On 1/13/2011 6:05 PM, Antonio Vernucci wrote:
Mikek,

on of the main problem of this newsgroup is that people write answers
without carefully reading the question.

Everyone tends to "convert" the question toward issues he is able to
write something about, Unfortunately those issues often have little to
do with the original question.

I am offering you my answer, which may be clear, so and.so, or hardly
understandable ... I do not know. But be sure that at least I paid
maximum efforts to appreciate your question (though my numbers do not
always match yours). I'll try to explain the issue in the easiest way I
can, assumimng that all components behave in an ideal manner.

Let us first resume your hypotheses:

- the antenna has an impedance equal to the SERIES of a 58-ohm
resistance and a capacitive reactance of -1,072 ohms which, at 1 MHz,
corresponds to a 148.5-pF capacitance
- your aim is to transform that complex impedance into a 1.5-Mohm
purely-resistive impedance, that would match that of your tank circuit.

That said, you must first appreciate that your antenna can be visualized
in two ways:

- as the SERIES of R=58ohm, C=148.5pF (as said above)
- or, by applying the series-to-parallel transformation formula, as the
PARALLEL of R=19,862ohm, C=148.1pF

These are just two fully equivalent ways of describing the same physical
antenna. You can freely use the one which suits you best. For our
purposes let us here visualize your antenna as the parallel of
R=19,862ohm, C=148.1pF.

That said, assume for a moment that you are able to eliminate in some
way (i'll tell you after how) the 148.1-pF parallel capacitance. What
would then remain is a 19,862-ohm resistance, a value which
unfortunately does not match the 1.5-Mohm figure you wish to get.

So, how to get just 1.5Mohm instead?

Playing with the transformation formulas you would realize that, if the
SERIES representation of your antenna would hypothetically be R=58 ohm,
C=54 pF (instead of R=58 ohm, C=148.5 pF as it is in the reality), the
corresponding PARALLEL representation would then become R=1.5Mohm,
C=53.9 pF. Just the resistance value you wish to get!

But modifying the SERIES representation of your antenna according to
your needs is very easy: if you put an 85-pF capacitance in series with
the antenna, its total capacitance would change from C=148.1 pF to
C=54pf. And the antenna SERIES representation would then become R=58
ohm, C=54 pF, as you were aiming at.

Antonio - I think you slipped a decimal point. The parallel equivalent
of the series combo 58R-2947j is actually 149k+2948j.

Once you have put such 85-pF capacitance in series with your antenna,
its PARALLEL representation becomes R=1.5 MHohm, C=53.9 pF, as said
earlier.

For removing the 53.9-pF residual parallel capacitance, just resonate it
with a 470-uH parallel inductance. The trick is then done: what remains
is just the 1.5-Mohm resistance you wanted to get!

In summary:
- put a 85-pF in series (i.e. in between your antenna and the tank circuit)
- put a 470uH inductance in parallel to the tank (in practice this just
means to increase the tank inductance by 470uH with respect to its
nominal value).

73

Tony I0IX
Rome, Italy