Miniature DBR filters compatible with low cost substrates: Formulation

This paper describes and formulates a miniaturization approach for bandpass filters. Based on an illustrated miniaturizing principle of stubs, the general fundamental equations for a miniaturized narrow bandpass DBR filter are derived for the first time. Equations for the transmission zeros, the fundamental resonance frequency and the higher order resonance frequencies (poles) are, thus, provided. Then, starting from these design equations, a first-order DBR filter is designed, measured and validated. Measurement results, which are in good agreement with the simulated ones, show a high degree of miniaturization of 83%, better insertion loss and better filter out-of-band rejection.