Koziel Slawomir, Pietrenko-Dabrowska Anna
Engineering Optimization & Modeling Center, Reykjavik University, 102, Reykjavik, Iceland.
Faculty of Electronics, Telecommunications and Informatics, Gdansk University of Technology, 80-233, Gdansk, Poland.
Sci Rep. 2022 Aug 3;12(1):13320. doi: 10.1038/s41598-022-17661-7.
Handling constraints imposed on physical dimensions of microwave circuits has become an important design consideration over the recent years. It is primarily fostered by the needs of emerging application areas such as 5G mobile communications, internet of things, or wearable/implantable devices. The size of conventional passive components is determined by the guided wavelength, and its reduction requires topological modifications, e.g., transmission line folding, or utilization of compact cells capitalizing on the slow-wave phenomenon. The resulting miniaturized structures are geometrically complex and typically exhibit strong cross coupling effects, which cannot be adequately accounted for by analytical or equivalent network models. Consequently, electromagnetic (EM)-driven parameter tuning is necessary, which is computationally expensive. When the primary objective is size reduction, the optimization task becomes far more challenging due to the presence of constraints related to electrical performance figures (bandwidth, power split ratio, etc.), which are all costly to evaluate. A popular solution approach is to utilize penalty functions. Therein, possible violations of constraints degrade the primary objective, thereby enforcing their satisfaction. Yet, the appropriate setup of penalty coefficients is a non-trivial problem by itself, and is often associated to extra computational expenses. In this work, we propose an explicit approach to constraint handling, which is combined with the trust-region gradient-search procedure. In our technique, the decision about the adjustment of the search radius is determined based on the reliability of rendering the feasible region boundary by linear approximation models of the constraints. Comprehensive numerical experiments conducted using three miniaturized coupler structures demonstrate superiority of the presented method over the penalty function paradigm. Apart from the efficacy, its appealing features include algorithmic simplicity, and no need for tailoring the procedure for a particular circuit to be optimized.
近年来，处理施加在微波电路物理尺寸上的约束已成为一项重要的设计考量。这主要是由5G移动通信、物联网或可穿戴/植入式设备等新兴应用领域的需求推动的。传统无源元件的尺寸由导波波长决定，减小尺寸需要进行拓扑修改，例如传输线折叠，或利用利用慢波现象的紧凑单元。由此产生的小型化结构在几何上很复杂，通常表现出强烈的交叉耦合效应，而解析或等效网络模型无法充分考虑这些效应。因此，需要进行电磁（EM）驱动的参数调整，这在计算上是昂贵的。当主要目标是减小尺寸时，由于存在与电气性能指标（带宽、功率分配比等）相关的约束，优化任务变得更具挑战性，而评估这些指标的成本都很高。一种流行的解决方法是使用惩罚函数。在这种方法中，对约束的可能违反会降低主要目标，从而强制满足这些约束。然而，惩罚系数的适当设置本身就是一个不平凡的问题，并且通常会带来额外的计算开销。在这项工作中，我们提出了一种明确的约束处理方法，该方法与信赖域梯度搜索过程相结合。在我们的技术中，关于搜索半径调整的决策是基于通过约束的线性近似模型绘制可行区域边界的可靠性来确定的。使用三种小型化耦合器结构进行的综合数值实验表明，本文提出的方法优于惩罚函数范式。除了有效性之外，其吸引人的特点还包括算法简单，并且无需针对特定要优化的电路定制该过程。
