# Application of Compact Folded-Arms Square Open-Loop Resonator to Bandpass Filter Design
###### Abstract  
Folded-arms square open-loop resonator (FASOLR) is a variant of the conventional microstrip square open-loop resonator (SOLR) that facilitates further device size miniaturization by having the two arms of the conventional SOLR folded inwards. This paper highlights the benefits of this brand of compact SOLR by implementing a five-pole Chebyshev bandpass filter (BPF) using compact FASOLR. The test BPF is presented, with centre frequency of 2.2 GHz, fractional bandwidth of 10%, passband ripple of 0.04321 dB, and return loss of 20 dB. The design is implemented on a Rogers RT/Duroid 6010 LM substrate with a dielectric constant of 10.7 and thickness of 1.27 mm. The filter device is manufactured and characterised, with the experimentation results being used to justify the simulation results. The presented measurement and electromagnetic (EM) simulation results demonstrate a good match. The EM simulation responses achieve a minimum insertion loss of 0.8 dB and a very good channel return loss of 22.6 dB. The measurement results, on the other hand, show a minimum insertion loss of 0.9 dB and a return loss of better than 19.2 dB. The filter component has a footprint of 36.08 mm by 6.74 mm (that is, 0.26 \(\mathrm{\SIUnitSymbolMicro\secondo\times 0.05}\)\(\mathrm{\SIUnitSymbolMicro g}\)), with \(\mathrm{\SIUnitSymbolMicro g}\) indicating the guided wavelength for the 50 Ohm microstrip line impedance at the centre frequency of the proposed fifth-order bandpass filter. resonator; half-wavelength; square open-loop; folded-arms square open-loop; bandpass filter; coupling; microstrip +
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The modern-day electromagnetic (EM) spectrum is becoming overcrowded and is heavily crammed with a variety of wireless signals and other communication and sensing circuits and components. EM waves of frequencies, varying from 300 MHz up to 300 GHz, remain classified as microwaves. This frequency band matches the free space wavelengths of 1 m to 1 mm, in that order. EM waves of frequencies varying from 30 GHz to 300 GHz stay classified as millimetre-waves due to their wavelengths that fall directly over 1 mm and directly under 10 mm. The radiofrequency (RF) band falls somewhere beneath the microwave range, though the boundary that separates the radio frequency and microwave bands is subjective and changes based on the method established for developing the band. Due to the overcrowding of modern radio frequency and microwave communication systems, researchers in this field have continuously worked on miniaturizing front-end components to ensure compact size and improved performance. The compact folded-arms square open-loop resonator (FASOLR) presented in this paper is one such research efforts aimed to further reduce the footprint of communication systems components. Microstrip folded-arms square open-loop resonators [13; 14; 15] are achieved by having the two arms of the conventional SOLR [16] folded inwards, as shown in Figure 1c. This leads to a further reduction of approximately 20% when compared to the conventional SOLR, which is already popular for its compactness. Though the coupling scheme of the FASOLR is like that of the SOLR reported in [16], the FASOLR has improved the physical device footprint by about a 20% reduction. The length of each side of the FASOLR is measured about 1/10 of a guided wavelength, as indicated in Figure 1c, while that of the SOLR is about 1/8 of the guided wavelength, as reported in [16] and shown in Figure 1b. The coupling between the two folded arms of the FASOLR ensures that the size reduction is greater than the 20% expected based on the resonator physical dimension [14]. Bandpass filters have been extensively researched and described in the literature [17; 18; 19; 20; 21; 22; 23]. This type of filter has wide applications in wireless communications, particularly in wireless transmitters and receivers [19]. In the transmitter, this type of filter is used to restrict the bandwidth of the output signal to the allocated channel for transmission.