Octaves in Bode Plot
In a Bode plot, an octave is a frequency interval where the frequency changes by a factor of 2.
Octave = f₂ / f₁ = 2
Examples of Octaves
- 100 Hz → 200 Hz = 1 octave
- 1 kHz → 2 kHz = 1 octave
- 2 kHz → 4 kHz = 1 octave
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Bode plots use a logarithmic frequency scale. Frequency changes are commonly measured in:
- Octaves → factor of 2
- Decades → factor of 10
Since:
10 = 23.322
one decade is approximately:
1 decade = 3.322 octaves
Gain Change per Octave
In Bode plots, slopes may be expressed in:
- dB/octave
- dB/decade
Example: A first-order low-pass filter has slope:
-20 dB/decade
Converting to dB/octave:
-20 / 3.322 ≈ -6 dB/octave
Therefore, every doubling of frequency reduces gain by approximately 6 dB.
Common Slopes
| Slope (dB/decade) | Slope (dB/octave) |
|---|---|
| -20 dB/decade | -6 dB/octave |
| -40 dB/decade | -12 dB/octave |
| -60 dB/decade | -18 dB/octave |
Conclusion: An octave in a Bode plot means the frequency doubles.