Professional Guide to Sealed Loudspeaker Enclosure Design -- Data and Chart Based Method (Part 1)
Published by IWISTAO
This article introduces a data-and-chart-based method for designing sealed loudspeaker enclosures. It can be regarded as a convenient and effective approach to sealed box design.
In a design process that relies on measured data, the key factor is in fact the selection of appropriate ratios, so that the coupled system formed by the enclosure and the driver produces results that meet the intended design objectives.
Qts
Why does the author refer to this method as a “data-chart method”? Because the design is fundamentally based on driver parameters. The first and most critical parameter is Qts.
In earlier standards, it was once stated that Qts, fs, and Vas together could determine the low-frequency performance of a loudspeaker. In simple terms, Qts is related to the height and sharpness of the impedance peak of a driver in free air (a descriptive but intuitive explanation). In practice, Qts can also be regarded as a form of damping factor.
When a loudspeaker is installed in a sealed enclosure, the air trapped inside the cabinet behaves like a spring, resulting in the formation of a new Q value.
Q Value, Enclosure Response, and f, fc, f3
It must be emphasized that Q is the primary consideration in sealed box design (see figure below). Q is a composite mathematical parameter used to describe the resonant behavior inside the enclosure. It represents the combined influence of electrical, mechanical, and acoustic (air compression) factors on resonance control when the driver and enclosure operate as a system.
The figure below shows the normalized low-frequency response of sealed enclosures when the system resonance Q ranges from 0.5 to 2.0, plotted against the normalized resonance frequency fc.
At first glance, this chart may be difficult to interpret. The author himself took many years to fully understand it.
- The vertical axis represents relative sound pressure output.
- The horizontal axis represents a frequency ratio, where f is the actual operating or measured frequency, and fc is the resonance frequency of the driver once mounted in the sealed enclosure.
Understanding f / fc
By using fc as the denominator, different frequencies are normalized, allowing systems with different resonance frequencies to be compared on the same scale.
This normalization is important because once a driver is installed in different enclosures, both fc and Qtc change, making direct horizontal comparisons difficult.
For example, if the same driver is mounted in two enclosures with different internal volumes, the smaller enclosure will result in a higher fc and a higher Qtc. By dividing the measured frequency f by the system resonance fc, the resulting ratio provides a common reference framework across different drivers and enclosure conditions.
Typical Qtc Values and Their Sonic Characteristics
Based on the chart and long-established practice, the following interpretations are commonly accepted, particularly from the historical context of loudspeaker design:
a) Qtc = 0.5
Known as critical damping. At f / fc = 1, the response rolls off smoothly at 6 dB per octave toward the cutoff frequency. Transient response is nearly ideal, but subjectively the sound may feel over-damped.
b) Qtc = 0.577
Corresponds to a Bessel D2 response. This alignment provides the maximum flat extension (not explicitly shown in the chart; refer to the Q = 0.5 curve).
c) Qtc = 0.707
Corresponds to a Butterworth B2 alignment (see Thiele’s work). This is the most widely used sealed box alignment. The response is maximally flat, with the −3 dB point occurring at fc, while maintaining excellent transient behavior.
d) Qtc = 1.0
Provides a wider low-frequency bandwidth. The −3 dB point shifts to approximately 0.8 fc, but at the cost of about 1.5 dB of response peaking above cutoff, and with some degradation of impulse response.
Increasing Q beyond this point does not extend low-frequency response. Instead, it produces a peak at the resonance frequency fc.
If a 2 dB peak is considered acceptable, this corresponds to a Chebyshev C2 alignment with Qtc ≈ 1.1, which yields the highest efficiency for a sealed enclosure.
C2 alignment is feasible for small, bandwidth-limited systems, such as those with fc ≥ 65 Hz. Specific recommendations include:
fc = 50 Hz → Qtc ≈ 0.6fc = 40 Hz → Bessel alignment, Qtc ≈ 0.52
Q Value and Subjective Sound Quality
Although these Q values represent only specific points along a continuous range, they reveal clear correlations with subjective sound quality:
- Higher Q (≈ 1.0): a warmer, more resonant low-frequency character.
- Moderate Q (≈ 0.8): more audible detail and better transient response, but leaner tonal balance.
- Qtc = 0.707: generally regarded as the best overall compromise, combining flat response, good transients, and a unique
f = f3characteristic.
At very low Q values (≈ 0.5), the sound may become over-tight and excessively damped.
Some experts still advocate Q values of 0.5–0.6 as offering the highest fidelity. However, notable exceptions exist, such as the BBC-derived Rogers LS3/5A, whose sealed enclosure Q reaches approximately 1.2. This high Q was intentionally used to enhance bass perception in outside broadcast vehicles.
In practice, sealed box designs typically aim for Qtc ≤ 1.2.
Case Study: LS3/5A and Practical Observations
Measurements of various LS3/5A units from different manufacturers have shown that some meet professional monitoring requirements in the low-frequency region.
The frequency response of the Rogers LS3/5A in a typical listening environment shows respectable low-frequency extension. Anechoic chamber measurements (available from historical archives) confirm this performance.
A noticeable response lift around 100 Hz reflects a listening-oriented bass enhancement technique, closely resembling the trend observed in systems with Qts ≈ 1.0.
In commercial products, designers sometimes intentionally increase Q to create a stronger sense of bass impact. This can result in an under-damped “boomy” character, which may appeal to certain musical genres and audiences. Whether this is desirable depends on design goals and listener preference.
Advances in cone material science, such as modified polypropylene (PP) cones with higher inherent damping, and the use of damping coatings, help compensate for electrical under-damping through material engineering.
Alternatively, high-power amplifiers with strong electrical damping can also improve low-frequency control—a common practice in high-end audio.
Summary
- The purpose of this article is to establish an understanding of the interaction between the driver and the enclosure, focusing on the relationship between cone compliance and air compliance. A basic understanding of thermodynamic gas behavior (isothermal, isochoric, isobaric compression) is beneficial.
- Intuitively, a smaller enclosure requires greater force to displace the cone, resulting in faster restoring force and higher resonance frequency.
