Mathematical model of low-pass filters

There are some recent patents and books which consider low-pass filters, in these patents and books, there are some circuits of low-pass first order filters. In this paper the mathematical models of two different first order low-pass filters are presented. The two filters are compared using the mathematical models, the magnitudes and the slope of the Bode gain, the first order filter two [6] improves the first order filter one [7] because in the design fequency 10 Hz the magnitude of the first order filter two is more approximated to 1 than the magnitude of the first order filter one. In addition, the comparison between the behavior of the real data of experiments with real circuits and the simulations of the mathematical models for the first order low-pass filters are presented. Two different second order low-pass filters are proposed. The two filters are compared using the mathematical models, the magnitudes and the slope of the Bode gain the second order filter two improves the second order filter one because in the design fequency 10 Hz the magnitude of the second order filter two is more approximated to 1 than the magnitude of the second order filter one. In addition, the comparison between the behavior of the data of experiments with the real circuits and the simulations of the mathematical models for the second order low-pass filters are presented.