The Functional Nature of Units, With Application to the Decibel in Propagation Calculations [Education Corner

Abstract

The decibel is widely used in signal propagation. Yet, as commonly presented, it does not behave like normal units in formulas, calculations, or dimensional analysis, which hampers understanding and practical use. All issues are resolved by defining the decibel as just an elementary function in calculus, called the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">direct</i> decibel, which reflects actual practice and is the simplest for a first introduction. Since students will certainly meet other variants, it is crucial they understand the wider picture and all definitional choices. Recognizing that units and scales are functions yields a unifying framework that explains the common conventions and eliminates unwanted effects. The standard decibel and the concept of level are explained rigorously and issues with the (in)famous “20 lg” rule are resolved. The use of the direct decibel in calculations is illustrated in examples from engineering in general, for propagation in cables and free space, noise, and satellite link budgets.