On Thu, 13 Jan 2011 12:42:01 -0600, "amdx" wrote:


"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.

Hi Mike,

Then your intuition is firing on all cylinders, great.

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.

This is classically true. The frill of "at any given frequency" can
be discarded.

We can use this property to transform the
real component
of an impedance to a much higher or lower value.

This concept is not a "property," however; more a transformation (as
should be apparent in the original statement). In other words
concept
equivalent
property
transform
use four words to describe one thing - transform (plain and simple).

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

Well, what looks like hand-waving is probably close to the numbers one
could expect.

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 reason why I say hand-waving (and this is probably your gut
reaction as to "why") is that the five lines of operations you quote
starts with a presumed requirement and then proves it has been met.

What happens if Xc series R series?
What happens if Xc series R series?
What happens if Xc series = R series?
What happens if Xc series R series?

This somewhat clouds the mystery for you of understanding Parallel to
Series conversion. I wonder too. Are we dropping in a new component
and stepping back with a wave and Voila! to find the Parallel circuit
has suddenly been transformed? Yeah, that WOULD be a mystery.

And what is this Xc(parallel) and Xc(series) stuff?

Xc is stricty a function of pi, capacitance, and frequency.

And what is this R(parallel) and R(series) stuff?

R is a function of its, well, resistance. No variables to be found.

No doubt there is more to be extracted from this article.

73's
Richard Clark, KB7QHC