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
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