How bandpass poles are formed

Start with low-pass Butterworth prototype poles in the left half-plane. Apply the bandpass transform s -> (s^2 + w0^2) / (B s) where w0 = sqrt(w1 * w2) and B = w2 - w1. Each prototype pole produces two bandpass poles.

Choose the band type first, then a standard center frequency to see the resulting analog poles.

Pole calculator (analog)

Poles are shown in rad/s. Digital pole locations depend on the bilinear transform and sample rate.

Results are generally calculated according to IEC standards. Any actions, advice, or expenses based on the analysis are the user's responsibility, not the Third Octave's or any subsidiaries.