Abstract: We propose a new type of oscillator sensor based on a self-modulated oscillator, exhibiting two concurrent oscillations at high and low frequency. To ensure a low phase noise, a high-frequency design is based on a stepped-impedance resonator, over which the material under test (MUT) is placed. The low-frequency oscillation is achieved through the introduction of feedback elements in the bias circuitry, by following a systematic procedure based on the use of stability circles and a rigorous two-stage stability analysis. The low-frequency oscillation modulates the high-frequency one and its harmonic components, generating multiple spectral lines around each of these components. For the first time to our knowledge, we demonstrate the simultaneous influence of the MUT on two concurrent oscillations, coupled through the nonlinear effects of the active device, as explained using an envelope-domain formulation. Thus, the sensing is based on the central frequency, frequency spacing, and amplitude of the spectral lines, enhancing both sensitivity and reliability. This multivariable approach enables robust multipoint detection and is expected to offer higher sensitivity compared with traditional methods that rely on a single oscillation frequency and amplitude. We present a calibration procedure, based on these measurands, to determine the real and imaginary parts of the MUT dielectric constant. The circuit has been fabricated and experimentally characterized, yielding very good results.

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