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Finding The Minimum Input Impedance Of A Second-Order Twofold-Gain Sallen-Key Low-Pass Filter Without Calculus, Kenneth V. Cartwright, Edit J. Kaminsky
Finding The Minimum Input Impedance Of A Second-Order Twofold-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 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 …
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 …