dBdecade

dB per decade, or dB/decade, is a unit used to describe how a quantity, typically the magnitude of a transfer function, changes with frequency on a logarithmic scale. It expresses the slope of the magnitude response in decibels per tenfold increase in frequency. In practice, when frequency is multiplied by 10, the magnitude in dB changes by the stated amount.

The magnitude of a transfer function is often given in decibels as 20 log10|H(jω)| for voltage ratios (10 log10 for power). A slope of -20 dB/decade means that increasing the frequency by a factor of 10 reduces the magnitude by 20 dB. Each pole in a system contributes about -20 dB/decade to the slope beyond its break frequency, while each zero contributes +20 dB/decade. Therefore, a single-pole low-pass network has approximately -20 dB/decade slope above its corner frequency; two poles yield -40 dB/decade, and so on.

In Bode plots, the dB/decade slope is part of the asymptotic, piecewise-linear description of the magnitude response. Real networks approximate these slopes, with deviations near break frequencies where the slope changes due to poles and zeros.

Caveats include the definition of a decade (a factor of 10 in frequency) and the distinction between voltage and power decibels. The concept is widely used in electronics, RF engineering, and control systems to assess bandwidth, filter behavior, and stability margins.