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 = l. 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 l/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 l, 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.
Figure 3-6. Directional characteristics of a circular-piston source mounted in an infinite baffle as a function of diameter and
l.
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