Thiele-Small Parameters

A.N. Thiele and Richard H. Small defined most of the relationships and terms we now use to describe what happens in a audio speaker and between a audio speaker and a particular enclosure's type and size. Their work has become the standard for audio speaker measurement criteria and is known as the Thiele-Small parameters. The Thiele-Small parameters are a set of electromechanical parameters that define the low-frequency performance of a loudspeaker driver. These parameters are used by loudspeaker designers to simulate and predict the performance of a speaker system in different enclosures. All audio speaker manufactures use the Thiele-Small parameters in describing their products which allow you to do a direct characteristics comparison of different audio speakers as well as give your the necessary information for designing the crossover network and enclosure.

The most commonly used Thiele-Small parameters are listed below:
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Thiele-Small Parameters - BxL

BxL is a Thiele-Small parameter that represents the product of the magnetic flux density (B) and the length of the voice coil (L). It's a measure of the magnetic field strength acting on the voice coil. A speaker with a high BxL value (e.g., 10 Tm) might be more efficient and have better power handling capabilities than a speaker with a lower BxL (e.g., 5 Tm)

Why is BxL important?

  • Force Factor: BxL determines the force that is exerted on the voice coil when a current is passed through it. A higher BxL value means a stronger force.
  • Efficiency: A higher BxL generally results in higher efficiency, meaning the speaker can produce a louder sound level for a given amount of power.
  • Power Handling: A high BxL can improve a speaker's power handling capabilities.
    • Key points about BxL:
  • Units: BxL is typically measured in tesla-meters (Tm).
  • Relationship to other parameters: BxL is related to the speaker's efficiency and power handling.
  • Voice Coil Design: A higher BxL can be achieved by increasing the magnetic field strength or the length of the voice coil.
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    Thiele-Small Parameters - Cms

    Suspension compliance (Cms) is one of the key Thiele-Small parameters that describe the mechanical characteristics of a loudspeaker driver. It measures how easily the driver's diaphragm can be moved back and forth.

  • C stands for compliance, which is a measure of how easily a system can be deformed.
  • ms indicates that the measurement is in meters per newton (m/N).

    • Why is Cms Important?

  • Enclosure Design: Cms is crucial for designing the correct enclosure volume for a speaker. A driver with a high Cms value requires a larger enclosure to achieve optimal performance.
  • Bass Response: A higher Cms value generally results in a deeper and more extended bass response.
  • Efficiency: Cms can also affect the driver's efficiency, which is the amount of acoustic power it produces for a given electrical input.

    • Factors Affecting Cms

  • Suspension Material: The material used for the driver's suspension (e.g., rubber, foam) significantly influences its compliance.
  • Suspension Geometry: The shape and design of the suspension can also affect Cms.
  • Diaphragm Mass: A heavier diaphragm will have a lower Cms value.

    • Measuring Cms

    Cms is typically measured using specialized equipment in a laboratory setting. It involves applying a known force to the driver's diaphragm and measuring its displacement.
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    Thiele-Small Parameters - EBP

    EBP, in the context of Thiele-Small parameters stands for Efficiency Bandwidth Product. While not directly measured, EBP is simply the result of dividing Fs by Qes (EBP = Fs / Qes). It's a calculated value derived from two other Thiele-Small parameters:

  • Fs (Free-Air Resonance Frequency) - This is the frequency at which the driver resonates most easily in free air.
  • Qes (Electrical Q) - This represents the electrical damping of the driver, primarily from the voice coil and magnetic system.

    • EBP serves as a quick guideline for determining the most suitable enclosure type for a given loudspeaker driver. EBP is a handy tool for narrowing down enclosure options when you have a set of Thiele-Small parameters for a driver. It can save time and effort by guiding you towards enclosure types that are more likely to produce the desired results.EBP is a helpful starting point, but it's not an absolute rule.

    Other factors like personal preferences, room acoustics, and the specific design of the enclosure can influence the final decision. It's essential to consider all Thiele-Small parameters together, not just EBP. For example, a driver with a high EBP might still be suitable for a sealed enclosure if it has a low Vas (equivalent air compliance), which indicates a stiffer suspension.

  • An EBP that is less than 100 generally indicates that the driver is better suited for a ported (bass-reflex) enclosure. These enclosures use a port (or vent) to extend low-frequency response and increase efficiency.
  • An EBP that is less than 50 typically suggests the driver is more suited for a sealed enclosure. These enclosures provide tighter bass and a smoother roll-off in the low frequencies.
  • An EBP that has a range between 50 - 100 may perform well in either a sealed or ported enclosure, depending on the specific design goals and desired sound characteristics.
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    Thiele-Small Parameters - EPB

    EPB stands for Equivalent Piston Area. It's a measure of the effective area of a loudspeaker's cone that contributes to sound radiation. A speaker with a large EPB value (e.g., 100 cm²) might be more efficient and produce a louder sound than a speaker with a smaller EPB (e.g., 50 cm²).

    Why is EPB important?

  • Sensitivity: A larger EPB generally results in higher sensitivity, meaning the speaker can produce a louder sound level for a given amount of power.
  • Efficiency: EPB is closely related to the speaker's efficiency. A larger EPB can improve efficiency.
  • Enclosure Design: EPB is a factor to consider when designing a loudspeaker enclosure, especially when determining the optimal port area or volume.

    • Key points about EPB:

  • Units: EPB is typically measured in square centimeters (cm²).
  • Relationship to other parameters: EPB is related to the speaker's sensitivity and efficiency.
  • Enclosure design: A larger EPB generally requires a larger enclosure or port area to achieve optimal performance.
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    Thiele-Small Parameters - Fb

    The Thiele-Small parameter Fb represents the resonance frequency of a loudspeaker driver in free air. It is the frequency at which the driver's moving mass and suspension stiffness are in balance, leading to a peak in the driver's impedance and output. Fb is crucial for designing speaker enclosures. It helps determine the optimal enclosure type (sealed, ported, etc.) and size to match the driver's characteristics and achieve the desired bass response. Fb is typically measured by analyzing the driver's impedance curve. The peak in the impedance curve corresponds to the resonance frequency. It can be measured using specialized audio measurement equipment or software.

  • When using multiple drivers in a system it's important to select drivers with similar Fb values for a smoother overall response and easier integration.
  • Fb can be used to assess a driver's low-frequency capabilities and suitability for different applications (e.g., subwoofers, mid-bass drivers).
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    Thiele-Small Parameters - Fc

    The Thiele-Small parameter Fc refers to the free-air resonance frequency of a loudspeaker driver.nIt's the frequency at which the driver's moving mass and suspension compliance naturally resonate together. This is an important parameter for designing speaker enclosures and crossovers, as it helps determine the optimal operating range of the driver. Fc is typically measured by suspending the driver in free air (away from any baffle or enclosure) and applying a small AC signal. The frequency at which the driver's impedance reaches its peak is the resonance frequency.

    Fc plays a crucial role in determining the type and size of enclosure best suited for a specific driver. For example, a driver with a low Fc might be well-suited for a ported enclosure, while a driver with a high Fc might work better in a sealed enclosure. Fc also helps determine the crossover frequency for multi-way speaker systems. The crossover point is often chosen to be above the Fc of the woofer and below the Fc of the tweeter.

    Fc values vary depending on the driver type and size:

  • Woofers typically have Fc values between 20 Hz and 80 Hz.
  • Midrange Drivers Fc values typically fall between 80 Hz and 500 Hz.
  • Tweeters Fc values usually range from 500 Hz to 4000 Hz.
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    Thiele-Small Parameters - Fcb

    Box Cutoff Frequency (Cabinet Resonance Frequency) is the frequency at which the output of a speaker in a closed enclosure starts to roll off significantly (usually defined as -3dB below the reference level). It's influenced by the driver's parameters (Fs, Qts) and the enclosure volume.

    Fcb, or Cabinet Resonance Frequency, is a crucial Thiele-Small parameter that directly influences a loudspeaker's low-frequency performance. Fcb is a vital Thiele-Small parameter that significantly impacts the low-frequency performance of a loudspeaker. By understanding its relationship to enclosure design and driver characteristics, designers can create enclosures that deliver the desired sound quality and bass response.

    It's the frequency at which the cabinet itself resonates causing a peak in the frequency response. This resonance can be either beneficial or detrimental, depending on the desired sound characteristics and the enclosure design. To achieve optimal performance, loudspeaker designers carefully tune Fcb by adjusting factors like enclosure volume, port dimensions, and even adding internal bracing or damping materials. This process involves careful calculations and simulations to ensure that Fcb aligns with the desired sound characteristics and avoids unwanted resonances.

    Factors Affecting Fcb

  • Beneficial Effects: When Fcb is carefully tuned to align with the desired bass response, it can enhance the overall output and efficiency of the loudspeaker. For example, in a bass reflex enclosure, a well-tuned Fcb can create a boost in the low-frequency range.
  • Detrimental Effects: If Fcb is too low, it can cause excessive bass boost and potentially lead to a "boomy" or "muddy" sound. Conversely, if Fcb is too high, it can result in a lack of bass extension and a less powerful low-frequency response.
  • Enclosure Volume: The size of the enclosure directly affects Fcb. Larger enclosures generally have lower Fcb values.
  • Port Tuning (if applicable): The length and diameter of the port in a bass reflex enclosure can significantly influence Fcb.
  • Driver Parameters: The driver's own characteristics, such as its resonant frequency (Fs) and effective mass (Mms), also play a role in determining Fcb.
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    Thiele-Small Parameters - Fp

    Port Tuning Frequency which is the most common usage of Fp and refers to the frequency at which the air inside a ported enclosure's port resonates. This resonance is designed to reinforce the speaker's low-frequency output, extending its bass response.

    In some cases, Fp might be used interchangeably with Fc to denote the overall resonance frequency of a ported speaker system. This includes the combined effects of the driver's resonance and the port tuning.
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    Thiele-Small Parameters - Fs

    Fs stands for Free-Air Resonance Frequency. This is a fundamental parameter that describes the frequency at which a loudspeaker driver's moving mass will naturally resonate most easily in free air (i.e., without any enclosure). Fs is a key indicator of a driver's ability to reproduce low frequencies. Generally, a lower Fs value suggests that the driver can produce deeper bass notes.

  • Enclosure Design - Fs is crucial for determining the optimal enclosure type and size for a given driver. Different enclosure types (sealed, ported, etc.) interact differently with the driver's natural resonance, and the Fs value helps designers choose the best match for the desired sound characteristics.
  • System Tuning - Fs is used in calculations to determine parameters like port length in ported enclosures or box volume in sealed enclosures. These calculations help ensure the system is tuned to achieve the desired frequency response.

    • Fs is determined by a combination of factors related to the driver's construction some of which include:

  • Moving Mass (Mms) - The mass of the cone, voice coil, and other moving parts. A higher Mms generally leads to a lower Fs.
  • Suspension Compliance (Cms) - The flexibility of the spider and surround. A more compliant suspension (higher Cms) allows for easier movement and results in a lower Fs.
  • Motor Strength - The strength of the magnet and voice coil assembly. A stronger motor can control the moving mass more effectively, leading to a higher Fs.

    • Typical Driver Fs Values

  • Subwoofers - Typically have very low Fs values (20 Hz - 40 Hz), as they are designed to reproduce the deepest bass frequencies.
  • Woofers - Generally have Fs values in the range of 30 Hz - 80 Hz, depending on their intended purpose.
  • Midrange Drivers - Often have higher Fs values (50 Hz - 200 Hz), as they focus on reproducing the middle frequencies.
  • Tweeters - Have the highest Fs values (200 Hz - 2000 Hz or more), as they are designed for high-frequency reproduction.
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    Thiele-Small Parameters - F3

    The Thiele-Small parameter F3 refers to the frequency at which the driver's output level is 3 decibels (dB) lower than its resonance frequency (Fs). This is a crucial point in the speaker's frequency response. If a speaker has an F3 of 50 Hz in a sealed enclosure, it means that at 50 Hz, the speaker's output will be 3 dB lower than its maximum output at its resonance frequency.

    The F3 parameter:

  • Indicates low-frequency performance - F3 gives you a good idea of how well a speaker can reproduce low-frequency sounds. A lower F3 value means the speaker can generally play deeper bass.
  • Determines enclosure design - For speaker enclosures like sealed or ported boxes, the F3 value helps designers calculate the ideal enclosure size and tuning frequency to achieve the desired bass response.
  • Varies with enclosure type - A driver's F3 in free air will be different from its F3 in a specific enclosure. The enclosure design significantly impacts how low the speaker can play
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    Thiele-Small Parameters - Le

    Le refers to a drivers inductance. It's a Thiele-Small parameter that describes the electrical characteristics of the loudspeaker driver's voice coil.

    Why is Le Important?

  • Impedance: Le is a major component of the driver's impedance, which is the opposition to the flow of electrical current. Impedance affects the driver's sensitivity and power handling capabilities.
  • Frequency Response: Le can influence the driver's frequency response, particularly at higher frequencies. A high Le value can cause the driver's impedance to rise at higher frequencies potentially leading to a less smooth response.
  • Power Handling: Le is related to the driver's power handling capabilities. A high Le value can limit the amount of power the driver can handle without overheating.

    • Factors Affecting Le

  • Voice Coil Design: The number of turns, wire gauge, and geometry of the voice coil all affect its inductance.
  • Magnetic Field: The strength and distribution of the magnetic field around the voice coil also influence Le.

    • Measuring Le

    Le is typically measured using specialized equipment that can determine the inductance of a coil. This might involve using an LCR meter or other similar instruments.
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    Thiele-Small Parameters - Lv

    Lv refers to the voice coil inductance. It's measured in millihenrys (mH) and describes the tendency of the voice coil to resist changes in the electrical current flowing through it. Audio signals are AC (alternating current), meaning the current flowing through a voice coil constantly changes direction. The voice coil needs to resist these changes to accurately reproduce the audio signal. This resistance to change is inductance. A higher Lv value means more inductance, which can affect the speaker's frequency response and impedance.
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    Thiele-Small Parameters - Mms

    Mms or Moving Mass, is a crucial Thiele-Small parameter used in loudspeaker design. It represents the combined mass of the speaker's moving parts, including the cone, voice coil, and the air mass that moves with the cone.

    Mms is typically measured in grams (g).

    A speaker with an Mms of 25g might be considered relatively light, which could lead to a higher resonant frequency and potentially better efficiency compared to a speaker with an Mms of 50g. A speaker with a high Mms value (e.g., 50g) might be better suited for a sealed enclosure, while a speaker with a lower Mms (e.g., 25g) might be more suitable for a ported enclosure. While a lower Mms might seem desirable for certain applications, it's important to consider other factors like cone stiffness and voice coil inductance, as they also influence overall speaker performance.

    Why is Mms is important?

  • Resonant Frequency (Fs): A higher Mms generally results in a lower resonant frequency. This means the speaker will produce deeper, more powerful bass.
  • Efficiency: A heavier Mms (higher mass) can reduce efficiency, meaning the speaker may require more power to produce the same sound level.
  • Enclosure Design: Mms is essential for determining the appropriate enclosure volume and tuning for a speaker.
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    Thiele-Small Parameters - Pe

    Pe, or thermal power handling is a Thiele-Small parameter that indicates the maximum continuous power a loudspeaker driver can handle before overheating and potentially being damaged. It is usually measured in watts (W). Pe is usually listed in the manufacturer's specifications for the speaker driver. You can typically find this information in the product manual or on the manufacturer's website.

  • Continuous Power (Pe) - Pe represents the power the speaker can handle continuously over an extended period. It's different from peak power handling, which is the maximum power the speaker can handle for a very short duration.
  • Heat Dissipation (Pe) - Exceeding Pe can cause the voice coil of the speaker to overheat due to the electrical current flowing through it. This excess heat can damage the voice coil and potentially the entire speaker.
  • Manufacturer's Recommendations (Pe) - It's important to follow the manufacturer's recommended power range for the speaker to ensure optimal performance and longevity.
  • Amplifier Matching (Pe) - When choosing an amplifier for your speaker, ensure the amplifier's power output is within the recommended power range of the speaker. An underpowered amplifier can lead to distortion, while an overpowered amplifier can risk damaging the speaker.
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    Thiele-Small Parameters - Power Handling

    Is rated on how much power a audio speaker can handle without causing damage. The most important consideration is the audio speakers ability to get rid of excessive heat. Factors that effect this include magnet and voice coil size and their ability to handle heat, venting, and the adhesives used in voice coil construction.

    Mechanical factors are also considered such as the power required to cause;

    1. The coil to hit the back plate or come out of the gap
    2. The cone buckling from too much outward movement
    3. The spider bottoming on the top plate

    But still the most common cause of audio speaker failure is simple abuse; cranking it up beyond its power rating while asking the audio speaker to produce frequencies lower than it's frequency rating. So be sure to take into account the suggested usable frequency range and the Xmech parameter in conjunction with the power rating of the audio speaker to avoid such failures.
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    Thiele-Small Parameters - Q

    Q represents the quality factor of the speaker driver.Q parameters are crucial for speaker enclosure design. They help determine whether a driver is better suited for a sealed or ported enclosure and guide the tuning of the enclosure for optimal performance. Q parameters also help assess how well a driver will match with a particular amplifier. Amplifiers with different damping factors can interact differently with drivers based on their Q values.

    Some more about the Q parameters:

  • The Q parameters help predict and understand a speaker's behavior, particularly around its resonant frequency.
  • The Q parameters are crucial in designing speaker enclosures to achieve the desired sound characteristics.
  • The Q parameters provide insights into a driver's efficiency and overall performance.
  • All Q values are unitless.
  • The Q parameters are typically provided by the manufacturer in the speaker's specifications.
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    Thiele-Small Parameters - Qec

    Qec represents the electrical quality factor of the driver. Generally, lower Qec values are associated with higher efficiency, meaning the speaker converts more electrical power into sound. A well-controlled speaker will typically have a balance between Qmc and Qec, ensuring a smooth and accurate frequency response.

  • Electrical Damping - Qec is a measure of the electrical damping in the speaker system. It relates to the resistance of the voice coil and the other electrical components. Higher Qec values mean less electrical damping.
  • Energy Dissipation - It reflects how effectively the speaker's motor system (voice coil and magnet) dissipates energy through electrical resistance.
  • Resonance - Like Qmc, Qec also influences the shape of the impedance curve around the resonant frequency. A higher Qec results in a sharper peak.
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    Thiele-Small Parameters - Qes

    The Thiele-Small parameter Qes refers to the electrical Q of a loudspeaker driver which measures how much electrical damping the driver's voice coil and magnet motor system provides at the resonance frequency (Fs). When a speaker driver operates near its resonance frequency, the voice coil moving through the magnetic field generates a back electromotive force (back-EMF) that opposes the applied current. This back-EMF acts as a form of electrical damping, reducing the driver's tendency to resonate uncontrollably.

    Qes helps determine the ideal enclosure type for a driver. Drivers with higher Qes values are generally better suited for sealed enclosures, while those with lower Qes are often better suited for vented enclosures. Qes is combined with the mechanical Q (Qms) to calculate the total Q of the driver (Qts). Qts provides a comprehensive view of the driver's damping characteristics and is a crucial factor in speaker design. Qes is derived from the driver's electrical characteristics, including the voice coil resistance (Re) and the impedance at resonance frequency (Zmax). A higher Qes indicates less electrical damping, while a lower Qes means more damping.

    Typical Qes values:

  • Woofers Qes values typically have Qes values between 0.2 and 1.0
  • Midrange Drivers Qes values typically fall between 0.3 and 1.5
  • Tweeters Qes values can range from 0.2 to 2.0 or even higher
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    Thiele-Small Parameters - Qmc

    Qmc represents the mechanical quality factor of the driver.It influences the character of the speaker in the following ways:

  • Energy Storage - Qmc reflects the ability of the loudspeaker's mechanical suspension (the surround and spider) to store energy.
  • Damping - It is inversely related to the amount of mechanical damping in the system. Higher Qmc values indicate less mechanical damping.
  • Resonance - It influences the shape of the driver's impedance curve around its resonant frequency. A higher Qmc results in a sharper, narrower peak at resonance.
  • Bass Response - A higher Qmc can lead to a slightly stronger bass output at the resonant frequency, but it might also result in a less controlled and "boomy" bass response.
  • Transient Response - Lower Qmc values generally contribute to improved transient response, meaning the speaker can start and stop more quickly, leading to tighter and more accurate sound reproduction.
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    Thiele-Small Parameters - Qms

    Is the measurement of control from the mechanical suspension system at resonance (Fs) which include the spider and the surround. They allow and control the movement of the audio speaker cone. This measures the driver's damping due to mechanical losses in the suspension (surround and spider). A higher Qms indicates lower mechanical losses and potentially a more pronounced peak in the impedance curve near the resonant frequency.

    Some more about Qms

  • Qms measures how well the speaker's mechanical suspension system (the surround and spider) controls its motion at its resonant frequency.
  • A higher Qms value indicates lower mechanical losses and better control over the speaker's movement.
  • A lower Qms value means higher mechanical losses, resulting in less control over the cone's movement.
  • Qms helps predict the speaker's behavior near its resonant frequency.
  • It influences the overall damping of the speaker system, which affects its low-frequency response and transient behavior.
  • A higher Qms can lead to a more pronounced peak in the speaker's frequency response at its resonant frequency.
  • Qms, along with Qes (Electrical Quality Factor) and Qts (Total Quality Factor), helps determine the suitability of a driver for different enclosure types (sealed, ported, etc.).
  • Qms is a unitless value.
  • It's typically provided by the manufacturer in the speaker's specifications.
  • It's an essential parameter for designing speaker enclosures and understanding a driver's characteristics.
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    Thiele-Small Parameters - Qtc

    Qtc stands for total quality factor and it represents the overall damping of the speaker system, combining both the electrical (Qec) and mechanical (Qmc) aspects. Qtc provides a comprehensive view of how quickly the speaker system's vibrations decay after the signal stops. Higher Qtc values mean less damping and longer decay times. While Qmc and Qec are inherent properties of the driver itself, Qtc takes into account how the driver interacts with the speaker enclosure. The enclosure type and size significantly affect the Qtc value

    Different Qtc values are suited for different enclosure types:

  • Sealed Enclosures - Typically aim for Qtc values around 0.707 for a balanced bass response.
  • Bass Reflex (Ported) Enclosures - Often target Qtc values between 0.5 and 0.6 for extended low-frequency output.
  • Transient Response - Lower Qtc values generally contribute to improved transient response, resulting in tighter and more accurate sound reproduction.

    • Qtc is not directly measured but is calculated using the following formula:

    1/Qtc = 1/Qmc + 1/Qec

    Put a audio speaker into an enclosure and you then change how that audio speaker will act due to the resistance of the air pressure inside of the enclosure. When the audio speaker cone moves in or out the air pressure within the enclosure will put a resistance on its movements. The size and type of enclosure you build will depends upon the Qtc value you desire.

    To decide upon your loudspeakers enclosure size you will need some loudspeaker software or good math skills and the math formulas; I prefer the software approach. In the software programs you will be asked to enter the required Thiele-Small parameters about the drivers such as the Q's, Fs, Vas, etc, some also ask enclosure type, number of drivers, etc. Then for the program to calculate the enclosure size it will want to know the Qtc value you want. The Qtc value you choose is a personal preference. A value of 0.707 is what most designers aim for, it will give you the flattest frequency response (accurate sound reproduction) and the lowest possible F3 (widest usable frequency range). Some people may not like this sound and want to enhanced base response so they may aim for 0.8 or higher.

    In general high quality accurate audio loudspeakers Qtc are around 0.707, while loudspeakers that are designed to enhance the base may range from 0.8 to a max of 1.1. The more you move away from 0.707 anything over that will slowly start to sound boomy and unnatural and the base response will become more restricted.

    If you want loud clean base go with larger audio drivers in larger enclosures, don't overwork a smaller audio speaker and try to increase the base by stuffing it in a small enclosure. Don't make the enclosures to big either; the more you oversize the enclosure (Qtc below 0.707) the more "tinny" it may sound, because you loose loudness (dB's) on the lower frequencies.

    Thiele-Small QTC Comparison Chart

    On this graph the vertical dB's represent how loud it is, the horizontal represents the frequencies. So looking at the chart you can compare the loudness of the various frequencies. Look at Qtc 1.500 and notice that all the frequencies below 60 Hz have been lost and then you have a huge (loud) peak at around 110 Hz and then it drops back rapidly, this is obviously not the desirable flat response that we want, unless all you want is single note boom box.

    Now compare it to the Qtc 0.500 and note that there are no loud peaks, but now a lot of the frequencies below 50 Hz (F3 Value) will be too quiet. The best compromise is the Qtc of 0.707, no loud peaks and the loudness of the lower frequencies build quickly.
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    Thiele-Small Parameters - Qts

    This is the overall quality factor of the driver, combining the effects of both mechanical and electrical losses. It's calculated from Qms and Qes using the following formula: Qts = (Qms * Qes) / (Qms + Qes)

    Qts Values and the type of speaker

  • Low Qts (0.3-0.5) - Typically suitable for sealed enclosures, as they offer good transient response and tight bass.
  • Medium Qts (0.5-0.7) - Can work well in either sealed or ported enclosures, depending on the specific design goals.
  • High Qts (0.7 and above) - Generally better suited for ported (bass reflex) enclosures, as they can extend the low-frequency response.
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    Thiele-Small Parameters - Re

    Re stands for Voice Coil Resistance. It's the electrical resistance of the voice coil wire in a loudspeaker. A speaker with a low Re value (e.g., 4 Ω) might be more efficient and have better power handling than a speaker with a higher Re (e.g., 8 Ω).

    Why is Re important?

  • Efficiency: A lower Re generally results in higher efficiency, meaning the speaker can produce a louder sound level for a given amount of power.
  • Power Handling: A lower Re can improve a speaker's power handling capabilities.
  • Amplifier Matching: Re is an important factor to consider when matching a speaker to an amplifier. A speaker with a low Re might require a more powerful amplifier.

    • Key points about Re:

  • Units: Re is measured in ohms (Ω).
  • Relationship to other parameters: Re is related to the speaker's efficiency and power handling.
  • Voice Coil Design: A lower Re can be achieved by using thicker voice coil wire or by reducing the length of the voice coil.
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    Thiele-Small Parameters - Sd

    Sd stands for effective piston or cone area. It's a crucial Thiele-Small parameter that represents the area of the loudspeaker driver's diaphragm that contributes to sound production.

    Why is Sd Important?

  • Sensitivity: A larger Sd generally results in a more sensitive driver, meaning it produces a higher sound pressure level for a given input power.
  • Bass Response: Sd also influences the driver's low-frequency response. A larger Sd can produce deeper and more powerful bass.
  • Enclosure Design: The enclosure volume needed for a driver is partially determined by its Sd. A larger Sd may require a larger enclosure.

    • Factors Affecting Sd

  • Diaphragm Size: The physical size of the driver's diaphragm is a primary determinant of Sd.
  • Voice Coil Winding: The way the voice coil is wound can affect the effective piston area.
  • Suspension Design: The suspension's geometry and compliance can influence how much of the diaphragm contributes to sound production.

    • Measuring Sd

    Sd is typically measured by determining the area of the driver's diaphragm that moves in a linear manner when driven by a signal. This might involve using a laser interferometer or other specialized equipment.
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    Thiele-Small Parameters - SPL (Sensitivity)

    SPL refers to the driver's sensitivity, which is a measure of how efficiently it converts electrical power into acoustic output. It's usually expressed in decibels (dB) at a specific voltage and distance (e.g., 1W/1m or 2.83V/1m). SPL directly influences how loud a speaker system can play. For louder listening environments or larger rooms, speakers with higher SPL are preferred. Less sensitive speakers (lower SPL) may require more powerful amplifiers to reach the same volume levels as more sensitive speakers. Higher SPL values mean the speaker can produce louder sound with the same amount of input power which directly relates to the efficiency of the driver. A more sensitive speaker requires less power to achieve the same loudness level. Knowing the SPL helps in choosing an amplifier that can provide enough power to drive the speaker to the desired volume.

    Keep in mind that it requires twice the power to increase the volume of a speaker by just 3dB. Don't look at efficiency alone; also consider that often there is a trade off between the low frequency reproduction capability and its sensitivity. Remember that lower frequencies require a lot of air to be moved and that requires a lot of power. So a audio speaker which is capable of doing very low frequencies will usually have lower SPL ratings.
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    Thiele-Small Parameters - Vap

    Is defined as the volume of air that has the same compliance as the suspension of a passive radiator. Vap is essential for designing passive radiator systems. It allows you to calculate and adjust the tuning frequency to achieve the desired bass response.Vap plays a crucial role in determining the tuning frequency of a passive radiator system. The interaction between Vap, the passive radiator's mass, and the enclosure volume dictates the frequency at which the system will resonate and reinforce bass frequencies. Vap represents the equivalent volume of air that would have the same acoustic compliance as the passive radiator's suspension (the surround and spider)and it is analogous to the Vas parameter for active drivers.

  • A lower Vap value indicates a stiffer suspension on the passive radiator, while a higher Vap value signifies a more compliant suspension.
  • Vap plays a crucial role in determining the tuning frequency of a passive radiator system. The interaction between Vap, the passive radiator's mass, and the enclosure volume dictates the frequency at which the system will resonate and reinforce bass frequencies.
  • The primary influence of Vap is on the tuning frequency of the passive radiator system. By adjusting Vap (often by adding mass to the passive radiator), you can fine-tune the frequency at which the system resonates, tailoring it to match the desired bass response.
  • Vap can also impact the output level of the passive radiator, with a more compliant suspension (higher Vap) typically resulting in slightly higher output at the tuning frequency.

    • How is Vap measured or calculated?

    Measuring Vap for a passive radiator can be a bit more challenging than measuring Vas for an active driver. It often involves adding a known mass to the passive radiator and observing the change in resonant frequency can be used to calculate Vap. Some speaker design software tools have built-in features for estimating Vap based on the passive radiator's physical properties and the target tuning frequency.
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    Thiele-Small Parameters - Vas/Cms

    Represents the volume of air that when compressed to one cubic meter exerts the same force as the compliance (Cms) of the suspension in a particular speaker. The compliance or stiffness of the audio driver suspension is determined by the surround and the spider. It is simply a measurement of its stiffness. In Thiele-Small parameters, Vas and Cms are closely related and describe the compliance or "stiffness" of a loudspeaker driver's suspension system.

    Vas (Equivalent Compliance Volume) Vas represents the volume of air that, when compressed to one cubic meter, would exhibit the same stiffness as the driver's suspension. It's a theoretical measure given in cubic meters or liters. A larger Vas indicates a more compliant (looser) suspension, while a smaller Vas signifies a stiffer suspension.

    Cms is the actual physical measurement of the driver's suspension compliance. It's expressed in meters per Newton (m/N) and quantifies how much the suspension displaces under a given force. A higher Cms value means a more compliant suspension, and a lower Cms means a stiffer one.Both Vas and Cms are critical factors in determining the optimal enclosure type and size for a driver. Drivers with high Vas/Cms values are generally better suited for vented or ported enclosures, while those with lower values are often better for sealed enclosures. The compliance of the suspension significantly affects the driver's low-frequency response and overall efficiency.

    How is Vas calculated?

    Vas and Cms are directly proportional. This means that if you know one value, you can calculate the other using the following formula:

    Vas = Cms * Sd^2 * rho * c^2

  • Sd - Is the effective surface area of the driver's diaphragm (in square meters)
  • rho - Is the density of air (approximately 1.21 kg/m^3 at room temperature)
  • c - is the speed of sound in air (approximately 343 m/s at room temperature)

    • The typical values for Vas and Cms vary depending on the driver type and size:

  • The higher the Vas value generally means the speaker needs a larger housing.
  • Woofers Vas can range from a few liters to several hundred liters, while Cms might be between 0.1 mm/N and 2 mm/N.
  • Midrange Drivers Vas usually falls between 1 and 50 liters, and Cms might be between 0.05 mm/N and 1 mm/N.
  • Tweeters Vas is typically less than 1 liter, and Cms might be less than 0.05 mm/N.
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    Thiele-Small Parameters - Vb

    Vb (Net Internal Volume of the Speaker Enclosure) refers to the internal volume of air enclosed within the speaker box, excluding the volume occupied by the driver itself and any other components like bracing or damping material. It is typically measured in liters. Choosing the right Vb is a crucial step in speaker design. It involves balancing various factors, such as the driver's Thiele-Small parameters, the desired frequency response, and the enclosure type. Speaker design software or online calculators can be helpful in simulating the system response and optimizing Vb for specific goals.

  • In ported (bass reflex) enclosures Vb in conjunction with the port dimensions determines the tuning frequency (Fb). This is the frequency at which the port resonance reinforces the output of the woofer, extending the low-frequency response.
  • In sealed enclosures Vb directly affects the resonance frequency of the driver-enclosure system (Fc). A larger Vb lowers the Fc potentially leading to a deeper bass response but at the cost of reduced efficiency.
  • The choice of Vb significantly influences the overall frequency response, efficiency, and power handling of the speaker system.

    • To calculate Vb you need to measure the internal dimensions of the enclosure (height, width, and depth) and subtract the volume occupied by the driver and other components. There are online calculators and software tools available to help with this calculation.
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    Thiele-Small Parameters - Vc

    Vc refers to the net internal volume of a sealed enclosure (box) that will produce a specific bass reflex alignment (e.g., Butterworth) for a given loudspeaker driver. While Vc itself is not a Thiele-Small parameter, it is calculated based on several Thiele-Small parameters, including Vas (equivalent air compliance of the driver's suspension), the Qts (total Q of the driver at resonance), and the Fs (resonant frequency of the driver in free air).

    Knowing Vc helps designers build sealed enclosures that match the characteristics of a specific driver, resulting in better bass response and overall sound quality and is used in calculations to determine other parameters like the box resonant frequency (Fc) and the system Q (Qtc). These parameters are crucial for tuning the speaker system to achieve desired sonic characteristics.

    Some more about Vc:

  • It's the ideal box size for a specific speaker driver if you're building a closed box (sealed) speaker enclosure.
  • A larger Vc value generally means the driver is more suited for larger enclosures, while a smaller Vc indicates a preference for smaller boxes.
  • Vc is measured in liters or cubic meters.
  • It is typically provided by the speaker manufacturer in their specifications.
  • It's a crucial parameter for designing sealed enclosures, as it directly influences the low-frequency response and overall performance of the speaker system.
  • Other factors like the desired sound characteristics and room size also play a role in choosing the final enclosure volume, so Vc is a starting point rather than a strict rule.
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    Thiele-Small Parameters - Vd

    No, it not that kind of VD. The Thiele-Small parameter Vd refers to the peak displacement volume of a loudspeaker driver. It's a measure of how much air the driver's cone can displace when moving at its maximum linear excursion. Vd is directly related to a driver's ability to produce low-frequency sounds. A larger Vd generally means the driver can move more air and produce deeper bass notes and is a critical factor in determining the optimal enclosure size for a driver particularly for vented or ported designs.

    Vd provides an indication of the speaker's potential for low-frequency output. A larger Vd generally means the speaker can move more air, which translates to greater bass capability. It's a crucial parameter when designing speaker enclosures, especially for vented (bass reflex) enclosures. The size of the enclosure and the tuning of the vent are often determined based on the Vd of the chosen speaker.

    VD Relationship with other T/S Parameters:

  • Vas - Equivalent compliance volume of the speaker's suspension. Vas and Vd are related, but not directly proportional. A speaker with a large Vd might have a relatively small Vas, and vice versa.
  • Fs - Free-air resonance frequency. A larger Vd tends to result in a lower Fs, all else being equal.

    • How Vd is Calculated?

    Vd is calculated by multiplying the effective cone area (Sd) by the peak linear excursion (Xmax) of the driver.
    Vd = Sd * Xmax
    Sd: Effective piston area of the diaphragm (in square centimeters or square meters).
    Xmax: Peak linear excursion of the diaphragm (in centimeters or meters).

    The typical Vd values of a driver vary widely depending on the driver type and size:

  • Subwoofers often have Vd values of several hundred cubic centimeters or even liters.
  • Woofers typically have Vd values ranging from tens to hundreds of cubic centimeters.
  • Midrange Drivers and Tweeters generally have smaller Vd values, often less than ten cubic centimeters.
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    Thiele-Small Parameters - Xmax/Xmech

    (Maximum Linear Excursion) By definition it is the peak linear travel of a driver. Speaker output becomes non-linear when the voice coil begins to leave the magnetic gap. Non-linearity the point at which the number of turns in the magnetic gap which is exposed to the voice coil decrease. This excessive movement will increases audio speaker distortion. Xmax is measured at the voice coil height minus top plate thickness, divided by 2. Xmech is expressed as the lowest of four potential failure condition measurement multiplied by 2. The four possible failures are;

    1. The spider crashing onto the top plate.
    2. The voice coil bottoming on back plate.
    3. The voice coil coming out of gap above core.
    4. The physical limitation of cone.

    Take the lowest of these measurements then multiply it by two. This gives a distance that describes the maximum mechanical movement of the cone.
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    Thiele-Small Parameters - Zmax

    Zmax is a key Thiele-Small parameter that represents the maximum impedance of a loudspeaker driver. Specifically it's the impedance value at the driver's resonance frequency (Fs). Zmax is the peak value on the driver's impedance curve occurring at the resonance frequency (Fs). At this frequency the driver's mechanical and electrical systems are most in sync resulting in increased back EMF (electromotive force) and a corresponding spike in impedance. Zmax is crucial for selecting an appropriate amplifier to power the speaker. Amplifiers are typically rated to handle specific impedance loads (e.g., 4 ohms, 8 ohms). Mismatched impedance can lead to poor performance or even damage to the amplifier or speaker.

    In multi-way speaker systems (those with woofers, tweeters, etc.), Zmax is considered when designing crossovers. Crossovers divide the audio signal into different frequency bands for each driver, and Zmax helps determine the optimal crossover points. Zmax can influence the design of speaker enclosures particularly for vented or ported designs as the enclosure's tuning frequency is affected by the driver's impedance. Zmax values typically range from a few ohms to several tens of ohms, depending on the driver type and design.
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    What is impedance?

    Impedance often denoted by the symbol Z is a measure of the total opposition a circuit presents to the flow of alternating current (AC). It's essentially the AC equivalent of resistance in direct current (DC) circuits. Unlike resistance, which is a purely real value, impedance is a complex quantity, having both magnitude (measured in ohms, Ω) and phase. Impedance can be thought of as having two main components:

  • Resistance (R): This is the opposition to current flow due to the material's inherent properties, like the thickness and composition of a wire.
  • Reactance (X): This is the opposition to current flow due to energy storage in the circuit. Reactance has two forms, Inductive reactance (XL) and Capacitive reactance (XC)
  • Inductive reactance (XL): Caused by inductors, which store energy in magnetic fields.
  • Capacitive reactance (XC): Caused by capacitors, which store energy in electric fields.

    • In AC circuits where the current and voltage change direction periodically the interaction between resistance and reactance becomes crucial. The frequency of the AC signal also plays a significant role in impedance. For instance at low frequencies inductive reactance is low, and capacitive reactance is high. At high frequencies inductive reactance is high, and capacitive reactance is low.

    How to calculating Impedance

    The total impedance (Z) of a circuit can be calculated using the following formula:

    Z = √(R² + X²)

    R = Resistance and X = Reactance (the difference between inductive reactance (XL) and capacitive reactance (XC))
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    Thiele-Small Parameters - Z

    The total impedance, this includes the reactive and resistive resistance's

    How Impedance (Z) is Affected

  • The impedance curve of a speaker is not flat. It varies with frequency.
  • At resonance (Fs), the impedance reaches its peak (Zmax).
  • Below resonance, the impedance is primarily determined by the voice coil's DC resistance (Re).
  • Above resonance, the impedance is largely influenced by the speaker's inductance.
  • The shape of the impedance curve around resonance is affected by the Q parameters (Qes, Qms, and Qts). A higher Q results in a sharper peak at resonance.

    • Why Impedance Matters

  • Impedance is important because it affects how much power a speaker will draw from an amplifier.
  • Amplifiers are typically designed to work with speakers of a specific nominal impedance (e.g., 4 ohms or 8 ohms).
  • Connecting a speaker with an impedance that is too low can cause the amplifier to overheat or even fail.
  • The impedance curve also provides insights into the speaker's overall performance and behavior.
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