Characteristics and design formulas of a microstrip stub-loaded multi-mode ring resonator

In this paper, the characteristics of a microstrip tab-coupled stub-loaded ring resonator are investigated, and design formulas for determining the 3dB bandwidth, passband reflection zeros, and transmission zeros of the resonator are derived based on the even- and odd-mode analysis of the equivalent circuit of the resonator. Design examples are provided which reveal that with appropriate choices of the ring resonator parameters, up to four modes can be observed in the passband of the resonator. This property can be exploited in the design of circuits using this type of resonators, with the expectation of significant improvements in the circuit performances.