11. Loudspeaker & Electroacoustics · Concept 1 of 11
Thiele–Small Parameters
A set of numbers that describe how a single speaker driver behaves, so you can match it to the right box.
Cone mass, stiffness and motor set Fs; Qts and Vas then decide whether the driver wants a sealed or ported box.
What it is
A driver's spec-sheet numbers (mass, stiffness, resonance, electricals) that predict its bass and tell you the box it needs.
Key facts
Fs = free-air resonance frequency in Hz; the pitch the cone naturally bounces at. Low Fs (20 to 40 Hz) = deep sub; high Fs (60 to 120 Hz) = a top/mid driver.
Qts = total Q (damping), unitless; Qts = (Qes x Qms)/(Qes + Qms), where Qes = electrical Q and Qms = mechanical Q.
Qts rule: <0.4 wants a vented (ported) box, 0.4 to 0.7 sealed, >0.7 best as a small sealed/infinite-baffle.
Vas = equivalent air compliance in litres; the air volume as springy as the cone's own suspension. Big soft cone = big Vas. Vas = rho x c^2 x Sd^2 x Cms (rho = air density 1.18 kg/m^3, c = 343 m/s).
Sd = effective cone area (m^2 or cm^2); Sd = pi x (effective radius)^2. A 12-inch driver is about 0.0530 m^2 (530 cm^2).
Xmax = peak one-way cone travel in mm. Output ceiling = Sd x Xmax = displaced volume (Vd); doubling Vd = +6 dB.
Mms = moving mass in grams (cone + coil + air load). Heavier Mms lowers Fs: Fs = 1/(2 x pi x sqrt(Mms x Cms)).
Cms = suspension compliance in mm/N (how far the cone moves per newton). Stiffer suspension = lower Cms = higher Fs.
Re = DC voice-coil resistance in ohms, NOT the rated impedance. An '8 ohm' driver usually measures Re about 5.5 to 6.5 ohms.
BL = motor force factor in tesla-metres (T.m); B = magnet flux density, L = coil length in the gap. Sensitivity is quoted in dB 1W/1m; +3 dB = double the acoustic output for the same power.
How it works
Clamp the driver in free air (no box) and sweep it with a small signal.
Measure the impedance curve; the peak's frequency is Fs.
Add a known mass or a known box volume, re-sweep, watch Fs shift.
Software (DATS, LIMP, Clio) crunches the two curves into Qts, Vas, Mms, Cms, BL.
Feed Fs, Qts and Vas into box maths or WinISD to get the box litres and port tuning.
Build the box, then re-measure to confirm the real response matches the prediction.
Real examples
Sub driver: Fs 28 Hz, Qts 0.34, Vas 120 L -> ported box tuned low for deep, loud kick.
PA top 12-inch: Fs 55 Hz, Qts 0.30, Vas 60 L -> small vented box, leave the lows to the sub.
Same driver, wrong box: too big & ported = boomy one-note bass; too small & sealed = thin, weak lows.
High Xmax (e.g. 12 mm) car-audio sub trades sensitivity for huge cone travel and loudness from a tiny box.
WinISD / VituixCAD let you type the T/S numbers and see the bass curve before cutting any timber.
How it helps in live sound
Match driver to box: never drop a recone or aftermarket driver into a cab unless its Fs/Qts/Vas suit that enclosure, or the bass goes boomy or thin.
For deep loud subs pick low Fs (<35 Hz) and low Qts (<0.4) and run them ported/tuned; for tight punchy subs go sealed.
Set amp gain and limiters off Xmax: exceeding Xmax = audible distortion then a blown coil; that is the real power limit, not the watt rating.
Power match to Re, not the '8 ohm' label; two 8-ohm (Re ~6) drivers in parallel can drop near 3 ohms and stress the amp.
Read sensitivity (dB 1W/1m) when picking tops: a 99 dB box needs half the amp power of a 96 dB box for the same level (+3 dB = 2x power).
Port tuning frequency (Fb) sets where output rolls off fast; below Fb the cone unloads and flaps, so high-pass there to protect the driver.
Everyday analogy
They are the speaker cone's spec sheet, like a car's kerb weight, power and tyre size, telling the box engineer exactly what chassis to bolt it into before anything is built.
Watch out
Myth: Re is the '8 ohm' impedance on the box. Wrong: Re is the DC coil resistance (about 5.5 to 6.5 ohms for an '8 ohm' driver), and impedance rises hugely at Fs.
Fun fact
A driver in free air and the same driver in a sealed box have different resonances: the trapped air acts as an extra spring, raising the system resonance above the driver's bare Fs, which is exactly how a small box gives tighter (but shallower) bass.
Key takeaways
T/S parameters = the numbers that let you design the box before building it.
The big three for box choice: Fs (resonance), Qts (damping), Vas (suspension springiness as air volume).
Qts picks the box type: low = ported, high = sealed.
Output ceiling = Sd x Xmax (displaced air); doubling it is +6 dB.
Sensitivity in dB 1W/1m tells you how much amp you actually need.
Wrong driver-to-box match = boomy or thin bass, every time.