User Guide

Sound System Design Reference Manual
The data of Figure 3-1 was generalized by
Molloy (7) and is shown in Figure 3-3. Here, note that
Dl and Q are related to the solid angular coverage of
a hypothetical sound radiator whose horizontal and
vertical coverage angles are specified. Such ideal
sound radiators do not exist, but it is surprising how
closely these equations agree with measured Dl and
Q of HF horns that exhibit fairly steep cut-off outside
their normal coverage angles.
As an example of this, a JBL model 2360
Bi-Radial horn has a nominal 90
0
-by-40
0
pattern
measured between the 6 dB down points in each
plane. If we insert the values of 90° and 40° into
Molloy’s equation, we get DI = 11 and Q = 12.8. The
published values were calculated by integrating
response over 360° in both horizontal and vertical
planes, and they are Dl = 10.8 and Q = 12.3. So the
estimates are in excellent agreement with the
measurements.
For the JBL model 2366 horn, with its nominal
6 dB down coverage angles of 40° and 20°, Molloy’s
equation gives Dl = 17.2 and Q = 53. The published
values are Dl = 16.5 and Q = 46. Again, the
agreement is excellent.
Is there always such good correlation between
the 6 dB down horizontal and vertical beamwidth of a
horn and its calculated directivity? The answer is no .
Only when the response cut-off is sharp beyond the
6 dB beamwidth limits and when there is minimal
radiation outside rated beamwidth will the correlation
be good. For many types of radiators, especially those
operating at wavelengths large compared with their
physical dimensions, Molloy’s equation will not hold.
A Comparison of Polar Plots, Beamwidth
Plots, Directivity Plots, and Isobars
There is no one method of presenting
directional data on radiators which is complete in all
regards. Polar plots (Figure 3-4A) are normally
presented in only the horizontal and vertical planes.
A single polar plot covers only a single frequency, or
frequency band, and a complete set of polar plots
takes up considerable space. Polars are, however,
the only method of presentation giving a clear picture
of a radiator’s response outside its normal operating
beamwidth. Beamwidth plots of the 6 dB down
coverage angles (Figure 3-4B) are very common
because considerable information is contained in a
single plot. By itself, a plot of Dl or Q conveys
information only about the on-axis performance of a
radiator (Figure 3-4C). Taken together, horizontal and
vertical beamwidth plots and Dl or Q plots convey
sufficient information for most sound reinforcement
design requirements.
3-3
Figure 3-4. Methods of presenting directional information