What Thiele/Small Parameters Mean
Thiele/Small (T/S) parameters describe a driver as a small-signal electro-mechanical system around resonance. Put them into WinISD or Hornresp and they predict the low-frequency response in any box. Below is what Thiele/Small parameters mean, worked through on the published WM1850/8 spec sheet.
| Parameter | What it is | WM1850/8 |
|---|---|---|
| Fs | Free-air resonance, set by moving mass against suspension compliance: Fs = 1 / (2π√(Mms·Cms)). | 42.9 Hz |
| Re | DC resistance of the voice coil. Below nominal impedance; a meter check against it is the first test for a damaged coil. | 6 Ω |
| Qms | Mechanical Q: damping from suspension losses alone. | 11.55 |
| Qes | Electrical Q: damping from the motor, set by Bl², Re and moving mass. Stronger motor, lower Qes. | 0.682 |
| Qts | Total Q: Qms·Qes / (Qms + Qes). | 0.644 |
| Vas | Volume of air with the same compliance as the suspension. Box volume for a given alignment scales with it. | 120.9 L |
| Cms | Suspension compliance. | 0.055 mm/N |
| Mms | Moving mass, including the air load. | 250.1 g |
| Sd | Effective piston area of the cone. | 1244 cm² |
| Xmax | One-way linear excursion of the coil in the gap. | 12 mm |
| Le | Voice coil inductance; shapes the impedance and response above the bass range. | 0.324 mH |
| η0 | Reference (half-space) efficiency. | 1.36% |
| EBP | Efficiency bandwidth product, Fs / Qes. | 62.9 |
How they fit together
- Qts from its parts: 11.551 × 0.682 / (11.551 + 0.682) = 0.644. With Qms this high, Qts is dominated by Qes, the motor.
- EBP: 42.9 / 0.682 = 62.9. Under about 50 points to sealed boxes, around 100 to vented or horn designs; 62.9 sits on the vented side of the middle.
- Displacement: Vd = Sd × Xmax = 1244 cm² × 1.2 cm = 1493 cm³. This sets excursion-limited output below and around tuning. See Xmax and excursion.
- Sensitivity from η0: 112.1 + 10·log₁₀(0.0136) = 93.4 dB, matching the published 93.5 dB within rounding.
- Power on top: 1800 W AES is 32.6 dB above 1 W, so the paper ceiling is about 126 dB at 1 m before power compression.
Using them
- Cab type: start with Qts and EBP. Low Qts (roughly 0.2 to 0.4) and high EBP suit horns and scoops; moderate Qts suits reflex. The WM1850/8's 0.644 and 62.9 point to ported boxes and mixed systems. See scoop vs reflex vs horn.
- Box size and tuning: Fs, Qts and Vas go into the simulator; add Xmax and Re to see the excursion and power limits. See cabinet tuning.
- Comparing drivers: parameters vary between samples and with measurement method, so treat small differences as noise. Compare continuous power ratings, not peak. See power ratings explained.
Full T/S data for the WM18X451 is available on request.
Sources: Wavemark WM1850/8 spec sheet. Relationships between parameters: R. H. Small, "Direct-Radiator Loudspeaker System Analysis", JAES 1972; sensitivity from η0 uses the standard 112.1 dB half-space reference. Calculated values rounded.
Questions
What does Qts mean on a speaker?
Qts is the driver's total Q at resonance, combining mechanical (Qms) and electrical (Qes) damping as Qms × Qes / (Qms + Qes). Low values, roughly 0.2 to 0.4, suit horns and scoops; moderate values suit reflex boxes.
What is EBP and how do I use it?
The efficiency bandwidth product is Fs divided by Qes. Under about 50 points to a sealed box, around 100 to vented or horn designs. It is a first filter; model the driver in the actual box before building.
What is Vas?
The volume of air with the same compliance as the driver's suspension. For a given alignment, box volume scales with Vas, so a higher Vas usually means a bigger box.
Which T/S parameters matter most for a sub?
Fs, Qts and Vas decide the box and tuning. Sd and Xmax give displacement (Vd), which sets maximum output at the bottom of the band. Re and the power rating set the thermal limit.