Theory of loss and gain trimming of resonator-type filters

The characteristic response of resonator-type filters is determined by the mutual resonator-to-resonator coupling coefficients, which are not readily trimmed once a device is fabricated. We show that loss and/or gain is a mechanism which can mimic the role of the coupling coefficients, and which can therefore be used for post-fabrication tuning or trimming. By using loss-only trimming, the throughput crosstalk performance can be improved by several orders of magnitude while incurring only small signal attenuation.