In 1971, memristor is claimed as a missing circuit element and almost 40 years later than its prediction a memristive system behaving as a memristor has been found in 2008. Memristor is accepted by many as the new and the fourth fundamental circuit element. Analog applications of memristor have emerged as a new research area in recent years. An analog filter with memristor can have automatically adjustable gain, quality factor and bandwidth characteristics etc. thanks to its variable memristance. In this paper, two different types of second-order Sallen-Key filters, which are the low-pass and the high-pass Sallen Key filters, are analyzed using simulations. The linear drift model of TiO2 memristor is used in all analysis and simulations. It has been found that the memristor in the filters can go into saturation at very low frequencies and both of the filters operate well at higher frequencies. A criterion is suggested to prevent memristor from going into saturation and to prevent distortion at low frequencies. Using the criteria and choosing a memristor with more appropriate parameters, the simulations are repeated for the low-pass filter and it is shown that the low-pass filter operates better with the new parameters chosen. The analysis and the criteria given in this paper can be used to design memristor-based Sallen-Key filters and adaptable to other memristor-based filters as well.