Capacitance of a wire above a foil:
The VHF bandpass filter designed for the first IF filter at 110 MHz uses
some unusual components. Especially unique are the 0.092 pF coupling
capacitors shown in the schematic. That circuit is repeated below.
An often voiced question from beginning filter builders is, "Where do I purchase
a capacitor with .092 pF?" The answer is that you don't.
Even the stray C of a common resistor is more than that. It
is necessary to fabricate your own capacitors, or to realize the same effect.
What is important is to couple energy between the first and second
resonator, and also to couple between the second and third resonators.
This can be through any means that works. An especially easy way to
realize the coupling is with a wire capacitor. A wire is attached
to the "hot" end of the first resonator (the left 7.32 pF variable cap).
That wire is then routed through a hole in the shield that isolates
the tuned circuit from the second resonator. The piece of wire is
then routed close to the coil
of the second resonator. But the critical questions become
how long the wire should be and how close it
should be to the second resonator. The cap from resonator 2
to #3 is obviously treated with the same care.
We did an experiment with an AADE L/C meter and a capacitor fabricated with
wire. We soldered a Teflon insulated terminal to a scrap of PC board
and then attached a wire to the terminal to generate a capacitor.
The wire length started at 1.5 inches, but was then reduced in small increments.
See the photo below.
The "zero" function was not used during this measurement, so there was about
3.9 pF of stray capacitance. That was subtracted from the data
during analysis with a spread sheet. The Incremental Capacitance
was plotted as a function of the wire length, which is shown below.
Of particular interest is the average slope of this curve, which is
0.28 pF per inch. This means that a wire of an inch will have C of
0.28 pF. The wire in the experiment was 0.4 inch from the ground
foil. Pushing it closer would cause C to increase. The
small valued 0.092 pF capacitor needed in our filter could be approximated
with a wire that is about half an inch. The half inch is not the total
wire length, but the amount of overlap with the coil.
Experimentally, the best way to set up a filter of this sort is to start
with very small wires as the coupling capacitors. One end of
the filter is driven with a 50 Ohm signal generator while the other end is
terminated with a 50 Ohm detector. The detector could be a 50 Ohm
power meter or spectrum analyzer, or even a 50 Ohm terminate scope of suitable
bandwidth. Using the curve above, a good start might be wires
that overlap the coil by perhaps 0.3 inch with a spacing of 0.4 inch.
The variable capacitors are all adjusted at 110 MHz for the highest output.
The filter insertion loss and bandwidth are measured. If they
do not fit the desired response, the length and/or position of the coupling
wires is changed and the process is repeated. If you ever reach
a stage when a multiplicity of peaks is seen, that suggests that there is
too much coupling.
There should be plenty of adjustment range available in this filter.
Without changing any coils or coupling capacitors, I was able to move my
filter from about 90 MHz up to about 130 MHz center frequency.
There were three peaks by the time I got to 130 MHz,
indicating over coupling. It is worthwhile to try moving the
filter from 110 to something slightly different just to be sure that none
of the variable capacitors are tuned to maximum or minimum value.
There is another problem that can come up with severe over coupling.
If the resonator to resonator coupling is severely high, one of the peaks
may be a long ways away from the desired filter center. So,
when evaluating the experimental filter, be sure to use a very wide sweep.
A swept instrument is not needed. However, a variable
frequency generator is desired. See the paper that we presented
in QST for December 1991 having to do with double tuned circuits.
For this particular filter, we would recommend an evaluation sweep from 50
to 200 MHz.
This photo is a close-up view of the second resonator. Note
the position of the wire coupling capacitors with respect to the body of
the coil. This appears to be a surprisingly good fit to the experimental
data. While the overall wire length exceeds 0.5 inch, the part that
overlaps the most sensitive "hot" end of the coil is only about half
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