Subwoofer tools.
DRIVERS & OUTPUT / THE TOOLKIT

Measure Thiele-Small parameters.

Estimate damping from the impedance peak, then choose added mass or a known sealed test box to estimate compliance and moving mass. Use low-level, consistent measurements.

01 / THE INPUTS
Impedance measurement
Ω
Ω
Hz
Hz
Measurement method
Hz
Air & conventions
m/s
kg/m3
02 / THE RESULTS
Estimated free-air resonance
40.00Hz
Moving mass
35.56g
Equivalent compliance volume
157.15L
Suspension compliance
0.4453mm/N
Mechanical Q
7.6222
Electrical Q
0.7081
Total Q
0.6479
Crossing impedance magnitude
11.66Ω

Read this result with its assumptions.

An isolated resonance, negligible inductance near fs, and low-level measurements are assumed. Both crossing frequencies must be measured at the stated crossing impedance.

Units & assumptions

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03 / UNDER THE HOOD

The math, in plain sight.

Measure the driver you will actually install.

Resonance and quality factors

An impedance sweep provides a useful check on a data sheet. Measure complex voltage and current at a low drive level. In an isolated, low-inductance resonance, find the two crossings at the geometric mean of DC resistance and peak impedance.

Z(f)=V~(f)I~(f),r0=Zmax⁡Re,Z∗=ReZmax⁡Z(f)=\frac{\widetilde V(f)}{\widetilde I(f)},\quad r_0=\frac{Z_{\max}}{R_e},\quad Z_*=\sqrt{R_eZ_{\max}}
fs≈fLfH,Qms=fsr0fH−fLf_s\approx\sqrt{f_Lf_H},\quad Q_{ms}=\frac{f_s\sqrt{r_0}}{f_H-f_L}
Qes=Qmsr0−1,Qts=Qmsr0Q_{es}=\frac{Q_{ms}}{r_0-1},\qquad Q_{ts}=\frac{Q_{ms}}{r_0}

Added-mass method

Attach a known mass securely and measure the new, lower resonance. This assumes that the added mass does not change suspension compliance.

Mms=Ma(fs/fa)2−1M_{ms}=\frac{M_a}{(f_s/f_a)^2-1}
Cms=1(2πfs)2Mms,Vas=ρc2Sd2CmsC_{ms}=\frac1{(2\pi f_s)^2M_{ms}},\qquad V_{as}=\rho c^2S_d^2C_{ms}

With fs = 40 Hz, fa = 32 Hz, and an added mass of 20 g, the estimated moving mass is 35.6 g.

Known sealed-box method

Use a rigid, airtight box with a known net volume. The resonance must rise. Changes in air loading and losses are assumed small. Keep driver orientation and temperature consistent, and use effective piston area.

Vas≈Vtest[(fcfs)2−1]V_{as}\approx V_{\mathrm{test}}\left[\left(\frac{f_c}{f_s}\right)^2-1\right]

A poorly sealed test box corrupts the result. These relationships assume negligible voice-coil inductance around resonance and a valid measured DC resistance.