Hairpin Resonators in Varactor-Tuned Microstrip Bandpass Filters

Resonance equations for two tunable symmetrical hairpin resonators with short-circuited ends are obtained for the first time. The case is considered when a parallel or series variable capacitance is connected to the middle of these resonators. It is established that odd resonance frequencies of such resonators do not depend on the variable capacitance value and they are constant. Two traditional symmetrical open-ends hairpin resonators, to which one or two variable capacitors are connected, are also considered. New resonance equations of the hairpin resonator with two capacitors have been obtained, where a segment of uniform transmission line is replaced by a segment of non-uniform transmission line. For all four hairpin resonators, the dependence of the resonant frequency ratio f_i/f₀ on the electrical length of the resonators was investigated. It was found that two hairpin resonators have the highest f_i/f₀ ratio: a resonator with two short-circuited ends and a parallel capacitance connected, and a loop resonator with two open ends connected by a variable capacitance. The capacitance of the first resonator is four times the capacitance of the second resonator, so it is advisable to use it at higher frequencies. The second resonator is most suitable for use at lower frequencies. Based on this resonator, a narrowband (2.4%) forth order microstrip bandpass filter (BPF) varactor-tuned in frequency range 225-400 MHz is designed. Due to the wide rejection band, the attenuation more than 40 dB at 3f₀ at all tuning range is achieved.