Frequency-Domain Analysis of a Coupled Oscillator Sensor with an Exceptional Point of Degeneracy
Camilo Moncada, Franco Ramírez, Almudena Suárez · 2025
We present, for the first time to our knowledge, a frequency-domain investigation of a sensor based on an oscillator with two coupled resonators, which exhibits an exceptional point of degeneracy (EPD). We will initially identify the kind of bifurcation associated with the EPD. Then, we will derive a mathematical condition to achieve this bifurcation in realistic circuits, which can be evaluated through standard small-signal simulations. We will also perform an exhaustive frequency-domain calculation of the periodic solutions versus the capacitor in one of the resonators. This will enable an understanding of the impact of the EPD on the geometry of the solution curves. Finally, we will present a first systematic procedure for the implementation of a permittivity sensor. This will involve a judicious substitution of one of the capacitors by a transmission line, over which the material under test (MUT) will be placed. The sensor has been manufactured and experimentally characterized.