Numerical simulations of electrochemical systems were used to explore the influence of large-amplitude potential perturbations on the measured impedance response. The amplitude of the input potential perturbation used for impedance measurements, normally fixed at a value of 10 mV for all systems, should instead be adjusted for each experimental system. Guidelines are developed for selection of appropriate perturbation amplitudes. A characteristic transition frequency is defined that can be used to tailor a frequency-dependent input signal to optimize signal-to-noise levels while maintaining a linear response.