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Thiele Small Parameters – A Quick Overview

Posted By Andy Kos

We’re still updating and improving these pages, they are intended as general guidelines to help with the understanding of T&S Parameters and their relevance to speaker design. In some cases, a simplified explanation or example is used to illustrate a point, and may not be 100% accurate in all circumstances.,

BL – Motor Strength or Force Factor > read more

BL (force factor) represents the strength of the magnetic motor system in a loudspeaker. It is calculated as the product of magnetic flux density (B) and length of wire in the magnetic field (L), measured in Tesla meters (T·m). A higher BL indicates a stronger motor, which generally improves control over the cone.

Mms – Moving Mass > read more

Mms refers to the total mass of all moving components of the driver, including the cone, voice coil, dust cap, and the air load around the diaphragm. A higher Mms generally results in a lower resonant frequency (Fs), which can help extend bass response, but it also requires more energy to move. Conversely, a lower Mms allows for better transient response, making it ideal for midrange drivers.

Cms – Compliance of the Driver Suspension > read more

Cms represents the compliance of a speaker’s suspension system, essentially measuring its flexibility. It’s the inverse of stiffness; a higher Cms indicates a more pliable suspension, allowing the cone to move more freely. This flexibility affects the driver’s resonant frequency (Fs); a more compliant suspension results in a lower Fs, enabling better low-frequency reproduction.

Rms – Mechanical Resistance of the Suspension > read more

Rms denotes the mechanical resistance within the driver’s suspension, quantifying the inherent damping due to the materials and construction of components like the surround and spider. Higher Rms values indicate greater energy loss, which can dampen cone movement and affect the driver’s transient response. Balancing Rms is crucial for achieving desired sound characteristics, as excessive mechanical resistance can lead to reduced efficiency and dynamic range.

Sd – Effective Diaphragm Area > read more

Sd refers to the effective surface area of the driver’s diaphragm (cone) that actively moves air. It’s typically measured in square meters (m²). A larger Sd allows the driver to displace more air, contributing to higher sound pressure levels, especially at low frequencies. Accurately determining Sd involves measuring the cone’s diameter and accounting for the surround’s contribution to the moving area.

η₀ (Eta Zero) – Reference Efficiency > read more

η₀ represents the efficiency of the driver, given as a percentage, showing how well it converts electrical power into acoustic output. A higher η₀ means the driver is more efficient and produces more SPL for the same input power. Efficiency is closely related to BL, Sd, and Mms, with high-efficiency drivers typically having a strong motor (high BL) and lightweight moving parts (low Mms).

Fs – Free Air Resonance > read more

Fs is the frequency at which the driver naturally resonates when not mounted in an enclosure. It is determined by the moving mass (Mms) and compliance (Cms) of the driver. Lower Fs values indicate better suitability for subwoofers, while higher Fs values are typical for midrange and tweeters, where tight cone control is needed.

Z – Nominal Impedance > read more

Z is the nominal impedance of the driver, typically 4Ω, 8Ω, or 16Ω, and represents the average electrical resistance presented to an amplifier. While Re (DC resistance) is slightly lower, the impedance of a driver varies across different frequencies due to Le (voice coil inductance) and resonance effects.

Vas – Equivalent Compliance Volume > read more

Vas represents the volume of air that exhibits the same compliance as the driver’s suspension. Measured in liters, it provides insight into how the driver interacts with the air in an enclosure. A larger Vas suggests a more compliant suspension, often necessitating a larger enclosure for optimal performance. Understanding Vas aids in designing speaker cabinets that complement the driver’s mechanical properties.

Pe – Power Handling Capacity > read more

Pe indicates the thermal power handling capacity of the driver, measured in watts. It defines the maximum continuous power the driver can handle without incurring thermal damage to components like the voice coil. Exceeding Pe can lead to overheating and potential failure. It’s essential to match the amplifier’s output with the driver’s Pe to ensure reliability and longevity.

Xmax – Maximum Linear Excursion > read more

Xmax defines the maximum distance the driver’s cone can move linearly in one direction without significant distortion. Measured in millimeters, it reflects the limits of the voice coil’s travel within the magnetic gap. Exceeding Xmax can cause nonlinear behavior, leading to distortion and potential mechanical damage. Designing with an appropriate Xmax ensures the driver can handle desired sound pressure levels without compromising sound quality.

Xlim – Maximum Physical Excursion Before Damage > read more

Xlim, also known as Xmech or Xdamage, specifies the absolute maximum excursion the driver can endure before mechanical failure occurs. Surpassing Xlim can result in physical damage to components such as the voice coil, spider, or surround. It’s crucial to ensure that the driver operates within safe excursion limits, especially in high-power applications, to maintain durability and performance.

Le – Voice Coil Inductance > read more

Le measures the inductance of the voice coil, typically in millihenries (mH). This parameter affects the driver’s impedance at higher frequencies, influencing the crossover design and overall frequency response. A higher Le can lead to a roll-off in the high-frequency response, making it essential to consider in the design of midrange and high-frequency drivers.

Re – DC Resistance of the Voice Coil > read more

Re denotes the direct current (DC) resistance of the voice coil, measured in ohms (Ω). It’s a fundamental parameter that influences the driver’s electrical damping (Qes) and overall impedance. Accurate knowledge of Re is vital for matching the driver with the amplifier and designing appropriate crossover networks.

Qes – Electrical Quality Factor > read more

Qes represents the electrical damping of the driver at its resonant frequency (Fs). It reflects how the driver’s electrical characteristics control its resonance. A lower Qes indicates higher electrical damping, leading to tighter control over cone movement, which is desirable in achieving accurate sound reproduction.

Qms – Mechanical Quality Factor > read more

Qms quantifies the mechanical damping of the driver, considering losses in the suspension system. It indicates how the mechanical properties influence the driver’s resonance. A higher Qms suggests lower mechanical losses, resulting in a more resonant system. Balancing Qms with Qes is essential for achieving the desired total damping (Qts) and overall sound quality.

Qts – Total Quality Factor > read more

Qts is the combined quality factor that accounts for both electrical (Qes) and mechanical (Qms) damping. It provides a comprehensive understanding of the driver’s damping characteristics at resonance. The value of Qts influences enclosure design decisions:

  • Low Qts (< 0.3): Suitable for horn-loaded enclosures, offering tight, controlled bass.
  • Medium Qts (0.3 – 0.5): Ideal for bass reflex (ported) enclosures, balancing efficiency and bass

Vd – Peak Displacement Volume > read more

Vd is the product of the effective diaphragm area (Sd) and the maximum linear excursion (Xmax). It quantifies the maximum volume of air the driver can displace, directly influencing its ability to produce low-frequency sound. A higher Vd indicates greater potential for bass output, making it a useful parameter when selecting a suitable woofer.

EBP – Efficiency Bandwidth Product > read more

EBP (Efficiency Bandwidth Product) is a quick way to estimate whether a driver is better suited for a sealed or ported enclosure, calculated as Fs / Qes. A low EBP (< 50) suggests the driver works best in sealed enclosures, while a high EBP (> 100) indicates it is more suitable for ported or horn-loaded designs. While useful as a guideline, EBP isn’t an absolute rule—other factors like Vas, Xmax, and BL also influence enclosure choice.

Filed in Loudspeaker Driver Parameters, TS Parameters | Tagged: , , , , , , , , , , , ,

Qts – Total Quality Factor: The Balance Between Electrical and Mechanical Damping

Posted By Andy Kos

Qts is one of the most critical Thiele-Small parameters when designing a speaker system. It represents the total quality factor of a driver, combining both electrical damping (Qes) and mechanical damping (Qms) into a single value. Understanding Qts is useful for determining the best type of enclosure for a driver. Getting the right Qts for a bass reflex enclosure ensures efficient output, strong transient response, and extended bass performance.

What Exactly Is Qts?

Qts is a dimensionless number that describes how well a driver controls its own resonance. It is calculated using the following formula:

Where:

  • Qms = Mechanical quality factor (how well the suspension controls cone movement)
  • Qes = Electrical quality factor (how well the voice coil and magnet control movement)

A lower Qts means more damping, resulting in tighter, more controlled motion. A higher Qts means less damping, allowing the driver to resonate more freely. A higher Qts driver tends to demand a larger cabinet to operate most effectively, so choosing the right driver with the right Qts is very important for almost every speaker cabinet design.

The Best Qts Range for PA Speakers

For PA speakers, especially bass reflex (ported) enclosures, the ideal Qts range is:

✅ 0.30 – 0.45 → Best for ported PA subwoofers & woofers
✅ 0.35 – 0.38 → The sweet spot, balancing efficiency, transient response, and bass output
✅ Above 0.45 → Can still work in ported enclosures, but requires a larger cabinet

A Qts below 0.3 is generally found in horn-loaded enclosures, where tight cone control and efficiency are prioritized, and the driver will work happily with a small rear chamber. There are sometimes exceptions, these are intended as guidelines only, to help make an informed choice if you’re just starting blindly at a wall of numbers.

How Qts Affects Ported Enclosures

  • Qts 0.30 – 0.38 → Balanced sound with good transient response and deep bass.
  • Qts 0.38 – 0.45 → More extended bass possible, but less transient snap.
  • Qts above 0.45 → Requires a larger cabinet to compensate for weaker motor control.

For PA subwoofers and woofers, the ideal Qts keeps the cabinet size reasonable while ensuring powerful, clean bass.


PA Speaker Examples

Driver TypeTypical Qts RangeBest Enclosure Type
PA Subwoofer (Ported)0.30 – 0.38Bass Reflex (Ported)
General PA Woofer0.35 – 0.45Ported, some larger designs
Horn-Loaded Subwoofer0.15 – 0.30Horn-Loaded

🔹 Example 1: A Qts = 0.35 subwoofer is ideal for high-efficiency ported enclosures, delivering tight, punchy bass.
🔹 Example 2: A Qts = 0.42 woofer can still work in a ported cabinet, but may require a larger box to compensate.
🔹 Example 3: A Qts = 0.20 subwoofer would likely underperform in a ported box, but excels in a horn-loaded design.

Final Thoughts

For PA systems, getting the right Qts for a ported enclosure is crucial.

✅ The sweet spot for PA ported enclosures → 0.35 – 0.38 (from our experience)
✅ Avoid Qts above 0.45 unless using a very large cabinet
✅ Below 0.3 is best suited for horn-loaded designs



Filed in Loudspeaker Driver Parameters, TS Parameters

Sd – Effective Diaphragm Area

Posted By Andy Kos

What Is Sd?

Sd (Effective Diaphragm Area) is the active surface area of a speaker cone that moves air to produce sound. It’s usually measured in square meters (m²), but sometimes also specified in square centimeters (cm²). Sd is most often used for calculating other TS parameters, and its fairly common for all woofers with a certain diameter to have virtually the same Sd, this is because it can be calculated directly from the speakers diameter:

Where:

  • Sd = Effective diaphragm area (m²)
  • D = Effective cone diameter (meters)
  • π (pi) = 3.1416

Note: The effective diameter usually excludes the surround—only the part of the cone that actively moves air is considered – this can be hard to determine in some cases as some of the surround does move with the cone. For precise Sd, advanced methods are required to accurately determine the active surface area.

Filed in Loudspeaker Driver Parameters, TS Parameters | Tagged: , , ,

Rms – Mechanical Resistance of Suspension

Posted By Andy Kos

Rms, or mechanical resistance, describes how much damping the speaker’s suspension provides to control cone movement. Think of it like shock absorbers in a car—too much resistance, and the suspension is stiff and unyielding; too little, and it becomes too loose, leading to uncontrolled movement.

Rms is directly linked to Cms and Fs, as can be seen in the formula below:

What Does Rms Actually Do?

Rms affects how quickly the cone stops moving after being displaced. A higher Rms means more damping, which helps prevent unwanted resonances but can reduce efficiency. A lower Rms means less damping, allowing for more movement but potentially leading to excessive ringing or overshoot.

How Rms Affects Speaker Performance

  • Higher Rms (More Damping) →
    • The cone stops moving quickly after a signal ends
    • Prevents excessive ringing and improves transient response
    • Often found in PA and midrange drivers, where control is crucial
    • Can reduce efficiency because more energy is absorbed
  • Lower Rms (Less Damping) →
    • The cone moves more freely, leading to longer decay times
    • More efficient at converting electrical energy into sound
    • Often found in subwoofers, where extended low-frequency response is desirable
    • May require careful tuning to avoid unwanted resonances

How Rms Relates to Qms

Rms directly affects Qms, the mechanical quality factor of a driver.

  • A low Rms results in a high Qms, meaning the driver has lower mechanical losses and rings for longer.
  • A high Rms leads to a low Qms, meaning mechanical energy is dissipated more quickly, reducing ringing.

For example:

  • A PA midrange driver may have Rms = 5 kg/s and Qms = 2-3 for precise, controlled response.
  • A subwoofer may have Rms = 1.5 kg/s and Qms = 7-10 to allow for more free movement and extended bass.

Rms and Speaker Efficiency

Higher Rms means more energy is absorbed as heat in the suspension, making the driver less efficient. That’s why high-efficiency speakers (like horn-loaded designs) often have low Rms, reducing mechanical losses.

Real-World Example of Rms in Different Drivers

Driver TypeTypical Rms (kg/s)Effect on Performance
PA Midrange4 – 6Tight control, minimal ringing
Hi-Fi Woofer2 – 4Balanced damping for clarity and bass extension
Subwoofer1 – 2More excursion, deeper bass, less damping

Final Thoughts

Rms might not be the most commonly discussed Thiele-Small parameter, as typically most people focus on Cms or Vas. These are ways of quantifiying more or less the same thing, just in slightly different ways.

Filed in Loudspeaker Driver Parameters, TS Parameters

Cms – Compliance: The Suspension’s Flexibility

Posted By Andy Kos

Cms, or compliance, is a measure of how flexible the suspension of a speaker driver is. If you’ve ever tapped on a speaker cone and noticed how easily (or not) it moves, you’ve just gotten a feel for Cms in action. It’s essentially the inverse of stiffness—a higher Cms means a more flexible suspension, while a lower Cms indicates a stiffer suspension.

How Does Cms Affect Speaker Performance?

Cms plays a critical role in determining a speaker’s resonant frequency (Fs). The relationship is simple:

  • High Cms (soft suspension) → Lower Fs (good for deep bass)
  • Low Cms (stiff suspension) → Higher Fs (better for midrange or high-output designs)

If you’re designing a subwoofer, you typically want higher Cms so the cone moves freely and reaches low frequencies more easily. On the other hand, PA midrange drivers often have low Cms, giving them a stiffer suspension for better control at higher frequencies.

Cms, Excursion, and Control

While a softer suspension helps a driver reach lower frequencies, it comes with trade-offs. If the suspension is too compliant, the cone may overshoot and take longer to return to rest, leading to poor transient response (i.e., sloppy bass). On the flip side, a stiff suspension keeps movement tight and controlled, but it also limits how deep the driver can go in the bass range.

This is why Cms is not just about flexibility, but about balancing flexibility with control—just like a car’s suspension. Too soft, and you’re bouncing all over the road. Too stiff, and every bump feels like a punch.

The Link Between Cms and Vas

If you’ve seen Vas (Equivalent Compliance Volume) on spec sheets, it’s directly related to Cms. Higher Cms leads to a larger Vas because a soft suspension behaves as if it’s moving a large volume of air. Likewise, a stiff suspension gives a smaller Vas.

In practical terms:

  • A high Cms (large Vas) driver generally needs a big box to work properly.
  • A low Cms (small Vas) driver can function well in a compact enclosure.

This is why subwoofers with soft suspensions are often found in huge cabinets—because they need that extra air volume to perform correctly.

You can calculate Cms from Vas and Sd using the formula below: ρ (air density) = 1.184 kg/m³ and c (speed of sound) = 343 m/s

Cms and Speaker Longevity

A well-designed suspension must not only be flexible enough to allow movement but also durable enough to maintain its characteristics over time. Over years of use, the spider and surround—the two key suspension components—can loosen up slightly, increasing Cms and slightly lowering Fs.

This is why some people notice their subwoofers playing deeper and looser after a break-in period—because the compliance has increased slightly as the suspension softens.

Final Thoughts

Cms is one of those Thiele-Small parameters that ties into everything—excursion, Fs, Vas, and even long-term speaker performance. It’s not just about how soft or stiff the suspension is, but how well it’s balanced for the intended application. Whether you’re tuning a subwoofer for deep bass or a midrange driver for accuracy, Cms is a key factor that shapes the final result. In modern speaker designs, with high BL, the motor force can over-ride the effects of Cms in determining the box size, as usual there are trade-offs and exception with all parts of speaker design.

Filed in Loudspeaker Driver Parameters, TS Parameters

Driver TS Parameters: BL (Motor Strength)

Posted By Andy Kos

BL is the product of the magnetic field strength (B) in the voice coil gap and the length of wire (L) within that field, measured in tesla-meters (T·m). It represents the force generated to move the cone.

For basic speaker design, motor strength (BL) isn’t a primary concern since manufacturers optimize it for the driver’s intended purpose. However, understanding BL helps in designing high-performance enclosures and matching drivers to specific applications.

Simply put, BL quantifies the strength of the motor system. It is calculated as the product of the magnetic field (B) and the active length of the voice coil (L) within that field. A stronger BL means greater force to move the cone, resulting in better control and efficiency. For a more detailed explanation, with diagrams, please see the article on Xmax: https://speakerwizard.co.uk/driver-ts-parameters-xmax/ which includes diagrams of the magnet structure, and magnetic fields.

With ferrite magnets, increasing motor strength typically requires a larger magnet, which adds weight and cost. However, magnet size alone isn’t an indicator of quality—some large-magnet drivers are poorly designed and inefficient, and the huge magnet is just for show – although a large magnet can have a side benefit of providing a large thermal mass and surface area for cooling.

Neodymium magnets offer high motor strength with minimal weight, making them ideal for portable and high-performance systems. However, they are significantly more expensive than ferrite alternatives.

BL depends not just on magnet strength but also on the voice coil’s wire length within the field. This means coil height, diameter, wire gauge, and even multi-layer winding techniques influence BL. Many modern drivers use inside-outside wound voice coils to maximize wire length while maintaining compact designs.

BL can be thought of as the “muscle” of the speaker motor. A high BL means the motor exerts greater force on the cone, improving control and efficiency. Drivers with high BL values tend to deliver tight, accurate sound, while low BL drivers may sound softer or “looser.”

To help put things into context, for a typical 18″ woofer a high BL figure would be considered 30 or higher. A driver with a BL in this range will exhibit very price cone control. A low BL figure would be 20 or less, a driver with a low BL will be significantly less able to control the cone accurately.

Depending on your application, you may still be wondering why you should care about BL? If you are planning on building a horn loaded bass bin, or scoop bin, a high BL is pretty much essential, you wont get away with just chucking any old driver into the cabinet and get the right results. If you consider that in most horn loaded applications you are having to compress air, you want a driver that exhibits a high force to achieve this compression, a strong motor makes this possible.

In other applications, if you were to make a listening comparison between a high BL driver with a low BL driver, you would find the high BL driver will sound much tighter and more accurate. Generally for live music applications this type of sound is preferred as it will more accurately reproduce the instrument sounds. Low BL driver can sound ‘woolly’ or ‘muddy’ because the cone does not respond to transients as quickly, and has the potential to introduce some distortion. Some people prefer this sound as it can give a warmer bass sound.

High BL drivers are generally needed for high power bass applications, where a large heavy cone is used. High BL drivers are usually more efficient, as the higher motor strength equates to more pushing power. For mid-range drivers, it is normal to use a much lighter cone, and a high BL is not necessarily needed, but can contribute to a more accurate response.

High BL drivers make it possible to use smaller sealed boxes in some designs, because the motor strength is so high, the restoring force of the air in the box, and the suspension of the driver, are small in comparison, making them relatively insignificant.

High BL increases electromagnetic damping, which can be problematic in bass reflex enclosures. Excessive damping may reduce the effectiveness of the port, requiring design adjustments for optimal performance. With bass reflex designs a slightly lower BL is often more appropriate to get a more balanced result.

We’ll discuss BL and voice coil geometry more in another article.

Filed in Loudspeaker Driver Parameters, TS Parameters | Tagged: , , , , , ,

Qms – Mechanical Quality Factor

Posted By Andy Kos

Qms represents the mechanical damping of a speaker driver, determined by the losses in the suspension system (spider & surround). It indicates how well the driver’s mechanical components control cone movement at resonant frequency (Fs).

What Qms Tells Us About a Driver

  • High Qms (> 5) → Low mechanical losses, meaning the cone moves more freely with minimal damping from the suspension.
  • Low Qms (< 3) → Higher mechanical losses, where the suspension provides more damping and absorbs energy.

How Qms Affects Speaker Design

Qms works alongside Qes (electrical damping) to determine the total damping (Qts) of a driver.

A high Qms driver has minimal mechanical resistance, allowing for greater resonance, but relies more on electrical damping (Qes) for control. A low Qms driver has more built-in damping from the suspension, reducing unwanted resonance but also limiting efficiency.

While Qms alone doesn’t dictate enclosure suitability, it plays a role in how much influence the motor vs. suspension has on cone movement, helping in overall system tuning.

Filed in Loudspeaker Driver Parameters, TS Parameters | Tagged: ,

Driver TS Parameters: Mmd & Mms

Posted By Andy Kos

If you’re comparing drivers in detail, it will help to understand some of the more intricate TS Parameters, as over time it will help you differentiate between different drivers and identify which applications they are more suited for.

For example, for a high power 18″ horn loaded bass bin, you will probably be looking for a driver with a high BL, and a strong, rigid cone. A strong cone will generally also be a heavier cone, so you’ll be looking for a driver with a heavier cone. Lightweight cones have been used in horn loaded bass bins, but usually for lower powered applications focusing on upper bass .

For a 12″ midrange driver focused on vocal reproduction, a lighter cone (lower Mms) improves transient response and accuracy.

Mmd is the mass of the moving parts of the driver;  the diaphragm, dust dome and voice coil. The diaphragm is the paper cone in a standard speaker. The voice coil includes the former and the copper wire.  Most definitions online for Mmd seem to just be copies of each other, citing that the surround and spider are included in the moving mass. A bit of further research has suggested that only part of the mass of the spider and surround should be included, as the outside edge of the surround, and the outside edge of the spider are both glued to the chassis, and therefore DO NOT MOVE.

Mms is commonly used in loudspeaker modelling software. It is Mmd plus the ‘air load’. The air load is the air just in front, and just behind the speaker cone that will tend to move back and forth with the cone. It’s just a few grams of air, but for mathematical modelling of speaker performance, needs to be added in. A larger cone will have a larger air load.

Mms is used to calculate other important TS Parameters, such as Qes and Qms which can not be measured directly.

There is one final significant point with regard to the Mms, and that is the relationship to Fs  (Free Air resonance). Mms directly affects Fs (free-air resonance). A heavier cone lowers Fs, while a lighter cone raises it. Fs is also influenced by Cms, the compliance of the suspension. The formula which connects Fs to Mms is as follows:

Fs_Formula

Click here to read more about Thiele Small Parameters: Fs (Free Air Resonance)

As with all Thiele-Small parameters, Mms interacts with other factors like BL, Cms, and cone stiffness. The fact that cone weight, voice coil geometry, magnet strength, cone stiffness all interact and affect each other in both positive and negative ways means that any speaker design always has some compromises. Some might call this optimisation – a driver specifically designed for the best sub-bass response will sacrifice mid and upper bass response.

Lower bass frequencies require a heavier, stiffer cone. However, increasing Mms reduces efficiency, which must be countered with a stronger magnet and a longer voice coil to maintain performance.. Its unsurprising that in many instances, a compromise is settled on, which balances efficiency, resonant frequency, and cost.

For better midrange response, reducing Mms improves accuracy but raises Fs. This works well for midrange drivers but is undesirable for mid-bass woofers. As with most things in life, you can’t have your cake and eat it too. The only way to effectively cover the full frequency range is to use different drivers optimized for specific tasks

Filed in Loudspeaker Driver Parameters, TS Parameters | Tagged: , , , , , , ,

Driver TS Parameters: Cms (Compliance) & Vas (Compliance Equivalent Volume)

Posted By Andy Kos

Cms is a measure of the suspension compliance. Compliance is the opposite of stiffness. A driver with a stiff cone suspension will have a low Cms, and a driver with a ‘loose’ cone suspension will have a higher Cms.

Vas is known as the compliance equivalent volume, and is specified in litres. Cms is proportional to Vas, a higher Cms will mean a higher Vas, but what does the Vas figure actually represent?

You could think of the stiffness of the suspension as providing a restoring force that brings the cone back to it’s central ‘neutral’ position. If you were to gently push the dust dome of a driver with your fingertips, one with a stiff suspension would push back harder than one with a loose suspension.

Imagine a situation where you have an imaginary driver  mounted in a sealed box, with an infinitely compliant suspension – ie a suspension that offers no resistance whatsoever to movement. If you were to push the driver cone back into the box, the cone moving back into the box would compress the air inside the box slightly, and when you release the driver cone, the air would push back to restore the cone to its original position. In a box with a small volume, the air would compress more, pushing back harder. As the box size increases, the same distance of movement of the cone will compress the air inside the box less, resulting in a smaller restoring force to push the cone back to it’s original position.

The Vas measurement in litres is the size of the ‘imaginary’ box described above, which has exactly the same restoring force as the suspension of the driver. Cms and Vas are effectively two different ways of describing exactly the same thing, the main reason for converting Cms to Vas is that Vas fits into a lot of formulae better, and allows easier modelling of driver performance.

Air temperature, air pressure and humidity can have a significant effect on Vas measurements, and it is quite common for variations of up to +/- 20% from published specifications. This is a combination of differences of measurement environment, and manufacturing tolerances.

Vas can be used for determining optimum box size for sealed speaker boxes (ie. NOT vented).

If your sealed box is too small, the when the driver cone moves backwards into the box, compressing the air inside the box, the restoring force will be higher than optimal, causing the driver to move back out a little too quickly and potentially gain too much speed, and overshoot, causing it to go further out of the box than it should do. On the return journey, the rarefaction of the air inside the box will pull the cone in too fast, potentially causing it to go in too far. This is known as underdamping, when the movement of the cone gets exaggerated and increased instead of being controlled. This is undesirable as it causes distortion, and potentially affects the cooling of the voice coil

If your sealed box is too big, the air inside the box will will slow the driver from returning to it’s central rest position rather than help it, this can make the box overdamped. Many people consider being slightly overdamped as the best option, as it gives a more accurate sound, but it will often reduce the output volume.

For Bass speakers, critical damping, or ‘perfect’ damping is often what is sought after, this gives the best compromise, where the air inside the box helps restore the driver to it’s natural position, but not too much, and not too little, but just right. A speaker box with a Q of 0.707 is generally regarded as perfectly damped, you could think of this as the Goldilocks Q, where it’s ‘just right’.

The ratio of Vas to box volume = (Qtc/Qts)2 – 1 : 1

Qtc is the desired Q of the speaker, let’s assume we are aiming for a Qtc of 0.7

Qts is the total Q of the driver, available from the manufacturer’s specification sheet. For purposes of some simple maths, let’s use an imaginary driver with a Qts of 0.35.

0.7/0.35 = 2 and 2 squared=4

So our formula gives:(4-1):1 or 3:1

If Vas for our imaginary driver was 180 litres, we would make our box 60 litres to achieve a Qtc of 0.7

Its not unusual to see boxes with a Qtc of up to 1.1, higher Qtc of around 1 is slightly underdamped and will cause a peak in bass response around the resonant frequency, giving the impression of a better bass response. In reality you will be sacrificing deep bass response for upper bass response, and with reduced sound quality and less control of the driver, increasing cone excursion and the possibility of over-excursion.

You may also find the formula written as

Qtc = Qts X (Square Root((Vas / Vb) + 1))

The results are the same, just the formula has been re-arranged. Vb is the box volume. Some people prefer to use Vc for closed box, and Vb for reflex box. As a general rule of thumb, drivers with a high Vas prefer a bigger box to get the best results, and you should take this into consideration when choosing the driver for your application.

The formulae here are for sealed boxes only, bass reflex boxes require different calculations which we will cover elsewhere.

 

 

Filed in Loudspeaker Driver Parameters, TS Parameters | Tagged: , , , , ,

Xlim – Xmech – Xdamage – Maximum Physical Excursion Before Damage

Posted By Andy Kos

Xlim (also called Xmech or Xdamage) represents the absolute maximum excursion a driver can reach before mechanical failure occurs. It accounts for physical limits such as:

  • The voice coil bottoming out or leaving the magnetic gap
  • The suspension (spider & surround) overstretching
  • The cone or coil colliding with the back plate

Unlike Xmax, which defines the linear range of motion before distortion increases, Xlim marks the point of no return—exceeding it risks permanent damage to the driver.

For subwoofers and high-excursion drivers, a well-designed suspension system should allow gradual soft limiting before reaching Xlim, reducing the risk of catastrophic failure.

Filed in Loudspeaker Driver Parameters, TS Parameters | Tagged: ,
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