We derive and implement analytic solutions for the description of batteries subject to cyclic voltage and current sources of varying amplitudes, consistent with vehicle drive events. An equivalent circuit comprising a resistor in series with a parallel resistor–capacitor combination is employed. The method we develop is applied to a high-power lithium ion cell, thereby allowing us to obtain parameters and overall characteristics useful for (1) representing the battery in system (e.g., vehicle) models and (2) providing a quantitative means of comparing and classifying battery systems. Closed-form analytic solutions derived using Fourier series are compared with experimental data.