Subwoofer tools.
SYSTEM PLANNING / THE TOOLKIT

Subsonic / high-pass filter.

Compare filter magnitude, phase, and group delay. Supply an excursion curve to check protection over that measured range, rather than trusting a one-size-fits-all cutoff.

01 / THE INPUTS
Filter design
Hz
Operating point
Hz
Excursion data

One row per point: frequency in Hz, one-way peak excursion in mm. Enter at least two increasing frequencies.

02 / THE RESULTS
Voltage attenuation at 20 Hz
-5.37dB
Filtered excursion at 20 Hz
8.09mm
Voltage amplitude ratio
0.5391
Filter group delay at 20 Hz
10.47ms
Phase at operating point (wrapped)
107.65°

Filter magnitude

LOG FREQUENCY
Filter magnitude: Voltage level (dB) against frequency in hertz.-43.2-33.92-24.64-15.36-6.083.25102050100200Voltage level (dB)Frequency (Hz)

Read this result with its assumptions.

Single-frequency excursion does not establish protection over the complete operating range. These are linear voltage-drive predictions.

Units & assumptions

Your calculations run in this browser. No account needed.

03 / UNDER THE HOOD

The math, in plain sight.

See what your high-pass filter really removes.

Second-order high-pass section

Q = 1/sqrt(2) gives a second-order Butterworth section. The custom-Q mode can show passband peaking; it is not automatically a Butterworth filter.

H2(s)=s2s2+(ωc/Q)s+ωc2,ωc=2πfcH_2(s)=\frac{s^2}{s^2+(\omega_c/Q)s+\omega_c^2},\qquad\omega_c=2\pi f_c
∣H2∣=x2(1−x2)2+(x/Q)2,x=ffc|H_2|=\frac{x^2}{\sqrt{(1-x^2)^2+(x/Q)^2}},\qquad x=\frac f{f_c}
AdB=20log⁡10∣H2∣A_{\mathrm{dB}}=20\log_{10}|H_2|

Butterworth and Linkwitz-Riley

∣HB,n(jω)∣=11+(fc/f)2n|H_{B,n}(j\omega)|=\frac1{\sqrt{1+(f_c/f)^{2n}}}
HB,n(s)=sn∏k=1n(s−pk),pk=ωcexp⁡[jπ2k+n−12n]H_{B,n}(s)=\frac{s^n}{\prod_{k=1}^n(s-p_k)},\qquad p_k=\omega_c\exp\left[j\pi\frac{2k+n-1}{2n}\right]
HLR4(s)=[s2s2+2 ωcs+ωc2]2H_{LR4}(s)=\left[\frac{s^2}{s^2+\sqrt2\,\omega_cs+\omega_c^2}\right]^2

A fourth-order Linkwitz-Riley filter is two cascaded second-order Butterworth sections. It is -6 dB, not -3 dB, at its named crossover frequency.

Compare the entire excursion curve

For a linear voltage-driven model, the complex acoustic pressure is multiplied by the same filter transfer function. Optional excursion data are evaluated at the submitted frequencies; no smoothing or interpolation is used to imply protection between samples. Phase is unwrapped for display and numerical group delay.

Xfiltered(f)=∣H(j2πf)∣Xunfiltered(f)X_{\mathrm{filtered}}(f)=|H(j2\pi f)|X_{\mathrm{unfiltered}}(f)

A single operating point does not establish minimum protection over a frequency range. Clipping, limiters, and nonlinear behavior invalidate simple scaling. A filter cannot repair inadequate port area, excess heating, or radiator travel limits.