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Finding The Maximum And Minimum Magnitude Responses (Gains) Of Third-Order Filters Without Calculus, Kenneth V. Cartwright, Patrick Russell, Edit J. Kaminsky
Finding The Maximum And Minimum Magnitude Responses (Gains) Of Third-Order Filters Without Calculus, Kenneth V. Cartwright, Patrick Russell, Edit J. Kaminsky
Electrical Engineering Faculty Publications
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.
Finding The Minimum Input Impedance Of A Second-Order Unity-Gain Sallen-Key Low-Pass Filter Without Calculus, Kenneth V. Cartwright, Edit J. Kaminsky
Finding The Minimum Input Impedance Of A Second-Order Unity-Gain Sallen-Key Low-Pass Filter Without Calculus, Kenneth V. Cartwright, Edit J. Kaminsky
Electrical Engineering Faculty Publications
We derive an expression for the input complex impedance of a Sallen-Key second-order low-pass filter of unity gain as a function of the natural frequency , o quality factor Q and the ratio of the resistors of the filter. From this expression, it is shown that the filter behaves like a single capacitor 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 highfrequency value. Approximations to …