Re: Why Bessel?

Don Lancaster wrote:
Roger Bourne wrote:
Hello all,

I recently was going over an old electronic design, and I noticed
that the designer used a 4rth order Bessel low pass filter where low
pass filtering was needed. (I know it was a Bessel filter because it
so marked ;) ). The bessel filter was realized with 2 op-amps and
many resistors and a few capacitors. Knowing the designer
(designer is overseas now for a few years...) was always making his
designs as compact as possible, - (had to twist both of to his arms
to make him insert failsafe redundancies :) ) - why would he use
such a bulky method for low pass filtering?
The bessel low pass filter cuttoff frequency is ~100Hz. It's
sharpness would have to be, hmmm, well pretty sharp. After all it
was initially intended for a medical application. I would hazard a
guess that is what warrants the 4rth order. But why a Bessel
topology? I know bessel filters are usefull in audio applications
because of the linear phase property they have, but this is not an
audio application. Basically, I am asking why Bessel ? Does Bessel
have anything special that I am anaware of?

-Roger

A Bessel filter offers the lowest possible time delay and group delay
distortion.

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.

Its falloff rate is an utter atrocity.

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.
431infoEXTRACT@xxxxxxxxxxxxx
http://www.anasoft.co.uk
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