MANUFACTURING TOLERANCE INVESTIGATION OF MICROSTRIP HAIRPIN FILTERS USING FULL-WAVE ELECTROMAGNETIC SIMULATION

Abstract

Two fourth-order hairpin filters with identical electrical specifications but different resonator widths (1 mm and 2 mm) were designed for operation in the 2.4 GHz frequency band. The design procedure combined analytical synthesis, full-wave electromagnetic simulation based on the finite-element method, preliminary sensitivity analysis, and numerical optimization using the Nonlinear Programming by Quadratic Lagrangian (NLPQL) algorithm. Physical prototypes were fabricated using a laboratory photolithographic process and experimentally characterized using a vector network analyzer. The measured scattering parameters were compared with simulation results to evaluate the influence of practical manufacturing limitations.

To assess the impact of fabrication accuracy, a detailed sensitivity analysis was performed by introducing controlled deviations of resonator width, resonator length, and coupling gaps from their nominal values. The considered deviations corresponded to the achievable manufacturing accuracy of approximately ±100 μm. The results demonstrated that coupling gaps represent the most critical geometrical parameters, producing the largest variations in return loss and passband characteristics. Deviations in resonator width and resonator length had a smaller but still noticeable influence on filter performance. Comparison of the measured and simulated responses showed generally acceptable agreement. The observed discrepancies can be explained by dimensional inaccuracies introduced during fabrication and by variations in the dielectric properties of the FR4 substrate.

The comparative analysis of the two filter configurations revealed that increasing the resonator width from 1 mm to 2 mm does not significantly improve tolerance robustness. Both filters exhibited approximately the same sensitivity to variations of the investigated geometrical parameters. The obtained results indicate that compact and inexpensive hairpin filters for the 2.4 GHz band can be successfully implemented on FR4 substrates using low-cost fabrication technologies. Since wider resonators did not provide a substantial tolerance advantage, the use of narrower resonators appears preferable due to reduced filter dimensions and larger achievable coupling gaps.

Keywords: hairpin filter, microstrip filter, manufacturing tolerance, full-wave electromagnetic simulation, finite-element method, FR4 substrate, sensitivity analysis, microwave filter design