Designing a 40 Hz Transmission Line Loudspeaker

Designing a 40 Hz Transmission Line Loudspeaker

Published by IWISTAO

An Engineering Case Study Using the Markaudio CHN-110

Transmission Line (TL) loudspeaker enclosures are widely regarded for their ability to extend low-frequency response while preserving transient accuracy and smooth impedance behavior.

This article presents an engineering-grade transmission line enclosure design optimized for the Markaudio CHN-110 full-range driver, targeting an acoustic F3 of 40 Hz.

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1. Design Objectives

• Achieve a true low-frequency extension of F3 ≈ 40 Hz
• Avoid Helmholtz resonance artifacts typical of bass-reflex enclosures
• Maintain smooth impedance behavior for Class-A and tube amplifiers
• Control cone excursion at low frequencies
• Prioritize transient accuracy and tonal linearity

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2. Driver Selection

The selected driver for this study is the Markaudio CHN-110, a 110 mm full-range unit known for its wide bandwidth and moderate total Q.

 

Key Thiele–Small parameters (manufacturer data):

• Fs ≈ 44.2 Hz
• Sd ≈ 109 cm²
• Qts ≈ 0.42
• Vas ≈ 24.7 L

The moderate Qts makes the CHN-110 particularly suitable for quarter-wave acoustic loading rather than aggressive bass-reflex tuning.

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3. Quarter-Wave Transmission Line Theory

Unlike bass-reflex enclosures, which rely on Helmholtz resonance, a transmission line enclosure operates primarily on quarter-wave acoustic resonance. The fundamental design relationship is:

L = c / (4 × f)

where L is the effective acoustic line length, c is the speed of sound (approximately 343 m/s), and f is the target frequency.

For a target F3 = 40 Hz:

L ≈ 2.14 m

After accounting for acoustic damping, which increases the effective acoustic length, the physical folded line length is approximately 1.9 m.

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4. Line Geometry and Enclosure Volume

Cross-Sectional Area

Engineering practice derived from quarter-wave modeling recommends that the starting cross-sectional area of the transmission line be proportional to the driver’s effective cone area:

S₀ ≈ (1.0–1.2) × S_d

For this design:

• Start of line: ~120 cm²
• End of line (tapered): ~65 cm²

A gentle taper helps suppress higher-order standing waves while preserving low-frequency loading.

Effective Acoustic Volume

Unlike bass-reflex enclosures, a transmission line does not have a single tuning volume. Instead, its effective acoustic volume is defined by:

V_TL = ∫₀^L S(x) dx

where S(x) is the cross-sectional area of the line as a function of distance, and L is the effective acoustic line length. For practical engineering work, this relationship is commonly approximated as:

V_TL ≈ S_avg × L

• Effective acoustic volume: ~18 L
• Total structural enclosure volume: ~21–22 L

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5. Predicted System Performance

Impedance Behavior

The transmission line system exhibits a single, low-Q impedance peak centered near 40 Hz, in contrast to the dual-peak impedance characteristic of bass-reflex enclosures. This results in improved amplifier stability and excellent compatibility with tube amplifiers.

Frequency Response

The predicted frequency response demonstrates smooth low-frequency extension with a −3 dB point at approximately 40 Hz, without the artificial bass emphasis typically associated with port tuning.

Cone Excursion

Because the transmission line continues to provide acoustic loading below resonance, cone excursion remains better controlled than in an equivalent bass-reflex enclosure, particularly in the 40–60 Hz region.

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6. Comparison with a Bass-Reflex Enclosure

Aspect	Bass-Reflex	Transmission Line
Low-frequency mechanism	Helmholtz resonance	Quarter-wave resonance
Impedance behavior	Dual peaks	Single smooth peak
Group delay	Higher near tuning	Lower and smoother
Port noise	Possible	None
Subjective bass	Emphasized	Natural and linear

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7. Practical Construction Notes

• Folded internal path using a three-section “Z” or “S” layout
• Cabinet material: 18 mm MDF or birch plywood
• Heavier damping near the driver, moderate in the middle, minimal near the terminus

 

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8. Conclusion

This engineering study demonstrates that a properly designed damped transmission line enclosure allows the Markaudio CHN-110 to achieve a genuine 40 Hz low-frequency extension without relying on aggressive bass-reflex tuning. Compared to enclosures of similar size, the TL approach offers smoother impedance behavior, improved cone control, and superior transient fidelity, making it an excellent choice for high-quality full-range loudspeaker systems.

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References

1. Martin J. King, Transmission Line Loudspeaker Design
   https://www.quarter-wave.com/
2. Martin J. King, Anatomy of a Transmission Line Loudspeaker (PDF)
   https://www.quarter-wave.com/TLs/TL_Anatomy.pdf
3. G. L. Augspurger, “Transmission Lines Updated,” Journal of the Audio Engineering Society, 1980
4. Markaudio Loudspeakers Ltd., CHN-110 Datasheet
   https://www.markaudio.com/
5. Wikipedia, “Transmission Line Loudspeaker”
   https://en.wikipedia.org/wiki/Transmission_line_loudspeaker