It is often desired that a transducer have a polar radiation pattern that is invariant with frequency, but there is currently no way of quantifying the extent to which a transducer possesses this quality (often called “constant directivity” or “controlled directivity”). To address the problem, commonly-accepted criteria are used to propose two definitions of constant directivity. The first, stricter definition, is that the polar radiation pattern of a transducer should be invariant over a specified frequency range, whereas the second definition is that the directivity factor (i.e., the ratio between the on-axis power spectrum and the average power spectrum over all directions), or index when expressed in dB, should be invariant with frequency. Furthermore, to quantify each criterion, five metrics are derived: (1) Fourier analysis of contour lines (i.e., lines of constant sensitivity over frequency and angle), (2) directional average of frequency response distortions, (3) distortion thresholding of polar responses, (4) standard deviation of directivity index, and (5) cross-correlation of polar responses. Measured polar radiation data for four loudspeakers are used to compute all five metrics that are then evaluated based on their ability to quantify constant directivity. Results show that all five metrics are able to quantify constant directivity according to the criterion on which each is based, while only two of them, metrics 4 and 5, are able to adequately quantify both proposed definitions of constant directivity.
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