In the thesis, the design of the slotline ring resonators is discussed. Due to a variety of resonators employed in circuit design, the feeding(or energy-coupling) strategy is always an important issue. Thus, different kinds of slotline feeds are discussed in the thesis. Based on the equivalent circuit models, we use a series of analyses to study the scheme of slotline ring resonators step by step. By analyzing the equivalent circuit models, we improve the feeding strategy and ring structure to realize a coplanar circuit which has the characteristic of ring resonator. The full-wave electromagnetic simulator, IE3D and HFSS, will be used in the design. The circuit simulator, ADS, will be used in the design of equivalent circuit model. Circuits will be realized using FR4 printed-circuit boards. The design will be validated by the comparison with experimental results.