Henry Kolesnik wrote:

In the Feb. 2004 QST there's an article by AD5X for a mobile antenna using a
Hamstick or Bugcatcher with shunt capacitor feed or an L match. Can someone
please explain, including the math, on how a ~500pf capacitor transforms 10
ohms to 50 ohms for 40 meters? I get no understand from reading either my
ARRL Handbook or ARRL Antenna Handbook. There are no stupid questions, only
stupid people asking!

I haven't read the article but it's probably a capacitor in parallel with
a 10+jXL feedpoint impedance. With the right amount of jXL, a parallel
capacitor will convert the impedance to 50 ohms resistive. In this case,
the antenna is operated at a frequency higher than its resonant frequency
and the feedpoint impedance is 10+jXL, i.e. the antenna is too long.

With a 10-jXC feedpoint impedance, a parallel inductor will convert the
impedance to 50 ohms resistive. I'm sure you've seen these coils
at the base of 75m & 40m mobile antennas. In this case, the antenna is
operated at a frequency lower than its resonant frequency and the feedpoint
impedance is 10-jXC, i.e. the antenna is too short.

In my old 15th edition of The ARRL Antenna Book, this is all covered on
page 16-11 under "Matching to the Transmitter". On my version 2 ARRL
Antenna Book CD it is on page 16-13 all explained in detail.
--
73, Cecil http://www.qsl.net/w5dxp



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Hank, W5JFR wrote:
"Can someone please explain including the math, on how a ~500pf
capacitor transforms 10 ohms to 50 ohms for 40 meters?"

Go back to the books and look at L-networks. It`s in the book.

In my 1970, 12th edition of the ARRL Antenna Book, an L-network example
is given for matching a mobile whip to a 50-ohm line. It says on page
296:
"For example, if it is desired to match a 50-ohm liner to a 20-ohm
resistance, Xc will be about 46 ohms, and Xl about 25 ohms."

Xl & Xc come from Fig. 15-12 which is used to match 50-ohm coax to whip
antennas between 10 and 36 ohms.

The Xc of 500pf at 7 MHz is 46 ohms.

Xc = 1 / (6.28)(f)(C)

Best regards, Richard Harrison, KB5WZI

Someone sed:
"In the Feb. 2004 QST there's an article by AD5X for a mobile antenna using a
Hamstick or Bugcatcher with shunt capacitor feed or an L match."
=========================
A well known circuit theorem states that any finite impedance, e.g an antenna,
can transformed to any other finite impedance, e.g. 50 + j0 Ohms, by an L
network consisting of no more than two lossless elements.

Given that you can use short or open circuits as one or both of the elements
there are 8 possible configurations of such a circuit.

I have the equations programmed into my H-P 48 calculator.

73 de Jack, K9CUN

Well sed!