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Third Order Exceptional Point of Degeneracy in Coupled Resonators at Radio Frequencies


Operation mechanism of many novel sensors is based on the detection of splitting of resonant frequencies. Recently emerged topic known as exceptional points of degeneracy (EPD) paves the way to engineer structures where they exhibit highly sensitive frequency splitting phenomenon. An EPD is a special point in the system parameter space at which at least two eigenmodes coalesce in both their eigenvalues and eigenvectors. The unique properties of higher order EPD can provide means of enhancing the frequency shift as they would increase the effect of perturbation which should lead to higher sensitivity. In this dissertation, we propose a circuit comprised of three RLC coupled resonators with balanced loss and gain that exhibits a third order EPD and investigate the conditions for a third order EPD to occur in such circuit. We validate the existence of the EPD by examining the behavior of the system at that special point. We finally illustrate the time domain response of such system operating at regular frequency (not an EPD frequency) and also at a third order EPD frequency where we show the quadratic growth of the system eigenstates in time.

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