Feature: Communications system design
where Z0
is the characteristic impedance, εr
is the relative
permittivity of the used substrate, h is the substrate’s height, w is the width of the strip line and t is the thickness of the copper.
(2) where εeff is the eff ective dielectric constant, εr is the relative
permittivity of the used substrate, H is the substrate’s height and W is the width of the strip line.
(3) where fr is the resonance frequency, εeff is the eff ective dielectric constant and L is the length of the strip line. (4) where BW is the bandwidth, fc eff ective dielectric constant εeff is centre frequency and Q is
the fi lter’s quality factor. T ese equations govern the characteristic impedance Z0
and resonant frequency fr , . By
fi ne-tuning the transmission line dimensions, we ensured optimal power transfer and eff ective coupling between the feedline and the resonator, thereby enhancing the fi lter’s overall performance. Special attention was given to the discontinuities introduced by the open-loop geometry, which are critical for achieving the desired coupling strength and fi ltering characteristics. In this work, we extend conventional design techniques
by incorporating a multi-objective optimisation strategy addressing electromagnetic fi eld distribution, sensitivity to fabrication tolerances and trade-off s between bandwidth and loss, coupled with a detailed transmission line analysis to refi ne the coupling mechanism between the resonator and the feedline.
Design process Filter geometry T e design begins with defi ning the resonator’s geometric parameters. Critical dimensions include the side length of the square loop, the width of the conductive trace, the gap between the loop and the ground plane and the dimensions of the fl oating blocks and slots. T ese parameters have a direct infl uence on the resonant frequency, bandwidth and selectivity. A systematic variation of these dimensions forms the basis of our optimisation, ensuring robust performance against manufacturing variations.
Substrate selection Selecting the appropriate substrate material is crucial for achieving high effi ciency in both, the simulation and
Figure 1: Top view of the fi nal resonator design
Figure 2: 3D view of the resonator geometry
Figure 3: Simulated S11 and S21 responses of the fi lter fabrication of the resonator. T e dielectric constant (εr ) and loss
tangent (tanδ) of the substrate signifi cantly impact the fi lter’s electrical characteristics, including bandwidth, insertion loss and return loss. To optimise fi lter performance, it is essential to choose a substrate with a low dielectric loss and a high dielectric
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