Resonator With Reflectors Based on Open-Circuited Stub

Introduction. A two-stub resonator is considered as an analogue of a parallel resonant circuit. Another scheme of the resonator is similar to the Fabry-Perot optical resonator, formed by a resonator cavity and two reflectors. In the presented paper it is proposed a combined reflector formed by a stepped-impedance one and an open-circuited stub. Resonators with such reflectors have a higher quality factor Q than those known based on open-circuited stubs and than the Fabry-Perot resonator. 1 Half wavelength resonator. One of the analogues of the Fabry-Perot resonator is a half wavelength section of the transmission line. The Q-factor of such a resonator is significantly limited by the possible value of the section characteristic impedance. 2 Combined reflector. A combined reflector formed by stepped-impedance and reactive reflectors is considered. The conditions for the high efficiency of such a reflector have been established. One of the conditions corresponds to a large capacitance or a small inductance. Such properties have an open-circuited stub in the vicinity of resonance, respectively before and after it. 3 Reflector on open-circuited stub. The frequency characteristics of the reflector are considered. Stub reflectors of the resonator must differ in their reactivity. In this case, the length of one of the stubs is slightly shorter than the resonant length, and the other one is slightly longer than the resonant length. When detuning from the resonant frequency of the resonator, stub reflectors with different reactivity have amplitude and phase mismatches that increase with detuning. As a result, the Q-factor is greater than that of the Fabry-Perot resonator, whose reflectors are frequency-independent. 4 Comparison of the characteristics of the proposed and known resonators. Transmission responses of two variants of the proposed resonator and, for comparison, known resonators on open-circuited stubs are given. Resonators on stub reflectors have a much higher Q-factor. Characteristics of the proposed resonator and known half-wave resonators are compared. The proposed resonator has a higher Q-factor, and its transmission response has deep suppression bands due to stub’s resonances. 5 Formulas for Q-factor of resonators. An approximate formula for the Q-factor of the proposed resonator is given, which makes it possible to predetermine the value of the design parameters of the resonator. The formulas for the Q-factor of all considered resonators are summarized in a table. The approximate Q-values are close to the exact ones. 6 Resonators based on the inverted microstrip line. The proposed solution can be realized in resonators based on various transmission lines (planar, in particular microstrip, coaxial, etc.). The realization of the proposed resonators based on the inverted microstrip line taking losses into account is considered. The reduction in the Q-factor of the two variants of the proposed resonator due to losses is 2.5 and 5.5%. 7 Results discussion. Near the resonance, the frequency dependence of the reactive conductance of the open-circuited stub has a high steepness. Thanks to this, resonator based on such stubs is characterized by a high Q-factor and a steep transmission response. Near the passband, the stubs form two zeros corresponding to their resonances. In a two-stub resonator, the stubs are similar to the capacitance and inductance of the parallel resonant circuit. In the proposed resonator, where the stubs are reflectors, the frequency response properties of the two-stub resonator are preserved with a significant increase in the Q-factor. Conclusion. The efficiency of the considered resonator with reflectors on an open-circuited stub is three times higher than that of a traditional two-stub resonator. Due to the frequency dependence of the reflection coefficient of the reflector on an open-circuited stub, the increase in the Q-factor in the considered resonators is 51 and 25% compared to the Fabry-Perot resonator. As compared with known half-wave resonators, the proposed resonator has a higher Q-factor, and its transmission response has deep suppression bands due to stub’s resonances. The obtained approximate formula for the Q-factor of the resonator with stub reflectors makes it possible to predetermine the value of the design parameters of the resonator for a given Q-factor. The approximate Q-values are very close to the exact ones. The reduction in the Q-factor of the two variants of the proposed resonator due to losses when it is realized on the basis of an inverted microstrip line is 2.5 and 5.5%.