Crystal filter passband shape

ashhar_farhan <farhan@...>
 

--- In BITX20@..., "n3ted" <tedkell@e...> wrote:

Did somebody already plot the passband shape of a resulting 4
crystal
filter?
How do you do that? Figure out the shape that is?
the shape is easy to figure out if you already know the crystal
parameters. the crystal parameters are easier to measure now thanks
to the G3UUR method. i have outlined it at
http://www.phonestack.com/farhan/xcvr1.html.

the essential idea is that a crystal filter looks like a capacitor
and an inductor in series (these are called motional capacitance and
motional inductance respectively). in addition to these, between the
leads of the crystal you will also be able measure a parallel
capacitance.

using the G3UUR method, you put each of the crystals into the
oscillator and measure its frequency. then you solder a 22pf or a
33pf in series with the crystal and measure the frequency shift. the
shift gives you a good approximation of the motional capacitance and
given the capacitance it is trivial to calculate the inductance
(given that we know the crystal's frequency). the parallel
capacitance is also approximated and the crystal is completely
modelled.

once you know the crystal parameters, you can spend a weekend
understanding the butterworth filter design. or you can use the
cookbook method in EMRFD like I did, or just use w7zoi program that
comes with his other book Introduction to RF Design.

using the my motional parameters, w7zoi did run it through his
program GPLA.exe and i have just uploaded the results to the
pictures folder.

i am including his comments that go with the picture below:
<snip>

The first file, ashhar01, part A, shows the
filter I designed with your motional L of 11.95 mH. I designed for
2200 Hz
bandwidth and a Butterworth response. Then the filter at part B
is a
more practical version of the same thing. It is much like the
filter that
you ended up building. My simulations suggest that is really is
worthwhile
to add the tuning capacitors at the ends though, for it produces a
much
smoother, ripple free response. The first analysis I did used
equal
terminations of 200 Ohms (perhaps 220) at each end and the response
was of
course text book. But the question remained -- what would the
response be
if the filter was terminated in other resistances. The file
ashhar02
shows what you get with a 50 Ohm source and a 200 Ohm load. This
is still
pretty good. The response is not nearly so good with 100 Ohms per
side,
which is about the characteristic Z0 of your amplifiers.

</snip>

- farhan

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