One resistor, one capacitor, f = 1/2πRC — design low-pass, high-pass and active filters free.
Cutoff frequency from R and C plus the exact gain and phase at any frequency — first-order filters done right.
Solve f₀ = 1/2π√LC any direction, plus characteristic impedance, Q from loss resistance and bandwidth.
Component values for a 2nd-order Sallen-Key low-pass — Butterworth, Bessel or Chebyshev, from one chosen capacitor.
R1/R2/R3 for a multiple-feedback band-pass from f₀, Q and gain — the workhorse active band-pass, with the GBW check.
Inverting and non-inverting gain from Rf and Rg, in ratio and dB — with noise gain and real-op-amp caveats.
Schmitt-trigger thresholds and window from your reference and feedback resistors — kill comparator chatter by design.
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