In this work, a new memristor-based low-pass filter topology is suggested. Memristor-based filters are nonlinear circuits and many of them cannot be solved analytically. To find an approximate analytical solution of the filter equations, MacLaurin series is used for the first time. Time and frequency domain behavior of the filter are obtained. Also, the frequency domain gain and total harmonic distortion characteristics of the filter are given. Results obtained by the small signal model have been compared with the dynamic model results. It is shown that the small signal model is able to predict the filter behavior very well.