Optimized fractal coils: Development of device modelling structure with artificial neural network

Abstract

The present research introduces a novel design for fractal coils and employs a machine learning algorithm to predict their resonance frequency. The proposed coil features a distinctive triangle-polygon structure, derived using the Sierpiński Gasket mathematical modeling method. The proposed coil features two layers of conductive copper planes (0.545 mm each), separated by a dielectric substrate layer (0.76 mm) made of Roger substrate material (RT 6010™) with a dielectric constant of 2.2, resulting in overall dimensions of 40 × 30 × 0.762 mm³. Simulation results have validated the stability of the proposed coil, which was tested using a Vector Network Analyzer (VNA-N5247A) and a Voltage Standing Wave Ratio (VSWR) meter with a bridge (MVS300B). The coil resonates at 3.35 GHz within a frequency range of 2.88–3.83 GHz and provides an input reflection coefficient of 40.69 dB with a VSWR of 0.025. A significant contribution of the methodology is the application of an Artificial Neural Network (ANN) to predict the coil's scattering parameters, specifically the resonance frequency. The ANN model, trained on datasets derived from the Sierpiński Gasket model and optimized using the Adam optimizer along with hyperparameter randomization techniques, accurately correlates with the hidden layers. This model has demonstrated precise and stable results, validated against both simulation and physical coil measurements. This proposed methodology not only advances the design of fractal coils but also optimizes the prediction of scattering parameters using ANN, paving the way for further research and applications.