Octave (electronics) explained

In electronics, an octave (symbol: oct) is a logarithmic unit for ratios between frequencies, with one octave corresponding to a doubling of frequency. For example, the frequency one octave above 40 Hz is 80 Hz. The term is derived from the Western musical scale where an octave is a doubling in frequency. Specification in terms of octaves is therefore common in audio electronics.

Along with the decade, it is a unit used to describe frequency bands or frequency ratios.^{[1] [2]}

Ratios and slopes

A frequency ratio expressed in octaves is the base-2 logarithm (binary logarithm) of the ratio:

numberofoctaves = log _{2 \left( (f _{2})/(f _{1})} \right)

An amplifier or filter may be stated to have a frequency response of ±6 dB per octave over a particular frequency range, which signifies that the power gain changes by ±6 decibels (a factor of 4 in power), when the frequency changes by a factor of 2. This slope, or more precisely 10 log₁₀(4) ≈ 6 decibels per octave, corresponds to an amplitude gain proportional to frequency, which is equivalent to ±20 dB per decade (factor of 10 amplitude gain change for a factor of 10 frequency change). This would be a first-order filter.

Example

The distance between the frequencies 20 Hz and 40 Hz is 1 octave. An amplitude of 52 dB at 4 kHz decreases as frequency increases at -2 dB/oct. What is the amplitude at 13 kHz?

numberofoctaves = log _{2 \left( (13)/(4)} \right) = 1 . 7 Mag _{13kHz} = 52 dB + ( 1 . 7 oct x -2 dB/oct ) = 48 . 6 dB .

See also

• Octave
• Octave band
• One-third octave

Notes and References

1. Levine, William S. (2010). The Control Handbook: Control System Fundamentals, p. 9–29. /.
2. Perdikaris, G. (1991). Computer Controlled Systems: Theory and Applications, p. 117. .