Fig. 3: Sensing properties as a function of feedback.

a, Amplitude of the sensor signal versus sound pressure amplitude for different values of feedback strength a to study the transfer characteristics of the sensor system (u_d.c. = −200 mV). Measurements were performed using a transducer with a resonance frequency of 14.2 kHz (Table 1 and Methods list the other properties) and chirped sound signals (12–16 kHz). Depending on a, the sensing behaviour in the active mode (a > 0) can be divided into an active, linear mode for a < 0.50; an active, nonlinear mode for 0.70 < a < 0.74; a mixture between the linear and nonlinear mode for 0.50 < a < 0.70; and sound-amplitude-independent, autonomous oscillations for a > 0.74. The intrinsic noise level due to electronics and so on is given by the dashed black line. b,c, Gain as a ratio of the active-mode amplitude to passive-mode amplitude for various sound pressure amplitudes in the two modes: active, linear mode (a < 0.50) (b); active, nonlinear mode (0.70 < a < 0.75) (c). Compressive amplification, yielding a higher gain for lower sound pressure amplitudes, is observed for the active, nonlinear mode. d, Power spectra maximum depending on positive feedback strength a without applied sound. Autonomous oscillations without a sound input occur for a > 0.74. e, Sensitivity of bio-inspired sensors, given by the slope of the ratio of sensing voltage to driving voltage of the loudspeaker, as a function of feedback strength a. A positive feedback strength strongly increases the sensitivity near the bifurcation point, namely, a ≈ 0.5 (left), whereas a negative feedback strength reduces the sensitivity (right). Using positive and negative feedback strengths together, the sensitivity (or gain) of the sensor can be varied by 44 dB, which is close to the 40–60 dB change in gain in the human cochlea due to the outer hair cell operation.