Calculate Back Loaded Exponential Horn

The KleinHorn Part 1 and Part 2 by Nelson Pass

A horn is an acoustic transformer, changing high pressure and low volume at the throat to low pressure and high volume at the mouth. It does so by slowly expanding the cross section of the tube down which the sound wave travels, and it creates an acoustic load for the driver as if it had a very large diaphragm, dramatically raising its efficiency.

A horn loudspeaker is characterized by several numbers; the area of the small end known as the throat, the wide end known as the mouth, the distance from the throat traveling down the length of the horn toward the mouth, and the expansion curve of the cross section of the horn as you travel that distance. In an exponential horn, this expansion is given by the initial throat area multiplied by the natural logarithm e raised by a power factor related to the distance down the horn and the lowest frequency we want to work at.

The exponential horn has an acoustic loading property that allows the speaker driver to remain evenly balanced in output level over its frequency range.
The benefits of the design were first published by C.R. Hanna and J. Slepian in 1924 for the American Institute of Electrical Engineers (AIEE).

A major drawback is that the exponential horn allows for a narrowing of the radiation pattern as frequency increases, making for high frequency 'beaming' on axis and dull sound off axis.

Another concern is that a throat of small diameter is needed for high efficiency at high frequencies but a larger throat is best for low frequencies. A common solution is to use two or more horns, each with the appropriate throat size, mouth size and flare rate for best performance in a selected frequency range, with sufficient overlap between the frequency ranges to provide a smooth transition between horns. Another solution tried in the late 1930s by Harry F. Olson of RCA was to use multiple exponential flare rates, either by connecting increasingly larger horns in series or by subdividing the interior of a single horn.

Lower Cut-Off frequency: 15-8000 Hz: Hz
Throat diameter 2-40 cm: cm
Steps 6-100: Steps
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Download: Design of a Back Loaded Exponential Horn written by Martin J. King, 04/10/07 PDF, 466kB

Horn Loudspeaker Design Part 1, PDF, 881KB

Horn Loudspeaker Design Part 2, PDF, 1426KB

Horn Loudspeaker Design Part 3, PDF, 971KB

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