Three common methods to characterize and diagnose battery behavior are electrochemical impedance spectroscopy (EIS), the potentiostatic intermittent titration technique (PITT), and the galvanostatic intermittent titration technique (GITT). All three methods rely on small signal excitation in order to linearize the system behavior and simplify analysis. Analytic solutions are derived that can be used in conjunction with EIS, PITT, and GITT experiments to identify governing resistances, and extract parameters and properties that characterize half-cell behavior using a lithium reference electrode. The solutions include the effects of intercalate diffusion, charge-transfer kinetics, and ohmic losses in the electrolyte and solid phase of the porous electrode. A simple modification also includes the effect of electrolyte diffusion, once it has reached a quasi-steady state. Comparisons are given to numerical solutions, including transient electrolyte diffusion, which show the accuracy of the derived formulas. These comparisons also indicate that electrolyte diffusion takes about 30 seconds from the start of a PITT or GITT experiment to reach quasi-steady state.The rate at which lithium diffuses into and out of solid phase intercalate materials is a primary limiting factor for lithium batteries operating at high rates of charge and discharge. Texts are available that review methods to characterize irreversible processes in electrochemical systems. 1-5 Specific to lithium ion battery systems, 6-17 the most common methods for determining the solid phase diffusion coefficient of lithium within the host material are (i) analysis of lowfrequency data from electrochemical impedance spectroscopy (EIS) measurements, 18-23 (ii) the potentiostatic intermittent titration technique (PITT), 24-36 and (iii) and the galvanostatic intermittent titration technique (GITT). [37][38][39][40][41][42] The analysis of data is aided by the use of analytic solutions; for the analytic solutions referenced, voltage losses in the electrolyte phase or ohmic losses in the solid phase of the porous electrode are ignored. The successful application of these analytic tools thus requires electrodes that are specially designed to make the above-mentioned losses negligible, and a set of inequalities that determines when such conditions hold has been given. 43 In contrast, optimized electrode design must balance voltage losses against power and capacity needs, and this is consistent with the observation that commercial electrodes used in traction batteries are not dominated by losses from solid-phase diffusion in comparison to other types of transport loss. It is the purpose of this work to generalize the analytic solutions mentioned above so that they can be applied to more general types of electrodes, such as those used in traction applications today, without the above-mentioned restrictions.The conventional governing equations for charge transport in lithium electrodes 4,7,8,10,17 will be employed in this work, and we shall not further question potential...