Yes, exactly. The minimum required Q scales proportionally to the
fractional bandwidth. Hence at a given frequency the required 400 Hz
filter demands resonator Q's 12.5 times higher than for a 5 KHz filter,
assuming a bunch of other factors remain constant. They don't, but this
is a good enough approximation for our purpose of a back-of-the-envelope
discussion.
Hence, the resonator Q requirements for a 5 KHz filter at 40 MHz are not
grossly different than for a 500 Hz filter at 4 MHz, which is quite
achievable. But for a 400 Hz filter at 45 MHz, the required resonator
Q's get into the million range.
I have in my junkbox a 20 KHz wide crystal filter with a center
frequency of 157 MHz used as a front end filter to improve VHF FM
receiver interference rejection from nearby paging transmitters. (Nearby
in both the geographical and frequency senses.)
Jack
Geoffrey Mackenzie-Kennedy wrote:
There are some many practical problems with the holder capacitance,
stray capacitance and the like that would make such a filter
challenging, even if someone were to deliver a box of 45 MHz crystals
with measured Qs of 2 million to my doorstep. And if the box of
crystals arrive, to obtain frequency stability might require
stabilizing the filter assembly in a temperature controlled oven.
The typical roofing filters at 45 MHz have a bandwidth of 20 KHz or
so. Thus the fractional bandwidth is 50 times larger and the Qx is
down into the 100K range, making these filters relatively easy to
realize.
--------------------------------------------------------------------------
An interesting 42.5 MHz filter design appeared several years ago using
just four crystals in ladder configuration. The designer was not
looking for narrow bandwidth nor good shape factor, but illustrating a
"method". The bandwidth was 5 kHz, the shape factor was 4, stopband
better than 80db and the response was symmetrical. In addition to the
usual inductors across each crystal to take care of holder
capacitance, as inspired by Zobel, two other other modifications were
incorporated. (1) Parallel tuned circuits were placed at each end to
prevent degeneration into a poor Cauer lowpass filter. (2) Parallel
tuned circuits were used as coupling elements, presumably to tweak
mesh frequencies. Insertion loss unknown, but a fair number of
elements to compensate for temperature change.
73,
Geoff
GM4ESD
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