The Decibel Done Right: A Matter of Engineering the Math

The dB is an important and widely used concept in relation to antennas, propagation, and other areas. However, its usual definitions contain idiosyncrasies that hamper clear understanding and symbolic calculation, thereby reducing general applicability to far below its potential. A novel perspective replaces the common view - namely, the dB as a unit, the logarithm, and ratios - by the dB as a function, the exponential, and numbers. This yields a pithy algebraic definition placing the dB among the elementary functions. Diverse examples show the advantages for calculation and widened applicability. Combination with units and scales as functions allows assigning meaning to ¿atomic¿ affixes like dBm by function composition such that, for instance, 30 dBm = 30 dBmW = (((30 d) B) m) W = 1 W. Unlike the usual definitions, this also enables dimensional analysis, which is crucial in physics and engineering. The approach is presented in the wider context of the principle that tools used by engineers should themselves be engineered for effectiveness, and mathematical tools are no exception. This is important for practice as well as for education.