-80 dB/DECADE
Higher Order Control Theory
A 4th Order System is the result of multiplying two 2nd-order transfer functions: H(s) = H₁(s) × H₂(s). In the frequency domain, this means their magnitudes add (in dB) and their phases add.
Roll-off Characteristics:
- 1st Order: -20 dB/decade (-6 dB/octave)
- 2nd Order: -40 dB/decade (-12 dB/octave)
- 3rd Order: -60 dB/decade (-18 dB/octave)
- 4th Order: -80 dB/decade (-24 dB/octave)
Butterworth & Linkwitz-Riley:
To create a "Butterworth" 4th order filter (maximally flat), you don't just set all damping to 0.707. You must stagger them!
Stage 1
ζ=0.924 and Stage 2 ζ=0.383. Try it!