Design equations are derived for a particular extremum-control system. The system has a single-input plant with input disturbances, measurement noise and an output lag; the control signal is generated by adding a sinusoidal perturbation to the plant input and demodulating the corresponding perturbations in the plant output. A linearised equivalent circuit is introduced, and a numerical measure of how accurately it approximates the system is determined experimentally. The measure of accuracy is combined with standard analytic results about the performance of the equivalent circuit to give an equation describing the performance of the system. The equation leads to design curves giving the best values of controller parameters for any given set of plant-parameter values. An experimental verification of the design procedure shows that it is valid for systems where the output lag is not the dominating factor.