The maximum and minimum gains (with respect to frequency) of third-order low-pass and high-pass filters are derived without using calculus. Our method uses the little known fact that extrema of cubic functions can easily be found by purely algebraic means. PSpice simulations are provided that verify the theoretical results.
Latin American Journal of Physics Education
Cartwright, K.V., P. Russell, and E. J. Kaminsky, “Finding the maximum and minimum magnitude responses (gains) of third-order filters without calculus,” Lat. Am. J. Phys. Educ., vol. 7, no. 4, Dec. 2013, pp. 582-587.