# 3D3A Publication

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## Metrics for Constant Directivity

**Authors:** Sridhar, R., Tylka, J. G., Choueiri, E. Y.

**Publication:** 140th Convention of the Audio Engineering Society (AES 140)

**Date:** May 26, 2016

Many transducer manufacturers claim to achieve "constant directivity" (also called "controlled directivity"), but there is currently no way of quantifying the extent to which a transducer possesses this quality. To address this problem, commonly-accepted criteria are used to propose two definitions, one more strict and one more lenient, of constant directivity: 1) that the polar radiation pattern of a transducer must be invariant over a specified frequency range, or 2) that the *directivity index* (see this report for more information), must be invariant with frequency. Furthermore, to quantify each criterion, five metrics are derived and computed using measured polar radiation data for four loudspeakers. The loudspeakers are then ranked, from most constant-directive to least, according to each metric, and the rankings are used to evaluate each metric's 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 and two of them are able to adequately quantify both proposed definitions of constant directivity.

## Errata:

- On page 4, Eq. (1) should read: $$\tag{1}\epsilon = 100 \times \frac{\displaystyle \sum_{u = 0}^{U - 1} \left| y_{u,0} \right|^2}{\displaystyle \sum_{u = 0}^{U - 1} \sum_{v = 0}^{V - 1} \left| y_{u,v} \right|^2}.$$