Abstract: We present an analysis and design methodology for high-sensitivity material sensors based on the integration of a long-delay self-injection loop with an existing oscillator. The proposed configuration supports two distinct modes of operation: one near a cusp point, which offers high sensitivity without exhibiting jump phenomena, and another with hysteresis, which triggers a state change only when the measurand crosses specific thresholds, corresponding to turning-point bifurcations. Here, we focus on the second mode. To gain insight into the system behavior, we first perform an analytical study of an oscillator with cubic nonlinearity. We derive its turning-point loci and, to the best of our knowledge, demonstrate for the first time a mathematical condition to impose the two hysteresis boundaries as a function of the measurand. This is achieved by appropriately selecting two auxiliary parameters: one being the loop delay, and the other being either the loop attenuation or an element value or bias voltage of the oscillator core. We then trace two bifurcation loci-one for each desired boundary of the measurand-in terms of these two auxiliary parameters, and calculate their intersection points. We demonstrate that at these intersections, a hysteresis cycle versus the measurand is obtained, with the two desired boundaries. The methodology is extended to a transistor-based oscillator, requiring the development of a numerical approach to determine the turning-point loci. This is based on the fundamental bifurcation relationship that defines the turning point. The method has been successfully applied to implement an oscillator-based sensor operating at 2.4 GHz, used for detecting defective solids. For sensing liquid mixtures, a purely empirical methodology has been developed, based on the same concept.

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