Resonant frequency of 30°-60°-90° triangular dielectric resonator at fundamental mode

Theoretical and experimental investigations on 30 degrees-60 degrees-90 degrees Triangular Dielectric Resonator (TDR) are presented here for TMz and TEz modes for the first time. Approximate expressions for eigenfunction and eigenvalue are given here. Fundamental TM101z mode is explored in detail. A qualitative explanation of decrease in effective dimensions from actual physical dimensions is explained here with help of internal electric field. Approximate curve fitted graphical solution is given here to predict the resonant frequency for 10 <= epsilon(r) <= 100 where er is relative permittivity of the TDR. Four 30 degrees-60 degrees-90 degrees TDRs are fabricated and tested. It is found that our theory is in excellent agreement with experimental data and data obtained using 3D EM simulator. It is found that for a given resonant frequency, height of TDR and epsilon(r) 30 degrees-60 degrees-90 degrees TDR takes just half volume compared to equilateral TDR. Mathematical explanation is also given here to justify this fact. Therefore, our theory on 30 degrees-60 degrees-90 degrees TDR will help to design compact microwave resonator. It is also believed that our theory can be applied to investigate 30 degrees-60 degrees-90 degrees triangular shaped circulators, oscillators, filters, dielectric resonator antennas etc.