Analytical Equations for Designing Meander Line Antennas

Abstract

Meander Line Antenna (MLA) is widely employed in compact electronic devices, such as cellular phones and WLAN terminals, owing to its electrically small size. To facilitate practical antenna design, essential equations encompassing self-resonant structure, input resistance, antenna efficiency, and Q factor have been systematically developed. However, the prior self-resonant equations included only inductive reactance (XC), neglecting the capacitive reactance (XD) equation. This manuscript addresses this gap by introducing new design equations, presenting a newly derived $\rm X_{D}$ equation and an improved Q factor expression. The inadequacies of the existing Q factor equation, reliant on the radius of a sphere encompassing the antenna, are addressed by proposing a more fitting expression that incorporates antenna structural parameters using the ratio of reactance to resistance. The overview of existing design equations sets the stage for the introduction of these newly developed equations. To assess the accuracy of electromagnetic (EM) simulation results, a comparative analysis is conducted between simulated and theoretically calculated input resistance values. The derivation of new reactance equations involves the development of $\rm X_{C}$ equations based on electromagnetic theory. The $\rm X_{D}$ equation is established by deriving the stored charge equation from electrical near-field distributions obtained through EM simulations. By applying the relationship between charge and capacitance, a new $\rm X_{D}$ equation is obtained. Subsequently, a new self-resonant equation is derived, and the validity of the newly derived equations is confirmed through EM simulation results, ensuring their accuracy. Two MLA prototypes, with lengths of 0.05 and 0.1 wavelengths at 405 MHz, are fabricated and experimentally validated. Smith chart measurements confirm the self-resonant condition and input resistance. By correlating with the VSWR characteristics, the obtained Q factor of approximately 100 aligns successfully with the results from the reactance equation. The antenna gain is verified at −7.7 dBi and −3.5 dBi for antennas with lengths of 0.05 and 0.1 wavelengths, respectively. These findings establish the practical applicability of the proposed equations for antenna design and elucidate the performance of practical antennas.

Keywords

• Meander line antenna
• Q factor
• Self-resonant