PROCEEDINGS of the23rd International Congress on Acoustics
9 to 13 September 2019 in Aachen, Germany

Evaluation of non-linear distortion in compression chamber of a lowfrequency hornTomasz NOWAK1; Andrzej DOBRUCKI1; Romuald BOLEJKO1
1

Wrocław University of Science and Technology, PolandABSTRACT
The subject of this study is to investigate non-linear behavior of air in a horn-loaded low frequency speakerdevice. Research and development of low frequency transducers continues to improve their linearity ofexcursion trough linearization of suspension compliance and BL factor as well as steadily increasing thermal
power handling. The use of those latest transducers promises to achieve unprecedented efficiency and soundpressure levels, especially when combined with high compression horn-loading. This raises questions: whatis the limiting factor of efficiency in those devices while retaining non-audible distortion? Should thetransducers be improved or we have reached the limits of air non-linearity? This paper will hopefully give an
insight on answers to those questions, trough analyzing a set of measurements and tests conducted with aprototype horn-loaded low-frequency loudspeaker device. High signal behavior of a technologicallyadvanced, professional transducer was evaluated with and without horn-loading to study the effects ofcompression chamber in those extreme working conditions.
Keywords: nonlinear distortion, horn loudspeaker

1. INTRODUCTION
The low frequency horn loaded loudspeakers lost their popularity in 1990’s due to reductio n of
amplification costs and introduction of digital sound processing. The industry switched to higher
quantity of direct radiating loudspeaker devices, arraying them and controlling the directivity withDSP. The horns themselves were no longer developed – the technology was utilizing transducer
capabilities of that time. Because of low efficiency of direct radiator devices, the low frequency
drivers were vastly improved over the last 30 years with solutions for high excursion linearization, likesplit windings, mirrored suspension and demodulation rings to name a few. Heat management
provided higher power handling and the introduction of neodymium magnets allowed weight reduction
at first, then unparalleled magnetic flux in the gap. Those advancements in tr ansducer construction
impact direct radiator devices performance, but those devices are limited by efficiency and Helmholtz
resonator compression. The current trend of constantly increasing power handling is questionable.
Technologically advanced transducers with robust diaphragms, high linear excursion and EBP
factor (Efficiency Bandwidth Product, calculated by dividing the driver’s resonance frequency by its
electrical quality factor) allow horn loading with high compression ratio compared to historical horns,
providing increased efficiency and wider bandwidth. Significant compression combined with highdiaphragm excursion results in large pressure in the horn throat, which can potentially be a source of
non-linear distortion.

2. LOUDSPEAKER DEVICE
2.1 Transducer
The loudspeaker for horn prototype is 300 mm (12 inch). It features aluminum demodulating ring,rubber surround, 100 mm diameter voice coil of 28.9 mm winding height and 12 mm magnetic gap
depth resulting in 12.45 mm of rated Xmax value (maximum linear one-way excursion).
17272{t.nowak, andrzej.dobrucki, romuald.bolejko}@pwr.edu.pl2.2 Horn
The acoustical transformer was designed in “Hornresp” software, using driver’s measured
Thielle-Small parameters with “complex inductance model (2)”. The resulting design is characterized
by hybrid of exponential and hyperbolic expansion ratios with total horn length of 3.5 m; fundamental
frequency of 39.5 Hz; 25 l rear chamber with acoustical lining; 130 cm2 throat and 2500 cm2 mouth.
2.3 Throat chamber
The actual, measured maximum displacement was higher than rated in the loudspeaker’s datasheet,resulting in values presented in table 1. Significant changes in throat volume during loudspeaker
operation at high excursions result in high particle velocity, which increases the probability of
non-laminar airflow through the throat. The actual horn is rectangular in cross sections, a throat
adaptor made with gradually expanding elliptical elements of constant surface area of 130 cm2 wasfabricated. To minimize turbulent behavior of air, a circular chamber adaptor was introduced . The
resulting prototype is presented in Figure 1.
Table 1 – Throat chamber characteristics

Diaphragm
surface area,
cm2476

Hornthroat

Compression

surfaceratioarea, cm2130

Peak-to-peakVolumeCompression

diaphragm

displacedCompression

chamber

excursion,

bychambervolumecm

diaphragm,

volume, cm3change, %3086.040.1

3cm
3.66 : 12.3

1237.6

Figure 1 – Picture of a throat adaptor prototype
2.4 Rear chamber
The transducer is mounted in a sealed enclosure with net volume of 25 l, complimented withacoustical lining 3 cm thick and multiple access hatches. The shape, bracing and building materials areexactly the same as in actual horn loaded cabinet, for future measurement compa rison.

3. MEASUREMENTS
3.1 Electrical impedance measurement
The loudspeaker impedance-frequency characteristics were measured in three cases: no rearchamber (transducer mounted in a baffle); sealed enclosure (direct radiator); sealed enclosure withcompression chamber and throat adaptor (Figure 2). Resonance frequ encies have been measured

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(Table 2).
Table 2 – Resonance frequencies
Transducer mounted in a baffle,

Transducer in sealed

Transducer in sealed enclosure withHz

enclosure, Hz

throat adaptor, Hz

46.80

66.15

59.80

Figure 2 – Impedance measurement, transducer in sealed enclosure with throat adaptor
3.2 Diaphragm vibration measurement
The loudspeaker cone displacement measurement was made with scanning head andcomplementary data acquisition system. The laser was pointed at the center of loudspeaker dust cap,with a right angle. Signal source was the same as in acoustical measurements and consisted of:
personal computer with ‘REW’ software; external soundcard; professional power amplifier in bridgemode, providing 80 V RMS at 0 dBFS soundcard setting. Test signal was defined as 10 s long chirp in
range of 10 to 300 Hz at 0 dBFS.
Because this is a Doppler effect measurement, the results were acquired in form of diaphragmvelocity as a function of time. Discrete data integration allowed to calculate the dis placement. Thespectrum analysis provided maximum peak-to-peak excursion of 26 mm which is close to the value
provided by loudspeaker manufacturer (24.9 mm). The maximum value was recorded at frequency of59 Hz which correlates with measured resonance frequency from impedance plot.
4 m/s
3 m/s
2 m/s
1 m/s
0 m/s
-1 m/s

0s

1s

2s

3s

4s

5s

6s

7s

8s

-2 m/s-3 m/s-4 m/sFigure 3 –Diaphragm velocity in function of time, with throat chamber, 0dBFS

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9s

3.3 Acoustical measurements
All acoustical recordings were made in an anechoic chamber, signal source and type were the sameas described in laser vibrometry. Measurements were taken at different power levels set on thesoundcard, from -20 to 0 dBFS.
At first, calibrated sound pressure meter was placed in volumetric center of the throat adaptor, 6 cm
from the center of diaphragm. The measurements were taken with and without throat adaptor, withconstant microphone position. At full power (0dBFS) without throat adaptor the microphone wasclipping, recording over 140 dB above 70 Hz, introducing high levels of distortion. Addition of athroat chamber resulted in 20 dB of increased SPL in the whole measured frequency range. Thisindicates sound pressure level inside the throat adapter of over 160 dB, possibly 170+dB at full power
input. High pressure 3.175 mm (1/8 inch) microphone will be used in future mea surements.
Second, undistorted set of measurements was made with calibrated microphone placed at a constantdistance of 2 m from loudspeaker diaphragm. Session resulted in 42 data sets of sound pressure andharmonic levels, 21 for the loudspeaker without throat chamber (Figure 4), 21 with (Figure 5).

Figure 4 – Frequency response measurement dataset -20 to 0 dB in 1 dB increment, without throat adaptor

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Figure 5 – Frequency response measurement dataset -20 to 0 dB in 1 dB increment, with throat adaptor

4. DATA PROCESSING
4.1 Harmonic levels
Every measurement file contained harmonic distortion data in function of frequency. The distortion
analysis should be made for the highest registered loudspeaker cone displacement, at the resonancefrequency of transducer in sealed chamber with throat adaptor, which is 59 Hz. Fundamental and first
four harmonic levels at 59 Hz were exported from every measurement file for loudspeaker without
throat adaptor (Table 3) same procedure was done for measurements with compression chamber (Table4).
Table 3 – Harmonic levels without throat adaptor

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Input level,

Freq,

Fundamental level,

THD,

H2,

H3,

H4,

H5,

THD

dBFS

HzdBdB

dB

dBdB

dB

ratio, %

059

110.6

85.1

80.6

82.9

71.4

59.5

5.333%

-1

59

109.8

83.1

78.7

80.7

69.6

61.5

4.627%

-2

59

108.8

80.6

76.7

77.8

67.0

63.0

3.897%

-3

59

107.8

78.1

74.7

74.8

64.9

62.1

3.278%

-4

59

106.8

75.9

73.6

71.3

61.3

60.4

2.858%

-559

105.8

74.0

71.8

69.2

59.2

58.8

2.566%

Table 4 – Harmonic levels with throat adaptor
Input level,

Freq,

Fundamental level,

THD,

H2,

H3,

H4,

H5,

THD

dBFS

HzdBdB

dB

dBdB

dB

ratio, %059113.1

91.7

88.1

85.8

85.0

81.0

8.516%

-1

59

111.9

89.7

85.8

84.7

80.9

81.6

7.837%

-2

59

111.2

89.4

88.3

80.2

79.0

71.2

8.107%

-3

59

109.7

82.7

80.8

74.1

70.8

74.8

4.480%

-4

59

108.9

78.7

74.3

74.5

65.4

71.9

3.087%

-5

59

107.9

77.6

74.8

71.7

62.8

70.1

3.039%

4.2 Throat chamber distortion
To calculate the throat chamber distortion product, the energy level of each harmonic inmeasurement without throat adaptor (Table 3) was subtracted from corresponding harmonic levels inmeasurements with throat adaptor (Table 4) using simple formula:

H C  10 log10 (10 0.1H B  10 0.1H A ) ,(1)where:
H C - resulting harmonic level (throat chamber contribution)

H B - harmonic level of loudspeaker with throat adaptor
H A - harmonic level of loudspeaker without throat adaptor
Calculated harmonic levels of throat chamber contribution have been juxtaposed with fundamental
levels of measurements with throat adaptor (Table 5). The THD is energetic sum of those harmonics,
THD ratio is percentage energy content relative to fundamental levels.
Table 5 – Harmonic levels as a throat chamber contribution
Input level,

Freq,

Fundamental level,

THD,

H2,H3,H4,H5,

THD

dBFS

HzdB

dB

dB

dB

dB

dB

ratio, %

0

59

113.1

90.6

87.2

82.7

84.8

81.0

7.516%

-1

59

111.9

88.7

84.9

82.5

80.6

81.6

6.946%

-2

59

111.2

88.8

88.0

76.5

78.7

70.5

7.559%

-3

59

109.7

81.9

79.6

74.1

69.5

74.6

4.052%

-4

59

108.9

75.5

66.0

71.7

63.3

71.6

2.129%

-5

59

107.9

75.1

71.8

68.1

60.3

69.82.277%

The THD ratio as a function of the input level from Table 3, 4 and 5 have been plotted in Figures 6,7 and 8 respectively.

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8,0%
7,0%
6,0%
5,0%
4,0%
3,0%
2,0%-20 dBFS -18 dBFS -16 dBFS -14 dBFS -12 dBFS -10 dBFS -8 dBFS -6 dBFS -4 dBFS -2 dBFS1,0%0 dBFS

Figure 6 – THD ratio, measurement without throat adaptor

8,0%
7,0%
6,0%
5,0%
4,0%
3,0%
2,0%-20 dBFS -18 dBFS -16 dBFS -14 dBFS -12 dBFS -10 dBFS -8 dBFS -6 dBFS -4 dBFS -2 dBFS

Figure 7 – THD ratio, measurement with throat adaptor

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1,0%0 dBFS

8,0%
7,0%
6,0%
5,0%
4,0%
3,0%
2,0%-20 dBFS -18 dBFS -16 dBFS -14 dBFS -12 dBFS -10 dBFS -8 dBFS -6 dBFS -4 dBFS -2 dBFS1,0%0 dBFS

Figure 8 – THD ratio, calculated throat chamber harmonic distortion contribution relative to measured
fundamental level with throat adaptor

5. CONCLUSIONSThe use of a compression chamber results in predicted increase of harmonic distortion, thecontribution is increasing with pressure level, especially after reaching certain pressure value in thethroat. Comprehensive measurements of pressure levels inside the throat adaptor are being planned,utilizing 3.175 mm (1/8 inch) microphone designed for high SPL. This research will hopefully help
determine the pressure limit value. This number could be a base for theoretical model evaluation andcalibration.
The variation of pressure in function of frequency for a few highest power input measurements(Figure 5) indicate possible turbulences, however those variations were not observed when themicrophone was placed inside the throat adaptor. This is probably a result of sudden pressure drop
outside the adaptor, measurements with full size horn are scheduled. The application of an acoustic
transformer will solve the turbulence problem and will have a significant impact on pressure inside thethroat adaptor as well as diaphragm displacement.

REFERENCES
1. Dobrucki A. Electroacoustic transducers (in Polish: Przetworniki elektroakustyczne), WNT, Warsaw,Poland, 2007.
2. Marshall Leach W. Loudspeaker Voice-Coil Inductance Losses: Circuit Models, Parameter Estimation,and Effect on Frequency Response. School of Electrical and Computer Engineering Atlanta, Georgia
USA: JOURNAL OF THE AUDIO ENGINEERING SOCIETY, VOL. 50, NO. 6, 2002.
3. Thorborg K. Measurement of the Advanced Loudspeaker Parameters using Curve-Fitting
Method. Joint Baltic-Nordic Acoustics Meeting, Odense, Denmark, 2012.
4. Klippel GmbH, Extended Creep Modeling, Application Note for the KLIPPEL R&D SYSTEM (AN49),
Dresden, Germany, 2013.

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