Abstract

This article presents a comprehensive analytical, numerical, and experimental study of the amplification and detection of weak signals in magnetically coupled electromagnetic systems, using an architecture consisting of three magnetically coupled coils. A rigorous mathematical model of the system is developed, which includes the formulation of the mutual inductance matrix and a state-space representation that captures the dynamic interaction between the coils. It is important to note that the electromagnetic subsystem is linear and that the stochastic resonance effect is achieved by incorporating an external nonlinear bistable element. In this configuration, a weak periodic signal below a threshold is applied to the primary coil, while a controlled source of Gaussian white noise is injected into a secondary coil. A third coil functions as a sensing element, capturing the superimposed magnetic response resulting from coupling effects. The voltage induced in the sensor coil is subsequently processed by a bistable nonlinear element implemented via a Schmitt trigger, which provides the nonlinearity and bistability necessary to enable stochastic resonance and the detection of the weak periodic signal. The conditions of the SR are analyzed in terms of noise intensity, coupling coefficients, and system parameters, highlighting the existence of an optimal noise level that maximizes the signal-to-noise ratio (SNR) at the output. A detailed simulation framework has been developed in MATLAB/Simulink, enabling a systematic exploration of the parameter space and the validation of theoretical predictions. The simulation results are further supported by experimental measurements obtained from a physical prototype, which show agreement with the proposed model. The main contribution of this work lies in demonstrating that magnetically coupled electromagnetic structures can effectively interact with nonlinear bistable elements to exploit stochastic resonance in the detection of weak signals, even when the electromagnetic domain itself remains linear. The results demonstrate that magnetic coupling is an effective mechanism for mediating constructive interactions between noise and weak signals, thereby improving the detection of the latter. These results extend the applicability of stochastic resonance to hybrid electromagnetic systems and demonstrate its relevance in practical applications. Potential applications include ultra-sensitive magnetic detection, low-power signal detection, magnetic transducers, and robust signal recovery in noisy electromagnetic environments, particularly in contexts where conventional linear amplification fails.

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