Thiele/Small parameters (Wikipedia)

The encyclopedic reference on the Thiele/Small parameter set — added to answer the spoke’s open question: how are these parameters actually measured? The founding trio (ts-parameters-explained, micka-enclosure-calculator, loudspeaker-primer-hackaday) used the parameters but never showed where the datasheet numbers come from. T2 (encyclopedic, established topic).

Who, and the small-signal caveat

A. Neville Thiele (Australian Broadcasting Commission) and Richard H. Small (University of Sydney) formalized the model; Small’s JAES articles from 1972 are the canonical references. A load-bearing caveat: most T/S parameters are linearized small-signal values — an idealization. Real values drift with drive level, voice-coil temperature, and the driver’s age, so a datasheet figure is a snapshot, and individual units vary within a tolerance rather than matching spec exactly.

How they’re measured (the missing piece)

The core technique is a free-air impedance sweep around resonance:

• Re — the DC voice-coil resistance, measured with the cone blocked (a free cone picks up ambient sound and corrupts the reading).
• Fs — read off the impedance peak: resonance is where the free-air impedance is maximal.
• The Q factors come from the impedance curve: Qes from Re and the peak impedance, Qms from the curve’s shape, and Qts = (Qms·Qes)/(Qms+Qes).
• Three impedance-rig methods, increasing in accuracy: constant-current (a large 500–1000 Ω series resistor — simple but errs on high-Zmax drivers); constant-voltage (impedance = V ÷ measured current); and the small-series-resistor method (~10 Ω, measuring voltage across driver/generator/ resistor) — “the method used by many computer loudspeaker measurement systems,” i.e. the accurate default.
• Vas is the one parameter the sweep alone can’t give; it’s recovered by a second measurement that perturbs the suspension’s apparent stiffness (added mass on the cone, or sealing it in a known box) and re-reading the shifted resonance — the standard added-mass / closed-box pair the design tools assume.

Why it matters here

It closes the loop the founding sources left open: the parameters feeding a box calculator are themselves derived from an impedance measurement, not handed down — and they’re small-signal snapshots with unit-to-unit tolerance, which is why a careful builder measures their own driver rather than trusting the datasheet.

Related

thiele-small-parameters · loudspeaker-driver · ts-parameters-explained · loudspeaker-primer-hackaday · synthesis