Why Bessel?

Question

Hello all,I recently was going over an old  electronic design, and I noticed thatthe designer used a 4rth order Bessel low pass filter where low passfiltering was needed. (I know it was a Bessel filter because it somarked ;) ). The bessel filter was realized with 2 op-amps and manyresistors and   a few capacitors. Knowing the designer (designer isoverseas now for a few years...)  was always making his designs ascompact as possible, - (had to twist both of to his arms to make himinsert failsafe redundancies :) ) - why would he use such a bulkymethod for low pass filtering?The bessel low pass filter cuttoff frequency is ~100Hz. It's sharpnesswould have to be, hmmm, well pretty sharp. After all it was initiallyintended for a medical application. I would hazard a guess that is whatwarrants the 4rth order. But why a Bessel topology? I know besselfilters are usefull in audio applications because of the linear phaseproperty they have, but this is not an audio application.Basically, I am asking why Bessel ? Does Bessel have anything specialthat I am anaware of?-Roger

John Popelish · Accepted Answer

Bessel filters don't ring when a step is applied to their inputs. Would that mean anything to this design?

Don Lancaster · Answer

A Bessel filter offers the lowest possible time delay and group delay distortion. Its falloff rate is an utter atrocity.See my Active Filter Cookbook.-- Many thanks,Don Lancaster                          voice phone: (928)428-4073Synergetics   3860 West First Street   Box 809 Thatcher, AZ 85552rss:    email: Please visit my GURU's LAIR web site at

Kevin Aylward · Answer

Err.. no it doesn't. Your statement is actually a bit vague.

The Bessel filter is a filter invented to produce a linear phase with frequency (or constant delay) that actually has an *explicit* mathematical method available to calculate its element values. This is a key, fundamental point for all of the standard filters. The ability to actually be able to mathematically calculate component values of a filter of arbitrary order with some explicit procedure.

If one uses other computer techniques, not available when "modern filter theory" was being invented, such as brute force least squares fitting it is strait forward to design filters with better performance then pretty much any of the standards such as chebychev, Butterworth, Bessel etc.

For example, the Q=2/pi 2nd order is a "better" least mean squares fit to a linear phase response, i.e. better than the Bessel filter of 2nd order.

Since it wasn't designed to be a frequency filter this is not surprising. The fact that it rolls off at all is incidental to its initial invention.

Kevin Aylward B.Sc. snipped-for-privacy@anasoft.co.uk

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Adrian Tuddenham · Answer

[...]Could you tell us who invented it - and a bit more about the designprocess they went through if they didn't intend it to be a 'frequencyfilter'?-- ~ Adrian Tuddenham ~(Remove the ".invalid"s and add "" to reply)

Roger Bourne · Answer

How bad is the rolloff (falloff) rate?We are talking about bessel low passes, rigth? Wouldn't it have to havea decent rolloff (falloff) rate to be used as a low-pass ?I assume that the rolloff rate would be ALSO among the parameters thatmake or break a filter. Having linear phase is a great property, but itwould also need to attenuate. Rigth?-Roger   -Roger

Why Bessel?

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