Mode charts for microstrip resonators on dielectric and magnetic substrates using a transverse-resonance method

Edge effects in planar resonators may be described by subdividing the resonators into thin strips and replacing each strip by an equivalent waveguide transmission line. The discontinuity between adjacent strips is accounted for by using a lumped-element inductor. The resonant frequency of the overall network is calculated by forming a transverse resonance condition. This approach has been used to obtain mode charts for planar triangular resonators on an alumina substrate and on a demagnetised-garnet substrate, and for circular and rectangular resonators on rexolite substrates. Experimental points show good agreement in each case. A theoretical mode chart for a hexagonal resonator, not previously described, is also evaluated.