# T/S parameters in five minutes

> The few Thiele/Small parameters that shape a speaker box, what each one does, and their values for the drivers in 00 Simulator’s examples.

Source: https://simulator.00aud.io/docs/start/ts-parameters

A driver’s Thiele/Small (T/S) parameters are the numbers 00 Simulator models it with. You need only a handful to choose a box: three set its size and tuning, two set how much air the cone can move, and four describe the motor and the power it takes.

- **Fs · Qts · Vas:** The box: its size, its tuning and the shape of the roll-off.
- **Sd · Xmax:** The air the cone can move, and so how loud it can play low down.
- **Re · Le · Bl · Pe:** The motor, the load the amplifier sees and the power rating.

## Fs, Qts and Vas: the box

- **Fs**, the resonance: the frequency where the cone’s moving mass bounces on its suspension, measured in free air. A box changes it: the air in a sealed box stiffens the suspension and raises the resonance.
- **Qts**, how damped that resonance is. It combines the electrical damping of the motor (Qes) and the mechanical losses of the suspension (Qms). Low Qts means a tightly controlled cone.
- **Vas**, the volume of air that is as springy as the suspension. A large Vas means a soft suspension, which needs a larger box for the same result.

In a sealed box of volume Vb the resonance rises to Fc = Fs × √(1 + Vas / Vb) and the Q to Qtc = Qts × √(1 + Vas / Vb). The Dayton Audio DCS205-4 in the 15 L [sealed example](https://simulator.00aud.io/app?template=sealed) has Fs 32.3 Hz, Qts 0.37 and Vas 27 L, so it settles at Fc 54.0 Hz with Qtc 0.62. The flattest response, Qtc 0.707, would take 10.2 L with Fc 61.7 Hz.

In this ideal sealed-box relation, Qtc stays above Qts. As Qts approaches 0.707 from below, the volume needed to reach that target becomes very large. At or above 0.707, no finite sealed volume reaches it.

For a rough enclosure suggestion, 00 Simulator uses the efficiency-bandwidth product, EBP = Fs / Qes. The **Add enclosure** dialog suggests **Vented** above 75 and **Sealed** below it. The **T/S Parameters** tile reads it more loosely: sealed below 50, vented above 100 and either in between.

The drivers in 00 Simulator’s examples. The suggestion only picks between Sealed and Vented, and it is a starting point: the sealed example’s driver, for one, is suggested Vented.

| Driver | Example | Fs | Qts | Vas | EBP | Suggested |
| --- | --- | --- | --- | --- | --- | --- |
| Dayton Audio DCS205-4 | [Sealed](https://simulator.00aud.io/app?template=sealed) | 32.3 Hz | 0.37 | 27 L | 81 | Vented |
| Ciare 12.00SW | [Vented](https://simulator.00aud.io/app?template=vented) | 29 Hz | 0.29 | 55 L | 88 | Vented |
| Dayton Audio DCS165-4 | [Passive Radiator](https://simulator.00aud.io/app?template=passive-radiator) | 35.7 Hz | 0.34 | 12.1 L | 99 | Vented |
| B&C 18SW115 | [Bandpass](https://simulator.00aud.io/app?template=bandpass) | 34 Hz | 0.30 | 149.1 L | 110 | Vented |
| B&C 21SW152 | [Tapped Horn](https://simulator.00aud.io/app?template=tapped-horn) | 32 Hz | 0.36 | 200 L | 84 | Vented |
| B&C 10PS26 | [Multiple-Entry Horn](https://simulator.00aud.io/app?template=multi-entry-horn) | 54 Hz | 0.29 | 38 L | 164 | Vented |

## Sd and Xmax: the air it can move

- **Sd**, the cone’s effective area.
- **Xmax**, how far the cone can travel one way before its motor and suspension stop behaving linearly. It is the maker’s figure for clean travel, not the point where the driver breaks.

Their product, Vd = Sd × Xmax, is the air one stroke can push. It sets how loud a driver can play low down: for the same level, a radiator has to move four times the air for every octave lower. In a sealed box the cone moves all of it; in a vented box the port takes over near the tuning. The B&C 21SW152 moves 34 times the air of the Dayton Audio DCS165-4 in one stroke.

| Driver | Sd | Xmax | Vd = Sd × Xmax |
| --- | --- | --- | --- |
| Dayton Audio DCS205-4 | 214 cm² | 8.8 mm | 188 cm³ |
| Ciare 12.00SW | 523 cm² | 13.5 mm | 706 cm³ |
| Dayton Audio DCS165-4 | 125 cm² | 6 mm | 75 cm³ |
| B&C 18SW115 | 1,210 cm² | 14 mm | 1,694 cm³ |
| B&C 21SW152 | 1,680 cm² | 15 mm | 2,520 cm³ |
| B&C 10PS26 | 320 cm² | 5.5 mm | 176 cm³ |

The **Excursion** tile draws each driver’s Xmax as a dashed line, and the **Max SPL (dB)** tile caps the level where the cone reaches it. [Limits: travel, heat and air](https://simulator.00aud.io/docs/start/limits) covers both, with the travel figures beyond Xmax.

## Re, Le, Bl and Pe: motor and power

- **Re**, the voice coil’s DC resistance. It sits a little below the nominal impedance (Znom), and the impedance dips close to it above resonance.
- **Bl**, the motor’s strength: force per amp of current. More Bl lowers Qes, so the motor damps the cone harder.
- **Le**, the voice coil’s inductance. It raises the impedance as frequency rises and trims the top of a woofer’s response.
- **Pe**, the rated power handling from the maker’s power test. It is a test rating, not the heat the coil can shed.

| Driver | Re | Znom | Le | Bl | Pe |
| --- | --- | --- | --- | --- | --- |
| Dayton Audio DCS205-4 | 3.9 Ω | 4 Ω | 1.78 mH | 10.7 T·m | 300 W |
| Ciare 12.00SW | 3.3 Ω | 4 Ω | 1.60 mH | 19.5 T·m | 2,000 W |
| Dayton Audio DCS165-4 | 3.4 Ω | 4 Ω | 1.43 mH | 9.2 T·m | 200 W |
| B&C 18SW115 | 3.3 Ω | 4 Ω | 1.36 mH | 26.0 T·m | 3,400 W |
| B&C 21SW152 | 6.0 Ω | 8 Ω | 2.20 mH | 39.0 T·m | 4,000 W |
| B&C 10PS26 | 6.0 Ω | 8 Ω | 1.20 mH | 14.1 T·m | 700 W |

> **Where Le shows up** The **Impedance** tile always includes Le. For SPL, box designs use **Settings › Simulation… › Non-horn upper response**. The default, **Estimated · BITS frequency limit**, assumes a flat driver and rolls off at the driver’s published upper frequency limit when the library has one. **Physical model** uses Le instead.

Pe feeds the heat limit on the Max SPL tile, which can read it three ways. [Limits: travel, heat and air](https://simulator.00aud.io/docs/start/limits) explains them.

## Where to find them in the app

- The **T/S Parameters** tile lists the selected enclosure’s driver under **Electrical**, **Mechanical** and **Physical**, then **Interpretation** (EBP and the suggested type) and **Sealed targets**: the box for a Qtc of 0.58, 0.71 or 0.90 and its Fc.
- Turn on the tile’s **T/S adjust sliders** to nudge a parameter and watch every graph move. They are temporary tweaks for exploring and do not change the driver.
- **Edit params** opens the driver’s values to change them and save over the driver or as a new one. [Drivers: find, create, import](https://simulator.00aud.io/docs/guides/drivers) covers entering a driver from a datasheet.

Every parameter the app stores, with its unit and range, is in the [T/S parameters reference](https://simulator.00aud.io/docs/reference/ts-parameters).

## Ask your AI

**Ask your AI**

Your assistant reads the same driver library and suggestion logic through the 00 Simulator connector.

> Using 00 Simulator, look up the B&C 18SW115 and tell me its Fs, Qts, Vas, Xmax and EBP, which enclosure type the suggestion logic picks for it, and the sealed box volume for a Qtc of 0.707.