Thiele-Small parameters (Neville Thiele 1961 + Richard Small 1972) ARE the analogy made practical: Fs, Qts, Vas, Re, BL, Sd.
Qts = total Q (no units) = how damped the driver is; typical 0.3-0.5 for sealed/vented designs.
BL = force factor (Tesla.metres, T.m) = magnetic flux B times voice-coil wire length L; sets how hard the cone pushes per amp.
Speed of sound in air = 343 m/s at 20 degrees C (wavelength = 343 / frequency, used for box tuning).
Double the distance from a point source = -6 dB SPL; double the voltage/excursion = +6 dB; half-power point = -3 dB.
How it works
Pick the moving part: cone mass, suspension spring, or friction.
Swap each for its electrical twin: mass to inductor, spring to capacitor, friction to resistor.
Add the voice coil's force factor BL as a 'transformer' linking the electrical side to the mechanical side.
Draw the whole driver as one circuit and solve it like any electronics problem.
Read off real-world behaviour: resonance Fs, damping Qts and the volume Vas pop straight out.
Feed those Thiele-Small numbers into box-design software to pick a sealed or vented enclosure.
Real examples
Speaker box software (WinISD, VituixCAD, BassBox) is the analogy running under the bonnet - you type T-S params, it solves the circuit.
A driver's datasheet (Fs, Qts, Vas, BL, Re, Sd) is the electroacoustic model handed to you ready-made.
Designing a vented sub: the port is modelled as an extra mass + spring in the same circuit to set the tuning frequency.
A passive radiator is just another capacitor-inductor branch added to the equivalent circuit.
Mic and headphone designers use the same trick in reverse to model tiny diaphragms.
How it helps in live sound
Read the spec sheet like a circuit: low Qts (~0.3) wants a vented box, higher Qts (~0.5-0.7) suits sealed.
Match Fs to the job: a sub with Fs ~30-40 Hz will reach lower than one at 55 Hz.
Use Vas to sanity-check enclosure size before you trust the marketing - small Vas = small box.
Higher BL (T.m) generally means tighter, more controlled bass and better motor strength.
Never run a ported box hard BELOW its tuning frequency - the cone unloads and can over-excurse.
Remember -6 dB per doubling of distance when planning sub spacing and coverage at an outdoor gig.
Everyday analogy
It is like drawing your plumbing using road signs because you already know how to read a road map, so the hard part becomes familiar.
Watch out
Myth: the analogy is the real physics. Correction: it is only a model - it ignores big-signal effects like heat-driven power compression and BL falling off at high excursion.
Fun fact
The very first version, the 'mobility analogy', was published by Floyd Firestone in 1933 - long before transistors existed, engineers were already turning speakers into circuit diagrams.
Key takeaways
Mass = inductor, spring = capacitor, friction = resistor - the whole driver becomes a circuit.
Thiele-Small parameters are this analogy packaged as numbers you can actually use.
Resonance Fs and damping Qts decide whether a driver wants a sealed or vented box.
Every box-design tool you will ever use is solving this hidden circuit for you.
It is a model, not the truth - it breaks down at high power and large excursion.