Message-ID: <23462.200006051241@gemini>
From: "James Moritz" <j.r.moritz@herts.ac.uk>
Organization: University of Hertfordshire
To: rsgb_lf_group@blacksheep.org
Date: Mon, 5 Jun 2000 13:48:45 +0000
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Subject: Re: LF: Bessel bandpass filter?
In-reply-to: <393881DE.3D9D@xtra.co.nz>
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Dear LF Group,

ZL2CA wrote: 
> But the intended thrust of this email is to ask about if anyone can find a
> reference to a BESSEL BANDPASS filter.  Text books all say that the Bessel
> low pass filter has the most linear phase response (best group delay) of
> the basic range of filters (Butterworth, Chebyshev, elliptic, Bessel). 
> But I can not find any reference to a BANDPASS variant of the Bessel
> filter.  I have a feeling that it is not realisable mathematically, and
> that is why it is obvious by its absence as a text book band pass filter,
> but if there is a filter theory guru on the reflector I would dearly like
> to hear a response.

Not sure if I could be called a 'filter guru', but I have a fair bit of 
experience designing filters. It is a huge area, and difficult to 
scratch the surface, but here are some useful bits of info:

You won't find tables of Bessel or other bandpass filter values very 
often - this is because the standard filter design procedure starts 
with a normalised low pass design (ie. designed for 1ohm source & 
load, 1rad/s cut off frequency) and transforms it into whatever low- 
high-, bandpass, or bandstop filter you desire. So the Bessel low 
pass tables are where you need to start to design a Bessel 
bandpass filter. For passive LC filters, these are usually given as a 
table of L and C values, but active filter designs usually start from 
the tables of pole locations (these effectively specify the cut off 
frequency and Q of each section of the filter).

The reason for doing this is that the possible permutations of 
bandwidths and centre frequencies are more or less infinite, so 
tabulating all the values would be impossible.

An alternative is the 'coupled resonator' approach, which is 
normally reserved for passive bandpass filters with bandwidths 
less than 5 or 10% of the centre frequency. This uses tables of k 
and q values for different types of filter response.

As to how to do it, the A.B. Williams / F.J. Taylor 'Electronic filter design 
handbook' is excellent for passive LC and active designs, and includes 
many worked examples and formulas for different types of circuit suitable 
for different applications. Later editions have a section on digital filters too. 
The bible for passive designs including crystal filters is A.I. Zverev's 
'Handbook of filter synthesis'. These are the two references I have used most, 
but there are others too.

As to different types of filter response, there is always 
compromise. Filters with sharp cut-off always have poor transient 
response, those with good transient response have lousy skirt 
selectivity. So Chebyshev and eliptic filters have lots of ringing and 
overshoot, but good selectivity, while Bessel, Gaussian, linear 
phase etc. have little ringing and overshoot, but poor selectivity. 
Increasing the number of poles (in a bandpass filter the number of 
resonators) will improve the selectivity / transient response trade-
off, but require higher Q for each element, and greater precision in 
component values, and have higher insertion losses.

There are also many compromise filter responses, which have both 
reasonable transient response and selectivity. These include the 
Butterworth, and various 'transitional' responses. I have had good 
results with 100 and 250Hz, 5 pole CW filters using a 'transitional 
Gaussian to -6dB' response; this has a rounded response like a 
Bessel filter until it falls of by 6dB, when the skirts get steeper like 
a Chebyshev filter. I was impressed by the 'crispness' of CW 
through these filters.

In general, any passive filter design can also be implemented using 
an active filter and vice versa. Passive filters have lower 
component count and better dynamic range, and work better at 
high frequencies. Active filters do not require inductors, and are 
better suited to very narrow band filters where very high Q is 
required. It seems to be difficult to design a passive CW audio 
filter with a bandwidth much less than about 50Hz, due to the finite 
Q of inductors available. This is fairly easy with active filters, but 
requires the use of multiple op-amp filter sections, rather than the 
single op-amp multiple feedback circuits. It gets increasingly 
difficult to make good active filters at high frequencies, but the 
audio range is no problem. Whether active or passive, it is usually 
neccessary to trim component values with narrow filters.

 For audio filters, BiFET op amps like TL071/81, LF351 etc and 
their dual and quad variants are a much better choice than 741 
type op amps; their lower bias currents make for more choice in 
the range of resistor and capacitor values. Some of the newer 
CMOS op-amps are good too, but relatively costly. The most 
important op-amp parameter for filters is the gain-bandwidth 
product - the higher it is, the higher the filter Q that can be obtained 
with a given circuit.

There are usually many ways of producing a given filter 
performance; it's best to have a read of one of the handbooks 
before you start.

Hope this E-mail is legible - something funny has happened to the 
text wrap on this software!

Cheers, Jim Moritz
73 de M0BMU