  We present a scheme for high-sensitive sensors based on an exceptional point
of degeneracy (EPD) in a circuit made of two LC resonators coupled by a
gyrator. We study two cases with series and parallel LC circuits. We obtain
conditions that lead to an EPD when one of the two resonators is composed of an
inductor and a capacitor with negative values. We explain the extreme
sensitivity to perturbations of such a circuit operating at an EPD and its
possible use for sensor applications. The EPD occurrence and sensitivity are
demonstrated by showing that the eigenfrequency bifurcation around the EPD is
described by the relevant Puiseux (fractional power) series expansion. We also
investigate the effect of small losses in the system and show that they can
lead to instability. The proposed scheme can pave the way for a new generation
of high-sensitive sensors to measure small variations of physical or chemical
quantities.
