This paper aims at modeling a typical battery using electrical circuit models that best fit its operational behavior. Battery models are essential in properly designing battery-driven systems, which are commonly used in practice. The circuit models are derived from previous literature, and potential improvements are taken into consideration. The parameters of the design are derived via a method based on least squares estimation that minimizes the sum of squares of errors between measured impedance values and impedance values given by the model. The measured values are obtained by impedance spectroscopy experimental means. The experiments are applied on a lithium-ion battery, as well as on a lead-acid battery. The experimental setup includes, in addition to the battery under concern, a variable resistive load to discharge the battery and an impedance meter device along with its graphical user interface (GUI) which runs on a standard computer. The experiment consists of measuring battery's real and imaginary impedances at different states of charge and frequencies using the impedance meter. The analyzed models cover a single-time constant Randles cell, Two-Randles cell, another circuit using a finite Warburg impedance element and a circuit with modified finite Warburg impedance.