Phase Velocities Equalization of Coupled Microstrip Lines Using $\Omega$-Shaped Particles and Suppression of the Second Harmonic

Abstract

This paper represents a new technique for equalization of phase velocities in coupled microstrip lines using <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\Omega$</tex> </formula> -shaped particles. In the first step, the initial idea is investigated by considering a homogenized model for the substrates, and the structure is analyzed using a developed numerical code. This analysis provides an overview in finding the proper orientation of the particles as well as examining the pseudochirality effect. It is demonstrated that placing the omega particles in a specific orientation inside the substrate leads to a remarkable increase in the phase velocity of odd modes and can provide the phase velocities equalization. In the second step, the proposed structure is simulated with few numbers of particles. The results confirm the considered effective medium for the substrate and the presented physical explanations. The dispersive characteristics of <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\Omega$</tex></formula> particles found to be valuable in proposing a simple and yet efficient method for designing coupled line filters. This procedure is based on finding the dimensions of a conventional filter with a narrower bandwidth than the desired one. In order to validate the effectiveness of the proposed method, a third order Chebychev filter is designed on FR4 substrate and a suppression level higher than 60 dB is achieved. Finally, the proposed structure is fabricated and it is observed that the experimental results are in good agreement with the simulated data.