"Richard Clark" wrote in message
...
On Thu, 13 Jan 2011 11:05:38 -0600, "amdx" wrote:

This is in regard to a crystal radio, so the match is for a low impedance
antenna to a high impedance tank circuit.
The antenna: R=58 ohms C=1072 ohms at 1Mhz.

Hi Mike,

Is this a fantasy antenna?

It's an example from an article, I don't like the number either, seems like
maybe
2 to 12 ohms would be more realistic. I think the capacitance is ok.

For the 58 Ohm resistive value, it would have to be about 300 feet
tall - not the size of operation one usually comes to expect for a
Xtal radio aficionado.

If it is that tall, it would exhibit 200 Ohms Inductive reactance (one
fifth of what you report, and the opposite sign).

Something doesn't wash here.

Ok, how about just working with the concept.

I calculate an 18.5pf cap for the match, making the antenna look like 58R
and 17pf.

58±j17 Ohms is still a complex impedance, and says nothing of match
which can only be expressed in terms of the expected load R.

Sorry, I missed a math step, the R was converted to 1.5M.
see formula below.

And I now have a 1.5 Mohms source feeding a 1.5 Mohm load.

How that is arrived at is something of a mystery. By the numbers, you
describe a 26000:1 mismatch.


Here's what is stated in the article:
" The concept is that at any given frequency, a parallel RC network has an
equivalent
series RC network, and vise versa. We can use this property to transform the
real component
of an impedance to a much higher or lower value.
As long as Xc series R series.
Xc (parallel) = Xc (series)
R (parallel) = XC^2 (series) / R (series)
The Xc of a 17pf at 1Mhz is 9368 Ohms.
To rewrite Rp= 9368^2 / R = 1.513 Mohms

The article then goes on to say,
The utility of this equivalence can be seen by choosing a sufficiently small
value of C series
(a large Xc series) A "small" resistance can then be transformed into a
"large" value.

The purpose of which is to cause minimal loading of the tank by the
antenna.

Mikek