John Ferrell wrote:

Is a resistor used in matching a bad thing? My intuition is that it
is, but I have no math to back up the position.

One of my current projects is to understand the matching problem for
an electrically short vertical.

Using EZNEC+, when I run the SWR function with the radiator (simulated
real ground) I get an indication of Z = R + j. If I add an inductive
load at the bottom of the radiator equal to the j value it brings the
match into a reasonable range. At this point I have not grasped the
relationship of the "R" in the equation. If I use the figure for R
equal to 10% of the XL, the match gets even better, but not 1:1. 10%
comes from the suggested estimate in the help file.

Question 1: What is this "R" thing? I started out thinking it was
series DC resistance and lower is better. My interpretation of the
EZNEC results contradict this position. More "R" seems better.

Let's suppose that your antenna was a black box instead of an antenna.
You connect a source to it and look at the impedance looking into the
black box. If the resistive part of the impedance (the R) was zero, the
box would contain the equivalent of only an inductor (if the X was
positive) or a capacitor (if the X was negative). Although you would
measure voltage and current at the box's terminals, you'd find that they
were 90 degrees out of phase with each other, and no power would be
delivered from the source or consumed by the box. Not the situation you
want with an antenna -- you need to deliver power to it so that power
can be radiated.

If, on the other hand, you see some R when you look into the box, you
can calculate that the power being delivered by the source and consumed
by the box is I^2 * R, where I is the RMS current at the box terminals.

So R is always present at an antenna feedpoint at any time the antenna
is radiating power, since part of the power "consumed" by the antenna
goes toward radiation. This R is called the "radiation resistance". Some
part of the power supplied by the source is also actually consumed by
heating the wire and ground. This increases the R seen at the feedpoint.
That part of the total R is called the "loss resistance".

What you want to do is to maximize the fraction of the power that's
radiated, and minimize the fraction that's wasted as heat. So you want
to make the ratio of radiation to loss resistance as large as possible.
If you have a short antenna, you'll find you can raise the radiation
resistance by lengthening it or adding a top hat. Center loading with a
coil also raises the radiation resistance, but you can end up increasing
the loss just as much due to coil resistance.

With EZNEC, you can set all losses to zero by setting wire loss and the
loss of all loads to zero and, if using a grounded vertical, using
MININEC type ground. Then the R you see is only the radiation
resistance, and the field strength is that of a 100% efficient antenna.
Reintroduce the losses and you'll see the loss resistance added to the
radiation resistance at the feedpoint. The field strength will drop
according to the reduction in efficiency.

Question 2: Is this an effective method of matching a 50 ohm line to
the vertical radiator?

Any resistance you intentionally add will increase the loss resistance
without changing the radiation resistance. More of your rig's power will
be spent heating the resistor and less will be radiated. In some
instances, such as military frequency-hopping applications, the trade of
greater bandwidth for less efficiency might be worthwhile. You'll have
to decide for yourself whether it is for you. There are certainly a host
of other matching methods which are less lossy, but few which can
achieve the extreme broadbanded match of a resistor. But don't be fooled
into thinking that because the match is broadbanded that you're
radiating the same amount of power over the band. The wider the
bandwidth, the larger the fraction of your power you'll dissipate in the
resistor.

I do understand this is a math model and it ignores radiation from the
inductor.

"Loads" don't radiate. Inductors modeled as wires using the helix
creation feature do.

Question 3: Looking ahead, I think the next matching technique should
be an inductor in series with the ground end of the radiator and the
ground. The 50 ohm line would feed a tap on the coil 50 ohms up from
ground.

That's not likely to work.

Do I compute XL from the bottom to equal 50 or is this strictly a cut
& try thing?

You don't want an XL of 50, you want the feedline to see an R of 50 with
no X, that is, 50 + j0.

I have yet to physically model anything with these tests but I am
getting close to it.

I know there are better matching methods than what I am attempting,
this is an academic exercise for me!

Look into making an L network. It would be a good opportunity to learn
how to use the Smith chart, and you'd end up with a low loss matching
solution.

Roy Lewallen, W7EL