How To Calculate Gain From Low Filters

Calculating gain from low filters is crucial in audio engineering to ensure optimal sound quality and prevent distortion. This calculator simplifies the process, helping you make informed decisions in your audio projects.

1. Enter the frequency in Hertz (Hz).
2. Enter the desired gain in decibels (dB).
3. Select the filter order.
4. Click ‘Calculate’.

The formula to calculate gain from a low filter is:

Gain = 20 * log10((1 + (Q * (2^(-order * (f / f0)) – 1)) / (1 + (2^(-order * (f / f0))))))

Where:

• Gain is the desired gain in dB.
• f is the frequency in Hz.
• f0 is the cutoff frequency in Hz (usually the same as ‘f’).
• Q is the quality factor (usually 0.707 for a Butterworth filter).
• order is the filter order.

Comparison of Gain from Low Filters with Different Orders

Frequency (Hz)	Gain (dB)	Order 1	Order 2	Order 3

• Always start with a lower filter order to avoid excessive phase shift.
• Consider using a higher order filter for steeper roll-offs, but be aware of increased phase shift.
• Experiment with different Q values for different filter responses.

What is the difference between a low-pass and a high-pass filter?

A low-pass filter allows low frequencies to pass while attenuating (reducing the amplitude of) high frequencies. A high-pass filter does the opposite.

For more information, see these authoritative sources:

IEEE Spectrum

University of Edinburgh