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

Craig Buck wrote:

I am baffled too., If the antenna is too short and therefore exhibits
capacitive reactance, why isn't the adding a coil (inductive reactance)
enough to balance it out? I guess I don't understand matching networks at
all. If the antenna is too capacitive or to inductive add the opposite to
get to zero. Seems like you add one or the other but not both to get a
match.

Just another dummy trying to figure it out.

Adding the proper reactance in SERIES in the antenna tunes it to
RESONANCE. But, the feedpoint, load resistance, will be low; example 10
+ j0 ohms, and the VSWR will be 5:1.

Keeping some reactance in the antenna allows a SHUNT REACTANCE to be
used for tuning. The input impedance then becomes the parallel
combination of the antenna impedance with the shunt impedance. If there
is Q in the circuit then an impedance transformation takes place based
on the value of [Q + 1].

DD, W1MCE

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!

You're making my head hurt but I think I am beginning to see the light.

--
Radio K4ia
Craig "Buck"
Fredericksburg, VA USA
FISTS 6702 cc 788 Diamond 64
"Bill Turner" wrote in message
...
On Sun, 18 Jan 2004 22:55:27 -0500, "Craig Buck" wrote:

I am baffled too., If the antenna is too short and therefore exhibits
capacitive reactance, why isn't the adding a coil (inductive reactance)
enough to balance it out? I guess I don't understand matching networks
at
all. If the antenna is too capacitive or to inductive add the opposite
to
get to zero. Seems like you add one or the other but not both to get a
match.

__________________________________________________ _______

You guys are making this way too complicated.

First, get an ARRL handbook and learn about L-matching networks
(entirely apart from antennas).

Then, picture your HF mobile antenna with no matching network, but tuned
to resonance. The feed point resistance will be typically 10-40 ohms or
so. Pure resistance, no reactance.

Now picture that same antenna with an L-network to raise the feedpoint
resistance to 50 ohms. Still pure resistance, no reactance.

Now, (here's the clever part) detune the antenna so it appears to have a
small amount of capacitance or inductance in series with it. This
becomes one of the two elements of the previous L-network. All you have
to do is add the other element of the L-network and connect the coax to
the junction of the other element and the base of the antenna.

Presto, it's matched! Make sense now?

--
Bill, W6WRT