automatic tuning of design parameters. In this work, a framework for low-cost automated design of compact BLCs using pre-defined CCs is proposed. The low cost of the presented design technique is ensured using equivalent-circuit models, space mapping correction methods, and trust-region-based local optimization algorithms. The performance of the framework is demonstrated based on three examples, concerning the design of unequal-power split coupler, comparison of automatically generated compact BLCs, as well as rapid re-design of the coupler for different substrates. Furthermore, the approach has been benchmarked against the state-of-the-art methods for low-cost design of circuits.

Low-Cost Unattended Design of Miniaturized 4 × 4 Butler Matrices with Nonstandard Phase Differences

“…Here, (11) is minimized based on the R T ( x e ) model responses, where x e = x e.k = [ z 1. k z 2. k φ 2. k φ 3. k ] T represents the vector of electrical parameters of k th BLC (note that φ 1. k = 90°). The parameter Δ C = || S 31 | − | S 21 || denotes the power-split imbalance at the center frequency f 0 , whereas M = max(| S 11 |, | S 41 |) is an in-band performance of the BLC over the frequency range of interest defined around f 0 [ 46 ]. The figures φ 1 = ∠( S 21 / S 31 ) and φ 2 = ∠( S 24 / S 34 ) are phase shifts at f 0 .…”

“…Shifting the optimization burden to the simplified models is important for maintaining low cost of coupler development. For more detailed discussion on design of miniaturized BLCs, see [ 29 , 34 , 46 , 51 ]. The optimized high-fidelity BLC designs x g .1 * and x g .2 * are used as the starting point for BM tuning.…”

“…The perturbations for generation of the Jacobian J are obtained using a large-step finite differentiation [ 45 ]. Note that the model G ( i ) may be constructed using a combination of the responses determined from evaluations of the low- and high-fidelity representations of the circuit under design [ 46 ]. The parameter r ( i ) represents the trust-region radius, which is iteratively updated based on the calculated gain ratio, i.e., the obtained versus predicted change of the objective function.…”

“…The radius is updated using standard rules [ 45 ]. A more detailed discussion of the algorithm can be found in [ 45 , 46 ].…”

“…Fine-tuning of the structure is again realized through minimization of (12). Here, the low cost of the process is maintained using a modified Taylor-expansion model (3), which exploits Jacobian J constructed based on simulations of the composite model, whereas the high-fidelity model simulations are performed only at the center design (i.e., R(x (i) ) = R Be (y (i) )) [46]. Consequently, each iteration of the tuning process requires only two EM simulations of each subcomponent (i.e., a total of four and eight simulations for couplers and phase shifters, respectively) and single evaluation of the assembled BM.…”