Sinusoidal voltammetry, where the excitation voltage is a simple sine-wave, is a powerful technique for investigating the electrochemical behaviour of surface-confined redox species. Here we derive an analytical solution for the current response of an ideal, surface-confined, quasi-reversible redox system subjected to large-amplitude sinusoidal voltammetry. The solution is valid whenever the frequency of the sine-wave is large when compared to the Butler-Volmer kinetic rate constant. We derive analytical approximations for the amplitudes of the faradaic harmonics and the initial transient behaviour of the current. From the analytical solutions, we develop a new experimental protocol which allows the underlying system parameters to be estimated directly from experimental current responses run at different excitation amplitudes or with different mean potentials. (C) 2011 Elsevier Ltd. All rights reserved.