Topology optimization of antenna matching networks: Theoretical modeling and numerical experiments

Topology optimization is an innovative computational technique that determines the optimal material distribution or structural configuration to meet the specific design criteria. This technique is crucial in the intelligent microwave device design due to its high degree of freedom compared with shape or size optimization. Microwave engineering is an important fundamental course for physics, electronic engineering, and communication engineering students. Incorporating device topology optimization experiments into the curriculum can make the abstract concepts in the microwave theory and network theory more easy to comprehend, this not only bridges classroom knowledge with advanced industrial design techniques but also cultivates students’ analytical, modeling, and engineering skills.

Using concrete examples of antenna matching network optimization, the experiment reported in this study explores the method and implementation techniques of topology optimization. The investigated network topology optimization experiment involves two interconnected phases: theoretical modeling and numerical optimization. Initially, this study uses the impedance matrix approach for the accurate and fast modeling of a grid-like antenna matching network. Once the connection relationship in the matching network is determined, a closed-form expression of the network scattering parameters can be obtained explicitly, eliminating the need for computationally expensive full-wave simulations and thus accelerating the forward problem solving during each iteration of topology optimization. Subsequently, a genetic algorithm, which is a type of powerful stochastic optimization algorithm, is leveraged to optimize the connection relationship in the grid-like network, achieving an intelligent on-demand design of the antenna operating frequency band. The genetic algorithm can handle the ill-posed optimization problem using mechanisms such as selection, crossover, and mutation to yield solutions that approximate the optimal solution of the search process.

This study demonstrates the resultant structures and performances of topology-optimized narrow-bandwidth monopole antennas operating at center frequencies of 1.00, 1.20, and 1.40 GHz, as well as a wideband antenna operating in the range of 1.099–1.395 GHz. The narrow-bandwidth design is achieved by introducing a single resonance of the matching-network-loaded antenna that closely matches the prescribed center frequency, while the wideband design emerges from creating two resonances with an appropriate frequency separation. Two important figures of merit—the reflection coefficient and antenna’s total efficiency—are introduced in these experiments to assess the antenna performance. These metrics measure the power reflection from the antenna feeding port and the ratio of the radiated power to the incident power, respectively. Following the topology optimization of the grid-like antenna feeding network, the values of the port reflection coefficients of the monopole antennas reduce notably from nearly 0 dB to below −10 dB over the specified frequency band, and the antenna efficiencies are generally higher than 90% over the operating band, with peak efficiency values exceeding 95%.

This study systematically elucidates the theory and workflow of network topology optimization, emphasizing the combined use of impedance matrix modeling and genetic algorithms. Numerical optimization experiments are conducted to obtain an on-demand intelligent design of the antenna matching network. These experiments reveal a substantial improvement in the antenna radiation performance after incorporating the topology-optimized matching network. This experiment serves as a comprehensive and advanced training opportunity for microwave- and antenna-related courses, significantly enhancing undergraduate students’ ability to tackle complex engineering problems.