A dual-mode microwave sensor for retrieving permittivity of materials based on multiple complementary rectangular ring resonators

A dual-mode microwave sensor based on multiple complementary rectangular ring resonators (CRRRs) are proposed to characterize the permittivity of material under test (MUT) in this manuscript. The designed microwave sensor is based on substrate integrated waveguide (SIW) with multiple CRRRs etched on the top plane. With comparison to traditional microstrip line excited sensors, the proposed SIW sensor has a higher quality factor. The SIW structure has the feature of bandpass filter, and the geometrical parameters of SIW are optimized to achieve an ultra-wideband with the cavity resonant modes of TE101, TE102, TE103, and TE104. The four cavity resonant modes (TE101, TE102, TE103, and TE104) substitute the pass-band, and by utilizing the characteristic of quasi bandpass filtering of SIW, four pairs of identical CRRRs can produce two resonant modes in the passband, named by mode1 and mode2. The electrical field distribution of mode1 is mainly confined at two intermediate resonators, and mode2 has an intensive electrical field at resonators on both sides. As the resonant frequencies are altered with the variations of permittivity of MUTs, thus the mathematical expressions can be obtained. By using the mathematical expressions, the permittivity of MUTs can be predicted. Moreover, the error model is used to decline the error of measurement. The equivalent circuit model is established to illustrate the operating principle of the sensor. A good agreement between circuit model and simulation is acquired. In the measurement, the average sensitivities of proposed microwave sensor are about 6.33% and 6.17% for mode 1 and mode 2, respectively. Besides, the errors of retrieving permittivity are about 0.5% and 0.9% for mode 1 and mode 2, respectively.