Bessel Filter Group Delay Calculator

How it is calculated

The tool uses a one-line approximation for the delay near DC: τ = 1 ÷ (2π × fc), where fc is the cutoff frequency in hertz and τ is in seconds. It is shown in scientific notation (seconds) and in milliseconds, τ(ms) = τ × 1000. The cutoff must be above zero. Notice that the order field has no effect: the formula does not use it, so changing the order from 2 to 8 gives exactly the same delay. A real Bessel filter's delay depends on its order and on how the cutoff is defined (for example the -3 dB point), so treat the result as a rough estimate of the order of magnitude, useful for comparing cutoffs, not a design value. Doubling fc halves the delay.

Common mistakes

• Expecting the filter order to change the answer. The order box is informational here, so a 2nd-order and an 8th-order filter show the same delay; do not use the figure to compare orders.
• Entering the cutoff in kHz. The field is in hertz, so 2 kHz must be typed as 2000, otherwise the delay is 1000 times too long.
• Reading the result as the delay at every frequency. It is the low-frequency (near DC) value; for a real Bessel filter the delay is nearly flat in the passband but falls off toward and beyond the cutoff.
• Treating it as the total latency of a circuit. Amplifiers, sampling, buffering and other stages add their own delays that this calculation does not include.
• Confusing group delay in seconds with a phase shift in degrees. The delay is a time; the phase at a given frequency is a different quantity.