LAUSR

Compact loop transmission line resonators, short-circuited in the middle part, are introduced and studied. These resonators are obtained by folding stepped-impedance resonators (SIRs) with two short-circuited ends. Two short-circuited ends of the SIR are connected together, resulting in a loop resonator that is short-circuited in the middle. The synthesis procedure of the SIR with two short-circuited ends and the required arrangement of resonant frequencies is proposed. It is found that the resonant frequencies of the synthesized microstrip loop resonator insignificantly differ from the resonant frequencies of the corresponding SIR with two short-circuited ends. This makes it possible to extend the formulas for describing the resonant frequencies of these SIRs to loop microstrip resonators. Two loop resonators are synthesized, which different from each other by the arrangement of resonant frequencies. The first of them has an increased ratio of the first two resonant frequencies $f_{2}/f_{1}$ . For the second loop resonator, the first three resonant frequencies $f_{1}$ , $f_{2}$ , and $f_{3}$ are close to each other, which is characterized by a reduced ratio $f_{3}/f_{1}$ . Based on a loop resonator with increased the ratio $f_{2}/f_{1}$ , a microstrip bandpass filter (BPF) with an extended stopband is developed. The measured and simulated results are presented.