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Professional Guide to Sealed Loudspeaker Enclosure Design -- Data and Chart Based Method (Part 2)
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posted by Vincent Zhang
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’sfsby 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 / afc = 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.
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