Octave (electronics)

In electronics, an octave is a doubling or halving of a frequency. The term is derived from the musical octave which similarly describes such frequency ratios, but the prefix octa-, denoting eight, has no significance in physics. A frequency ratio expressed in octaves is the base-2 logarithm (binary logarithm) of the ratio.

An amplifier or filter may be stated to have a frequency response of ±6dB per octave over a particular frequency range, which signifies that the power gain changes by ±6 decibels (a factor of four in power), when the frequency changes by a factor of 2. This slope, or more precisely $10\log_{10}(4) \approx 6.0206$ decibels per octave, corresponds to a gain proportional to frequency, which is equivalent to ±20dB per decade (factor of 10 gain change for a factor of 10 frequency change).

Example

1. The distance between the frequencies 20 Hz and 40 Hz is 1 octave.

2. A magnitude of 400 (52 dB) at 4 kHz decreases as frequency increases at −2 dB/octave. What is the magnitude at 13 kHz?

$\text{number of octaves} = \log_2\left(\frac{13}{4}\right) = 1.7$

$\text{Mag}_{13\text{ kHz}} = 52\text{ dB} + (1.7\text{ octaves} \times -2\text{ dB/octave}) = 48.6\text{ dB} = 269.\,$

References