User Guide

Sound System Design Reference Manual
The values of DI and Q given in Figure 3-6 are
the on-axis values, that is, along the axis of
maximum loudspeaker sensitivity. This is almost
always the case for published values of Dl and Q.
However, values of Dl and Q exist along any axis of
the radiator, and they can be determined by
inspection of the polar plot. For example, in Figure
3-6, examine the polar plot corresponding to
Diameter = λ. Here, the on-axis Dl is 10 dB. If we
simply move off-axis to a point where the response
has dropped 10 dB, then the Dl along that direction
will be 10 - 10, or 0 dB, and the Q will be unity. The
off-axis angle where the response is 10 dB down is
marked on the plot and is at about 55°. Normally, we
will not be concerned with values of Dl and Q along
axes other than the principal one; however, there are
certain calculations involving interaction of
microphones and loudspeakers where a knowledge
of off-axis directivity is essential.
Omnidirectional microphones with circular
diaphragms respond to on- and off-axis signals in a
manner similar to the data shown in Figure 3-6. Let
us assume that a given microphone has a diaphragm
about 25 mm (1”) in diameter. The frequency
corresponding to λ/4 is about 3500 Hz, and the
response will be quite smooth both on and off axis.
However, by the time we reach 13 or 14 kHz, the
diameter of the diaphragm is about equal to λ, and
the Dl of the microphone is about 10 dB. That is, it
will be 10 dB more sensitive to sounds arriving on
axis than to sounds which are randomly incident to
the microphone.
Of course, a piston is a very simple radiator —
or receiver. Horns such as JBL’s Bi-Radial series are
complex by comparison, and they have been
designed to maintain constant HF coverage through
attention to wave-guide principles in their design.
One thing is certain: no radiator can exhibit much
pattern control at frequencies whose wavelengths
are much larger than the circumference of the
radiating surface.
3-5
Figure 3-6. Directional characteristics of a circular-piston source
mounted in an infinite baffle as a function of diameter and λ.