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La dB Per Octave Calculator helps users determine the rate of gain or atenuación over frequency changes in audio engineering, electronics, and signal processing.
An octave represents a doubling (or halving) of frequency, so this calculator is useful for:
- Ecualización de audio – Adjusting speaker and filter responses
- Loudspeaker design – Understanding high-frequency roll-off
- Filter slopes – Measuring attenuation in low-pass and high-pass filters
- Room acoustics and sound analysis – Evaluating how frequencies change across different environments
By using this tool, audio engineers, sound designers, and RF technicians can optimize frequency response and improve system performance.
Formula for Db Per Octave Calculator
La fórmula para calcular dB per octave :
Formula general
dB per Octave = (dB Change) / (log2(Freq2 / Freq1))
Lugar:
- dB Change = Gain or loss in decibels between two frequencies
- Freq1, Freq2 = The two frequencies where medidas fueron tomadas
- log2 = Base-2 logarithm (since an octave represents a doubling of frequency)
Simplified Formula (for 1-Octave Differences)
Desde un octave means the frequency doubles (Freq2 = 2 × Freq1), la ecuación se simplifica a:
dB per Octave = dB Change / Number of Octaves
This means if a system experiences -6 dB attenuation sobre una octava, su slope is -6 dB per octave.
Reference Table – Common dB Per Octave Slopes
To make frequency response estimation easier, here is a tabla de referencia de común filter slopes and signal attenuation rates:
| Tipo de filtro | dB per Octave | Solicitud |
|---|---|---|
| First-Order Filter | -6 dB/octave | Simple tone control, basic crossover design |
| Second-Order Filter | -12 dB/octave | Active crossovers, equalization circuits |
| Third-Order Filter | -18 dB/octave | Steeper filtering for precise frequency control |
| Fourth-Order Filter | -24 dB/octave | High-precision filtering in audio and RF circuits |
| Atenuación acústica | -3 dB/octave | Air absorption of high-frequency sounds |
Esta tabla ayuda audio professionals and engineers entiendes how signals change per octave and how steep a filter or system response will be.
Example of Db Per Octave Calculator
1. Calculate dB Per Octave for a Sound System
A speaker system has a -12 dB loss entre 500 Hz y 2000 Hz.
- Find the number of octaves:
Octaves = log2(2000 / 500)
Octaves = log2(4) = 2 octavas - Aplicar la fórmula:
dB per Octave = (-12 dB) / (2 octaves)
dB per Octave = -6 dB por octava
This means the system attenuates by 6 dB for every frequency doubling.
2. Calculate dB Per Octave for a High-Pass Filter
A low-frequency signal cae por -18 DB entre 250 Hz y 1000 Hz.
- Find the number of octaves:
Octaves = log2(1000 / 250)
Octaves = log2(4) = 2 octavas - Aplicar la fórmula:
dB per Octave = (-18 dB) / (2 octaves)
dB per Octave = -9 dB por octava
This suggests the filter roll-off is steeper than a second-order filter (-12 dB/octave), making it closer to a third-order filter (-18 dB/octave).
Preguntas frecuentes más comunes
dB per octave measures how fast a signal’s amplitude changes as frequency ¡se duplica. La higher negative dB per octave significa un steeper attenuation (signal loss).
A -6 dB per octave slope se usa comúnmente en simple filters and crossovers porque proporciona una smooth transition between frequency ranges.