Time domain quantification of the performance of a nonlinear dynamic device in the presence of a noise floor

We consider the performance of a nonlinear dynamic device, operated as a threshold detector, in the time domain. The device is characterized by a figure-of-merit that involves the mean residence times in its two stable steady states, as well as the dispersion in this quantity stemming from a noise floor. As a particular example, we consider a coupled (overdamped) oscillator system, the underpinnings of a coupled core magnetometer (CCM). We provide a detailed discussion of how the device is used, in practice, to detect a weak dc target magnetic field, and explain the importance of characteristic time-scales in the problem specifically the device time-constant, the noise correlation time and the observation time (to obtain an averaged reading in the presence of noise). A device “Resolution” is introduced as a performance measure and is, analytically, computed under specific (but realistic for practical applications) conditions. This measure is shown to be independent of the target signal; in fact it depends only on the noise and device parameters, in the weak signal limit (that is of interest in most applications). The resolution is seen to be analogous to the inverse of a response signal-to-noise ratio.