Showing posts with label Thiele Small parameters. Show all posts
Showing posts with label Thiele Small parameters. Show all posts

Thursday, November 5, 2026

How Driver Parameters Determine Full-Range Speaker Dimensions: A 4-Inch Markaudio CHR-70 Example

Published by iwistao · DIY Audio

The nominal diameter is only a size category. Actual frame, cutout, mounting, and depth dimensions determine whether the driver fits the baffle; Thiele/Small parameters, the target bass alignment, and cabinet construction determine enclosure volume and final outside dimensions.

A full-range loudspeaker cabinet is not scaled directly from the cone diameter. The label “4 inch” is useful for product classification, but it does not specify the air volume behind the cone, the desired low-frequency response, the port tuning, or the panel thickness. Those decisions are made from the driver's measured electro-mechanical behavior and the intended use.

Figure 1: Markaudio CHR-70 Gen.3 full-range drivers. 

1. Why a 4-Inch Label Does Not Determine Box Size

The driver's frame diameter sets a minimum baffle size. Its Thiele/Small parameters set the range of useful acoustic alignments. A sealed box, bass-reflex box, transmission line, and horn can therefore use the same driver yet have very different external dimensions.

The correct sequence is: choose the acoustic target, calculate or simulate the required net air volume, arrange that volume around the driver and port, then add construction thickness to obtain the external size.

Thiele's vented-box analysis showed that low-frequency behavior can be predicted from resonance frequency, equivalent compliance volume, and damping, while Small described a closed box as a second-order high-pass system. In practical design language, Fs, Vas, and Qts do not output one compulsory box; they allow a family of trade-offs among cabinet size, cutoff frequency, damping, efficiency, and excursion.[3][4]

2. The Driver Parameters That Matter

Markaudio publishes the following representative data for the CHR-70 Gen.3. Values should be checked against the datasheet supplied with the exact production version before a final build.[1][2]

Parameter CHR-70 value How it affects the enclosure
Fs 65.4 Hz The driver's free-air resonance; it helps set the practical bass-alignment region.
Vas 5.17 L An equivalent air-compliance volume. It is an input to box calculations, not an automatic box-volume recommendation.
Qts 0.55 Total damping around Fs. Together with the target system Q or vented alignment, it strongly influences required volume and response shape.
Sd 50.2 cm² Effective radiating area; it combines with excursion to indicate low-frequency displacement capability.
Xmax 4.3 mm one way Linear travel limit used to check bass output and safe power, especially below a vented box's tuning frequency.
Nominal power 20 W A thermal/mechanical constraint. It does not independently determine cabinet volume.
Mechanical size 124 mm frame, 112 mm mounting-hole circle, 102 mm cutout, 56 mm front-to-back depth; 69.5 mm motor diameter Sets the minimum front-panel area, cutout, fastener positions, and rear clearance.

Figure 2: CHR-70 mechanical dimensions. The drawing identifies 56 mm as the front-to-back dimension and 69.5 mm as the motor diameter; it also notes a 2 mm gasket that should be considered when routing a rebate. Verify the current production drawing before cutting the baffle. 

3. From Acoustic Volume to Outside Dimensions

Step 1: Select the system type and response target

A sealed box needs a target system Q, usually written as Qtc. A bass-reflex design needs both net box volume Vb and tuning frequency Fb. These are acoustic choices: compactness, bass extension, maximum output, amplifier power, and intended placement must be considered together.

Step 2: Calculate net air volume

Net volume is the working air space seen by the rear of the cone. For a sealed enclosure, the ideal small-signal relationship is:

Vb = Vas / ((Qtc / Qts)² - 1)
Fc = Fs × (Qtc / Qts)

This simplified relationship is useful for a transparent first calculation. It does not include leakage, damping losses, temperature, production tolerance, or the acoustic effect of stuffing.[3]

Step 3: Convert net volume to gross internal volume

Vgross = Vnet + Vdriver + Vport + Vbracing + Vhardware

The driver basket, magnet, port tube, braces, terminal cup, and any internal partitions displace air. A cabinet drawn to the net target without adding these items will finish undersized.

Step 4: Choose internal proportions and add panel thickness

Vgross (litres) = Win × Hin × Din / 1,000,000   [dimensions in mm]
Wout = Win + 2t; Hout = Hin + 2t; Dout = Din + 2t

The last line applies to a simple six-panel box with panel thickness t. Rebates, inset backs, doubled baffles, curved walls, and non-rectangular cabinets require their own construction drawing.

4. Worked Sealed-Box Example: Markaudio CHR-70

For a calculation that can be checked by hand, choose a sealed target of Qtc = 0.707. Using Vas = 5.17 L and Qts = 0.55:

Vb = 5.17 / ((0.707 / 0.55)² - 1)
Vb = 7.92 L net

Fc = 65.4 × (0.707 / 0.55)
Fc = 84.1 Hz

At Qtc 0.707, Fc is also the idealized -3 dB frequency for the second-order response. The result illustrates the trade-off clearly: the sealed box is manageable, but it does not provide the same nominal bass extension as a larger, tuned system.

For this geometry exercise only, reserve a combined 0.58 L illustrative allowance for the driver, brace, terminal cup, and other solid parts. This is not a Markaudio-published displacement value. It represents the Vdriver + Vbracing + Vhardware terms in the gross-volume equation above; before building, replace it with measured or CAD-derived displacements for the exact parts used.

One possible 18 mm panel layout

  • Target net air volume: 7.92 L
  • Gross internal volume: about 8.50 L, using the illustrative 0.58 L allowance
  • Internal W × H × D: 170 × 244 × 205 mm = 8.50 L
  • External W × H × D: 206 × 280 × 241 mm

This is a worked geometry example, not a Markaudio cabinet recommendation. The 206 mm baffle easily accommodates the nominal 124 mm frame, but the response still needs simulation and measurement with the actual driver, damping material, amplifier source impedance, and listening position.

5. Comparison with Markaudio's Official Vented Cube

Markaudio also publishes a vented-cube stand-mount drawing for the CHR-70.3. It uses an external cube of 268 × 268 × 268 mm, assumes 18 mm material, doubles the front and top baffles, and specifies a 35 mm diameter by 87 mm total-length vent. The drawing lists Fb = 50 Hz and a nominal anechoic F6 = 40 Hz.[5]

Figure 3: Markaudio CHR-70.3 vented cube. The plan shows how a lower tuning target, a vent, double panels, and damping produce a different exterior from the sealed calculation.

The marked inner dimensions imply roughly 10.6 L of rectangular gross interior space before subtracting the driver, vent, and other occupied volume. That inferred figure is not a printed net-volume specification. The important lesson is that the same CHR-70 parameters support more than one rational enclosure: the sealed example prioritizes simplicity and controlled roll-off, while the official vented design uses more space and a tuned resonator to extend bass.

6. Baffle, Port, Panel, and Proportion Checks

Baffle width is acoustic as well as mechanical

A wider baffle changes the transition from approximately full-space to half-space radiation and changes edge-diffraction timing. Rectangular proportions and an off-center driver can spread diffraction features, but the final on-axis and off-axis response should be measured rather than assumed from one rule of thumb.[6]

Port size must satisfy tuning and airflow

In a bass-reflex box, port area, effective length, box volume, and end correction interact. A smaller port can be shorter but may become noisy; a larger port reduces air velocity but may be too long to fit. Port turbulence, flow separation, compression, resonance, and clearance from internal walls also matter. This is why Fb and vent behavior should be simulated with the actual geometry instead of copied from an unrelated “4-inch speaker” plan.[7]

Panel thickness changes both inside and outside

If the target internal dimensions remain fixed, moving from 12 mm to 18 mm material adds 12 mm to each external axis. Doubling a front baffle adds still more depth. Bracing can allow a lighter panel to behave more rigidly, but the brace itself reduces net volume.

Cabinet proportions control internal modes

Two boxes can have equal volume but different resonant-mode distributions because rectangular-cavity mode frequencies depend on the three internal dimensions. Avoid making all three internal dimensions identical unless the design specifically addresses the resulting coincident modes. Driver position, lining, stuffing, and braces are part of the acoustic layout, not afterthoughts.[8]

7. What Must Be Verified Before Cutting Wood

  1. Confirm the exact driver version. Production data and measured T/S parameters can vary.
  2. Model the intended alignment. Check frequency response, impedance, group delay, cone excursion, and port velocity at realistic amplifier power.
  3. Build net volume from actual displacements. Include the driver, port, braces, terminal cup, and partitions.
  4. Check physical clearances. Leave room behind the magnet, around the terminals, and at both ends of the vent.
  5. Prototype and measure. Verify impedance tuning, near-field bass response, leakage, and audible port or panel noise before applying the final finish.

The driver parameters therefore determine the acoustic starting point, not the final silhouette by themselves. Outside dimensions appear only after the response target, topology, net air volume, occupied volume, baffle layout, and construction method have all been specified.

Frequently Asked Questions

Is Vas the recommended enclosure volume?

No. Vas describes the driver's suspension compliance as an equivalent volume of air. It is used with Qts and the chosen alignment to calculate or simulate Vb.

Can every 4-inch full-range driver use the same cabinet?

No. Drivers with the same nominal diameter can have different Fs, Vas, Qts, excursion, frame dimensions, and frequency response. Reusing a cabinet without modeling can change bass extension, damping, and safe output.

Which CHR-70 enclosure is better: sealed or vented?

Neither is universally better. A sealed design is simpler and rolls off more gradually. A properly modeled vented design can extend bass and increase output around tuning, but it requires more careful control of port geometry and excursion below Fb.

Does damping material count as solid displacement?

Porous lining or loose fill does not behave like a solid block, and it can change apparent acoustic compliance. Dense boards, braces, ports, and hardware do physically displace air and should be included explicitly.

Can I build directly from the 206 × 280 × 241 mm sealed example?

Treat it as an educational starting point. Verify your driver, material thickness, component displacement, damping, expected listening level, and measured response before committing to a finished pair.

Find More

References

  1. Markaudio. “CHR-70.” Product description, parameters, images, and cabinet-plan index. https://www.markaudio.com/online_shop/ch/chr-70/
  2. Markaudio. “CHR-70A Gen.3” datasheet, linked from the manufacturer's product page. https://www.kjfaudio.com/wp-content/uploads/2016/12/CHR-70A_Gen.3_champ_Eng.pdf
  3. Small, Richard H. “Closed-Box Loudspeaker Systems—Part 1: Analysis.” Journal of the Audio Engineering Society, Vol. 20, December 1972, pp. 798–808. AES E-Library record.
  4. Thiele, A. N. “Loudspeakers in Vented Boxes: Part 1.” Journal of the Audio Engineering Society, Vol. 19, May 1971, pp. 382–392. AES E-Library record.
  5. Markaudio. “Vented Cube Standmount for Markaudio CHR-70.3.” Cabinet drawing, August 2024. Official drawing.
  6. Linkwitz, Siegfried. “Diffraction from Baffle Edges.” Linkwitz Lab. https://www.linkwitzlab.com/diffraction.htm
  7. Bezzola, Andri; Devantier, Allan; and McMullin, Elisabeth. “Loudspeaker Port Design for Optimal Performance and Listening Experience.” AES Convention 147, Paper 10311, October 2019. AES E-Library record.
  8. Smedley, Jack. “Sound Waves in a Cavity.” Physics 104 laboratory, Bates College. https://abacus.bates.edu/~jsmedley/phys104/cavity.htm

© 2026 IWISTAO. All rights reserved.

Wednesday, December 17, 2025

Professional Guide to Sealed Loudspeaker Enclosure Design -- Data and Chart Based Method (Part 2)

Professional Guide to Sealed Loudspeaker Enclosure Design -- Data and Chart Based Method (Part 2)


Published by IWISTAO

After studying Part I, it should now be clear that the core issue in sealed enclosure design lies in the selection of enclosure air volume.

Key Factors in Selecting Enclosure Volume

The choice of internal air volume directly affects the following parameters:

  • Low-frequency cutoff
  • Transient response speed
  • Enclosure size
  • Frequency response characteristics
  • Harmonic distortion
  • Phase behavior

These parameters are not listed to intimidate the reader. On the contrary, they provide practical and measurable guidance for in-depth research and for achieving higher-quality low-frequency reproduction.

From practical experience in standardized, factory-oriented production, the first priority is often to ensure that the objective performance data appear optimal.

Therefore, the enclosure design method presented below deliberately simplifies the process, analyzing the system from an idealized perspective.



Assumptions of the Idealized Model

Under this ideal assumption:

  • The driver losses are low
  • The enclosure losses are low

If the loudspeaker cone is excessively compliant and the enclosure panels are also overly flexible, the resulting errors become significant and the theoretical model loses validity.



Enclosure Dimensions and Parameter Calculations

Designing a sealed enclosure requires a suitable driver.

Drivers intended for sealed-box applications typically exhibit:

  • Low resonance frequency
  • Relatively heavy cone mass
  • Long voice-coil excursion

Regarding Qts, drivers used in well-performing sealed systems generally fall within a Qts range of approximately 0.3–0.6, which implies that small-magnet designs should be avoided.



EBP Criterion (R. Small)

Professor Richard Small recommended using an evaluation parameter before enclosure design to determine whether a driver is more suitable for a sealed box, a vented box, or both.

This parameter is known as the Efficiency Bandwidth Product (EBP):

EBP = f0 (or fs) / Qes

where:

  • f0 or fs = free-air resonance frequency
  • Qes = electrical Q of the driver

Interpretation of EBP Values

  • EBP ≤ 50 → suitable for sealed enclosures
  • EBP ≈ 100 → suitable for vented enclosures
  • EBP ≈ 60–80 → suitable for either type


Required Thiele/Small Parameters for Sealed Box Design

The calculation of sealed-box volume is relatively straightforward. The required Thiele/Small (T/S) parameters are:

  • f0 (or fs) – free-air resonance frequency of the driver
  • Qts – total Q of the driver
  • Vas – equivalent compliance volume of the driver
  • Cms – mechanical compliance, expressed as equivalent air volume

These constitute the most essential elements in sealed-box design and are, in principle, provided by the manufacturer.



Table-Based Design Method (Vance Dickason)

To determine the enclosure volume that produces the optimal system response, one may consult the tables recommended by Vance Dickason in the Loudspeaker Design Cookbook.

Specifically, Table 8-4 is used here. (The original reference includes multiple tables covering Q values from 0.5 to 1.5. In this article, only the “optimal” alignment Qtc = 0.707 is selected.)

Using these tables, one can determine:

  • The compliance ratio a
    → enclosure volume:
    Vb = Vas / a
  • The sealed-box resonance frequency fc
    → obtained by multiplying the driver’s fs by the table value:
    fc = fs × (fc / fs)

The −3 dB cutoff frequency f3 can then be determined using the relationship between Qtc and (f3 / fc) (Table 8-3):

f3 = fc × (f3 / fc)

 



Fundamental Equations of Sealed Box Design

In addition to table lookup, some basic calculations are often required. These can be regarded as the fundamental equations of sealed-box design. In essence, they relate the driver’s free-air parameters to the system parameters after enclosure loading (Vb, Qtc, fc, and f3).

In this context, the most frequently used relationships are:

  • Vb = Vas / a
  • fc = fs * (fc / fs from table)
  • f3 = fc * (f3 / fc from table)

When Qtc = 0.707, theory predicts that f3 coincides with fc.

 

 

As verification below,


 



Step-by-Step Use of the Design Tables

Referring to Table 8-4, the enclosure design process proceeds as follows:

 

Step 1 — Determine Enclosure Volume

Select the compliance ratio a based on the driver’s Qts, then calculate the enclosure volume using a rearranged form of the design equation:

Vb = Vas / a

where Vb is the target enclosure volume.

Step 2 — Calculate System Resonance Frequency

Determine the sealed-box resonance frequency:

fc = x* fs

where x is the value of (fc / fs) obtained from the table.

Step 3 — Determine −3 dB Frequency (Optional)

Using the verification formulas and Table 8-3, calculate the −3 dB low-frequency cutoff:

f3 = fc * (f3 / fc)

In theory, when Qtc = 0.707, the −3 dB frequency coincides with fc.



Notes on AS and IB Terminology

When examining the referenced charts, special attention should be paid to the abbreviations:

  • AS – Air Support, indicating a sealed enclosure, where the enclosed air provides spring-like support.
  • IB – Infinite Baffle, meaning an extremely large enclosure volume.


“Air-Spring” Sealed Box Concept

A particular variant of sealed-box design deliberately exaggerates the air-spring effect of the enclosed air to stiffen a driver with a very compliant suspension.

This approach involves designing the driver with:

  • Low free-air resonance frequency (fs)
  • Low Qts

When such a driver is installed in a relatively small enclosure, both fs and Qts rise, providing a form of mechanical compensation.

This type of enclosure can be subjectively identified by gently pressing the mounted cone:

  • The cone moves inward slowly.
  • Upon release, it returns slowly.

This behavior reflects the air-spring support effect. Historically, some sealed-box loudspeakers (e.g., early AR designs) promoted this concept as an “air-cushion” principle. Today, such marketing is less common, although the basic physics remains valid.



Efficiency and Sensitivity Considerations

In sealed enclosures, efficiency and sensitivity are also critical. Larger enclosure volumes generally yield higher sensitivity.

Some drivers are designed with relatively high Qts and Vas, which helps achieve higher low-frequency sensitivity in the final system.



Example and Practical Reference

An example is provided using the table-based design method. Note that since only the Qtc = 0.707 table is presented in this article, the third row of the table is used.

There is an 8-inch woofer with Qts = 0.45, Qes = 0.53, Qms = 0.30, f0 = 31.5 Hz, and Vas = 83L. Design a sealed enclosure for it.

According to formula (8-1), check if the speaker is suitable for a sealed enclosure: EBP = 31.5 / 0.53 = 59, which indicates it is a suitable driver. Then, starting from Qts, select five different Qtc values from Tables 8-2 to 8-11, and compare the characteristics of the sealed enclosure for different Qtc values in Table 8-12 as below.

Figure 8-8

From Table 8-12, we can see that when Qtc = 0.5, except for the larger enclosure volume, the low-frequency cutoff frequency f3 is actually different from fc.  Refer to Figure 8-8; the only difference is that the frequency fc at the impedance curve peak is to the left of the frequency response curve.

Only when Qtc = 0.7 are f3 and fc the same. When Qtc > 0.8, the positions of f3 and fc are as shown in Figure 8-8, and peaks and valleys begin to appear on the low-frequency response curve. Some say that increasing the Vb of a sealed enclosure will lower f3. It should be remembered that this is only true when the selected Q ≥ 0.7.

If Qtc < 0.7, then f3 will actually increase when Vb increases. As shown in Table 8-12, when V = 354 L, f3 rises to 54 Hz. In addition, when calculating Vb, especially for small enclosures of only a few liters, the volume occupied by the woofer and crossover components inside the enclosure must be added.

 


Additional Observations: ATC Sealed Two-Way Loudspeaker

An ATC sealed two-way loudspeaker is cited as another example. It employs a long magnetic gap with a short voice coil, a configuration that yields lower harmonic distortion and a smooth, controlled sound character.

A notable feature of ATC drivers is the use of proprietary cone coatings on all woofers and midrange units.



Final Summary

Using the table-based method, especially with Qtc ≈ 0.7, allows designers to rapidly obtain a neutral baseline enclosure design with minimal complexity.

This approach is well suited for:

  • Preliminary design
  • Academic or engineering validation
  • Improving design efficiency

Even when computer-aided design tools are available, it is strongly recommended to start with the chart method to quickly understand the behavior of a driver before refining the design further.