What Are Speaker Parameters?

A loudspeaker is much more than a cone, voice coil and magnet. Its performance can be described mathematically using a collection of electrical and mechanical parameters.

These parameters are commonly called Thiele-Small parameters when they are used to describe the low-frequency behaviour of a loudspeaker driver.

The most important parameters include:

• Fs — free-air resonance frequency
• Re — DC resistance of the voice coil
• Le — voice-coil inductance
• Qms — mechanical Q
• Qes — electrical Q
• Qts — total Q
• Vas — equivalent compliance volume
• Sd — effective diaphragm area
• Mms — moving mass
• BL — motor strength
• Xmax — maximum linear excursion
• η₀ — reference efficiency

Why Speaker Parameters Matter

The parameters allow engineers and DIY speaker builders to predict how a driver will behave before constructing an enclosure.

For example, the parameters can help determine:

• Suitable enclosure type
• Enclosure volume
• Bass extension
• Port tuning frequency
• Expected efficiency
• Maximum acoustic output
• Electrical loading
• Driver suitability for a particular application

Two speakers with the same diameter can have completely different performance because their electrical and mechanical parameters may be very different.

Thiele-Small Parameters

Thiele-Small parameters are a standardized set of measurements used to describe the low-frequency behaviour of loudspeaker drivers.

They are particularly useful for enclosure design.

Electrical
    │
    ├── Re
    ├── Le
    └── BL
          │
          ▼
Mechanical
    │
    ├── Mms
    ├── Cms
    ├── Rms
    └── Qms
          │
          ▼
Acoustic
    │
    ├── Fs
    ├── Vas
    ├── Qes
    └── Qts

1. Fs — Free-Air Resonance Frequency

Fs is the free-air resonance frequency of the loudspeaker driver.

It is normally expressed in hertz (Hz).

At Fs, the mechanical system consisting of the cone, voice coil and suspension reaches its fundamental resonance.

A simplified relationship is:

Fs = 1 / (2π√(Mms × Cms))

where:

• Mms = total moving mass
• Cms = mechanical compliance

A lower Fs generally indicates that the driver can potentially operate at lower frequencies, although Fs alone does not determine the final bass extension.

2. Re — Voice-Coil DC Resistance

Re is the DC resistance of the voice coil.

It is measured in ohms (Ω).

A multimeter connected to the speaker terminals primarily measures this parameter.

Re is normally lower than the speaker's nominal impedance.

For example, an 8 Ω nominal driver may have a DC resistance of only several ohms.

The difference exists because speaker impedance is frequency dependent.

3. Le — Voice-Coil Inductance

Le represents the inductance of the voice coil.

It is normally specified in millihenries (mH).

Because the voice coil is an inductor, its impedance increases with frequency.

XL = 2πfL

where:

• XL = inductive reactance
• f = frequency
• L = inductance

This is one reason why a loudspeaker's impedance does not remain constant across the audio spectrum.

4. Mms — Moving Mass

Mms is the total moving mass of the loudspeaker system.

It includes more than just the cone.

Depending on the measurement definition, it includes components such as:

• Diaphragm
• Voice coil
• Former
• Dust cap
• Relevant portions of the suspension

Mms is normally specified in grams (g).

A lower moving mass can make it easier for the driver to respond quickly, but moving mass must always be considered together with motor strength and suspension characteristics.

5. Cms — Mechanical Compliance

Cms represents the mechanical compliance of the speaker suspension.

It describes how easily the suspension can move.

Compliance is related to the stiffness of the suspension.

A softer suspension has greater compliance, while a stiffer suspension has lower compliance.

Cms is commonly expressed in metres per newton (m/N).

6. Rms — Mechanical Resistance

Rms represents mechanical resistance in the moving system.

It accounts for mechanical losses in components such as the suspension and other parts of the driver's mechanical system.

Mechanical losses influence the sharpness of the driver's resonance.

7. Qms — Mechanical Quality Factor

Qms describes the mechanical damping of the speaker system.

It is related to the ratio between stored mechanical energy and mechanical energy lost during each cycle.

A higher Qms generally indicates lower mechanical damping.

Qms is dimensionless.

8. Qes — Electrical Quality Factor

Qes represents the electrical damping of the loudspeaker.

It is strongly influenced by the motor system and the electrical resistance of the voice coil.

Qes is dimensionless.

A simplified relationship involving motor strength can be expressed through the driver's electrical and mechanical parameters.

9. Qts — Total Quality Factor

Qts represents the total Q of the loudspeaker, combining the electrical and mechanical damping.

It is approximately related to Qes and Qms by:

Qts = (Qms × Qes) / (Qms + Qes)

Qts is one of the most important parameters when considering sealed and bass-reflex enclosure designs.

Qms, Qes and Qts Compared

10. Vas — Equivalent Compliance Volume

Vas is the equivalent volume of air that has the same acoustic compliance as the speaker's suspension.

It is normally expressed in litres.

Vas does not mean that the speaker requires an enclosure with exactly that volume.

Instead, it is a parameter that describes the compliance of the driver's suspension in an acoustically useful way.

Vas is particularly important in enclosure calculations.

11. Sd — Effective Diaphragm Area

Sd is the effective radiating area of the speaker diaphragm.

It is normally expressed in square metres (m²) or square centimetres (cm²).

Sd is important because the amount of air displaced depends on both cone area and excursion.

Displacement ≈ Sd × X

where X represents diaphragm excursion.

For the same excursion, a larger diaphragm can displace more air.

12. Xmax — Maximum Linear Excursion

Xmax describes the approximate maximum linear excursion of the speaker's moving system.

It is normally specified in millimetres.

Xmax is particularly important for low-frequency reproduction because bass requires significant cone movement.

A driver with high Xmax can potentially move more air without leaving its intended linear operating region.

However, the exact definition of Xmax can vary between manufacturers, so the manufacturer's method should be considered when comparing drivers.

13. BL — Motor Strength

BL describes the strength of the electromagnetic motor.

It is related to the magnetic flux density and the effective length of wire in the magnetic field.

A simplified expression is:

BL = B × L

where:

• B = magnetic flux density
• L = effective conductor length

BL is normally expressed in tesla-metres (T·m), which is equivalent to N/A.

A higher BL generally indicates a stronger motor, but BL must be considered together with moving mass, compliance and other parameters.

14. η₀ — Reference Efficiency

The reference efficiency, often represented by η₀, describes the electro-acoustic efficiency of the driver under specified conditions.

Conventional direct-radiating loudspeakers typically have relatively low efficiency.

Horn loading can substantially improve acoustic efficiency by improving the coupling between the driver and the surrounding air.

15. Sd, Xmax and Air Displacement

One of the most useful concepts in speaker design is the relationship between cone area and excursion.

A simplified estimate of maximum volume displacement is:

Vd = Sd × Xmax

where:

• Vd = displacement volume
• Sd = effective cone area
• Xmax = maximum linear excursion

A driver with a large Sd can move a large volume of air even with moderate excursion.

A smaller driver may require much greater excursion to achieve a similar displacement.

Example: Cone Area

For a circular diaphragm, a simplified estimate of area is:

A = πr²

where r is the radius.

For a nominal 200 mm diameter circular diaphragm:

r = 100 mm

A = π × 100²

A ≈ 31,416 mm²

However, the effective Sd used in loudspeaker specifications is not necessarily equal to the full geometric circle because the effective radiating area depends on the driver construction.

Speaker Parameters and Enclosure Design

The most important parameters for enclosure design are generally:

• Fs
• Qts
• Vas
• Sd
• Xmax

Other parameters are also important when modelling the driver and predicting its complete behaviour.

For example, Fs, Qts and Vas are commonly used when estimating the appropriate volume and alignment of a sealed or vented enclosure.

Sealed Enclosure

A sealed enclosure places the rear radiation of the driver inside a closed volume of air.

The trapped air adds acoustic stiffness to the system.

The resulting system resonance and Q depend on the driver's parameters and enclosure volume.

Driver

   │
   ▼

┌───────────────┐
│               │
│     Air       │
│               │
│               │
└───────────────┘

     Sealed box

The enclosure volume therefore cannot be selected independently of the driver parameters.

Bass-Reflex Enclosure

A bass-reflex enclosure uses a port to create an additional acoustic resonance.

The driver, enclosure volume and port tuning frequency interact to determine the low-frequency response.

Thiele-Small parameters are particularly useful when designing this type of enclosure.

Why Fs Matters

Fs provides an indication of the driver's natural low-frequency resonance in free air.

A lower Fs can be advantageous for low-frequency reproduction, but it does not automatically mean that the driver will produce deep bass in any enclosure.

Enclosure alignment, excursion capability, efficiency and other parameters also matter.

Why Qts Matters

Qts is especially useful when considering enclosure alignment.

Drivers with different Qts values can behave very differently when installed in the same enclosure.

It is therefore important to consider Qts together with Fs and Vas rather than selecting a driver using only one parameter.

Why Vas Matters

Vas describes the compliance of the driver's suspension in terms of an equivalent air volume.

A driver with a large Vas generally has a more compliant suspension, while a driver with a smaller Vas generally has a stiffer suspension, although the complete system behaviour depends on the other parameters.

Why Xmax Matters for Subwoofers

Low-frequency reproduction can require substantial cone excursion.

A driver may have a high electrical power rating but still reach its mechanical excursion limit at relatively low frequencies.

This is why power rating alone should not be used to determine how loudly a subwoofer can reproduce deep bass.

Power Handling vs Xmax

There are two important limitations to consider:

At high frequencies, thermal limits can become particularly important. At low frequencies, mechanical excursion can become the dominant limitation.

Speaker Parameters on a Datasheet

A typical driver datasheet may contain information similar to:

The values above are illustrative examples only. Actual driver parameters must be obtained from the manufacturer's datasheet or measurement.

How Parameters Interact

One of the most important lessons in loudspeaker design is that the parameters cannot normally be evaluated independently.

For example:

Fs + Vas + Qts
       │
       ▼
Enclosure alignment


Sd + Xmax
       │
       ▼
Maximum displacement


BL + Mms
       │
       ▼
Motor strength / acceleration


Re + Le
       │
       ▼
Electrical impedance

The final performance of a driver is determined by the interaction of these characteristics.

Electrical Parameters

Mechanical Parameters

Acoustic Parameters

Measuring Speaker Parameters

Speaker parameters can be obtained from the manufacturer or measured using specialized test equipment.

A basic multimeter can measure DC resistance, but it cannot determine the complete set of Thiele-Small parameters.

Specialized impedance measurement methods can be used to determine the resonance characteristics and derive parameters such as Fs, Qts and Vas.

The accuracy of the measurements depends on the test method, calibration and measurement conditions.

Why Datasheet Values Can Differ From Measurements

The parameters of a driver can vary due to manufacturing tolerances, temperature, mounting conditions and measurement methods.

For example, voice-coil resistance changes with temperature. Mechanical properties can also change with age and operating conditions.

Therefore, measured values may not exactly match the manufacturer's published values.

Parameters and Speaker Design

When designing a speaker system, the correct approach is to start with the intended application and then select a driver whose parameters are appropriate for that application.

For example:

• A subwoofer requires strong low-frequency capability and sufficient excursion.
• A midrange driver requires suitable response through the vocal range.
• A tweeter requires low moving mass and suitable high-frequency performance.
• A bass-reflex woofer must have parameters compatible with the desired enclosure alignment.

Common Mistakes

• Choosing a driver based only on diameter.
• Choosing a driver based only on wattage.
• Assuming lower Fs automatically means better bass.
• Ignoring Qts when designing an enclosure.
• Ignoring Vas when selecting enclosure volume.
• Ignoring Xmax when estimating maximum low-frequency output.
• Confusing Re with nominal speaker impedance.
• Comparing Xmax values without checking how manufacturers define it.
• Assuming datasheet parameters are exact for every individual driver.

Quick Reference

Key Takeaways

• Speaker parameters describe the electrical and mechanical behaviour of a driver.
• Fs is the driver's free-air resonance frequency.
• Re is the DC resistance of the voice coil.
• Le describes voice-coil inductance.
• Mms describes moving mass.
• Cms describes mechanical compliance.
• Qms, Qes and Qts describe mechanical, electrical and total damping.
• Vas describes the driver's equivalent compliance volume.
• Sd describes effective diaphragm area.
• Xmax describes approximate linear excursion capability.
• BL describes the strength of the electromagnetic motor.
• Fs, Qts and Vas are particularly important for enclosure design.
• Sd and Xmax are important when estimating maximum air displacement.
• Speaker power handling should not be evaluated without considering both thermal and mechanical limitations.