#### Document Type

Article

#### Publication Date

12-2014

#### Abstract

We derive an expression for the input complex impedance of a Sallen-Key second-order low-pass filter of twofold gain as a function of the natural frequency ωo and the quality factor Q. From this expression, it is shown that the filter behaves like a Frequency Dependent Negative Resistance (FDNR) element for low frequencies and as a single resistor at high frequencies. Furthermore, the minimum input impedance magnitude is found without using calculus. We discovered that the minimum input impedance magnitude is inversely proportional to Q and can be substantially less than its high-frequency value. Approximations to the minimum input impedance and the frequency at which it occurs are also provided. Additionally, PSpice simulations are presented which verify the theoretical derivations.

#### Journal Name

Latin American Journal of Physics Education

#### Recommended Citation

Cartwright, K.V. and E. J. Kaminsky, “Finding the minimum input impedance of a second-order twofold-gain Sallen- Key low-pass filter without calculus,” Lat. Am. J. Phys. Educ., Dec. 2014, pp. 4316-1–4316-8.