Loudspeaker Directivity: An Ongoing Experimental Survey
This work is sponsored by the Sony Corporation of America
Loudspeaker directivity is the extent to which loudspeakers focus the sound in a particular direction (typically towards the listener) instead of broadcasting it in all directions around the room. Highly directive loudspeakers are ideal for 3D audio with crosstalk cancellation (XTC), since room reflections (which are weaker when using more directive loudspeakers) directly degrade the level of XTC. Consequently, the 3D3A Lab is conducting detailed measurements of the directivity of various loudspeakers using the lab's anechoic chamber. This study on loudspeaker directivity is also important for our ongoing Sony-sponsored research on head-externalization of 3D sound through headphones, since some of the relevant techniques rely on emulating the radiation characteristics of real loudspeakers.
Directivity Index Spectra
A directivity index (DI) spectrum quantifies the directivity of a loudspeaker as a function of frequency. For a given frequency, a higher DI value indicates a more directive loudspeaker. For each loudspeaker in this survey, frequency responses measured at discrete points along two orbits (horizontal and vertical) around the loudspeaker are used to compute six DI spectra. These spectra describe the directivity of the loudspeaker within different regions of space, and are defined as:
- Full-sphere DI spectrum: the difference (in dB) between the 0°, on-axis frequency response and the average frequency response over all directions along both orbits.
- Frontal hemisphere DI spectrum: the difference (in dB) between the 0°, on-axis frequency response and the average frequency response over all directions on the frontal hemisphere.
- Horizontal DI spectrum: the difference (in dB) between the 0°, on-axis frequency response and the average frequency response over all directions along the horizontal orbit.
- Frontal horizontal DI spectrum: the difference (in dB) between the 0°, on-axis frequency response and the average frequency response over all directions along the front half of the horizontal (vertical) orbit.
- Vertical DI spectrum: the same as 3, but along the vertical orbit.
- Frontal vertical DI spectrum: the same as 4, but along the vertical orbit.
Average values of these spectra (henceforth referred to as "average DI values") are used to directly compare the directivities of different loudspeakers. This report more precisely defines all of the DI spectra listed above and provides a detailed description of how the average DI values are computed.
For many loudspeakers in this survey, directivity measurements were made along the entire horizontal and vertical orbits. For such loudspeakers, all six DI spectra have been computed. For certain loudspeakers, however, measurements along the vertical orbit were not possible due to physical constraints. For these cases, only the horizontal and frontal horizontal DI spectra have been computed. Additionally, some of the first measurements of loudspeaker directivity were only made on the frontal hemisphere. For such cases, only the frontal hemisphere, frontal horizontal, and frontal vertical DI spectra have been computed.
Table of Measured Loudspeakers
All of the loudspeakers measured for this survey are listed in the table below and ranked according to their directivities. The table consists of three columns: Rank, Loudspeaker Name, and Frontal Horizontal Directivity. The values in the Rank column are obtained by considering every computed average DI value for each loudspeaker, a spreadsheet of which can be found here. The Loudspeaker Name column lists the manufacturer and model of the loudspeaker. The Frontal Horizontal Directivity column contains a contour plot depicting the frontal horizontal directivity for each loudspeaker along with the corresponding average frontal horizontal DI value. This column is included in the table to provide an "at-a-glance" impression of each loudspeaker's overall directivity.
The frontal horizontal directivity contour plots can be used to visually compare the directivities of different loudspeakers. Shown below are three contour plots arranged from left to right in order of decreasing directivity. Each contour plot depicts the departure from the on-axis (0°, straight-ahead) frequency response of the loudspeaker as a function of azimuthal angle; regions of red indicate very similar output levels to the on-axis response, whereas regions of violet indicate a significant decrease in output level. Therefore, a plot with a narrow region of red surrounded mostly by violet typically denotes a loudspeaker with high directivity, whereas wider regions of red (or, alternatively, plots consisting of mostly non-violet regions) denote less directive loudspeakers.
Interacting with the table
Clicking on any of the column headers sorts the table (in either ascending or descending order, as indicated by the arrows) according to the respective column, and clicking again reverses the order. For example, clicking on Frontal Horizontal Directivity sorts the table by the loudspeakers' average frontal horizontal DI values, and clicking on Loudspeaker Name sorts the table alphabetically. Clicking on a loudspeaker name or on the corresponding contour plot thumbnail navigates to more detailed information on the directivity of that loudspeaker.
Note: Since the loudspeakers have been ranked using all available average DI values, the rank assigned to a given loudspeaker may not correspond with its average frontal horizontal DI value. Therefore, even a loudspeaker with a relatively high average frontal horizontal DI value may be ranked worse than another with a lower average value.
Click here to download a .zip file containing all directivity plots. (Last updated December 16th, 2014)
Click here to download a .csv file containing the tabulated average DI values for all measured loudspeakers. (Last updated January 7th, 2015)
All directivity measurements are carried out in the anechoic chamber of the 3D3A Lab using a B&K Microphone Type 4189. The loudspeaker is placed on a rotation stage in the chamber and rotated in increments of 5°. At each orientation, the loudspeaker's impulse response is measured with, unless otherwise noted, an exponential sine sweep at a sampling rate of 96 kHz. To align the microphone, the loudspeaker is placed at 0° (facing straight ahead) and the microphone is positioned such that the barrel of the microphone points straight at the center of the loudspeaker cabinet (or some other logical alignment point). Due to the physical limitations of the anechoic chamber, a time-window is applied to each measured impulse response to remove any reflected sound. The measured data are processed and plotted using custom software developed in-house at the 3D3A Lab.
If you know of any loudspeakers that may have particularly high directivity, please inform the 3D3A Lab. We will try to acquire these loudspeakers and measure their directivity.
J. G. Tylka. On the Calculation of Full and Partial Directivity Indices. Technical report, 3D Audio and Applied Acoustics Laboratory, Princeton University, November 2014. (pdf)