On Oct 24, 6:48 am, Michael Coslo wrote:

Trying to make a "readers Digest" version here....

If I'm following so far:

The lowered frequency of resonance is due to changes in the velocity factor.

The lowered vf is somewhat due to increased capacitance, and an increase
in inductance - the latter part I'm still trying to grok. I think there
is likely something more going on.


No to all of that... the changes in apparent C and L are a poor
model.

Consider that each little section of the antenna has a EM field that
interacts with each other section. Say you sliced the antenna up into
little strips lengthwise, and measured the inductance of one strip by
itself and then measured the inductance of all in parallel. If the
little strips are "far away" from each other the inductance will be
less (i.e. 1/Nstrips)... but they're not "far away".. the field from
strip 1 couples to strip 2. So there's a nonzero mutual inductance you
have to take into account. You need to calculate the M between strip 1
and strip 2 and strip 3, etc.

Same thing applies to capacitance. There's a capacitance of each
little chunk of the antenna to the surroundings. There's also a
capacitance to adjacent chunks. And to chunks that are 1 chunk away.
So, you can't just say.. I know the C of one long strip, and there are
N strips, so the C is N*C..

In the case of an infinitely thin wire, you CAN make some simplifying
assumptions AND use some analytical approximations (i.e. the
inductance between a segment of an infinitely thin filament and
another segment is well defined, so you integrate over all segments,
which are themselves infinitely small).

There's also the propagation speed issue. Say you slice the antenna
up crossways (like a salami).. there's a L and a C between each slice
(i.e. N^2 Ls and Cs for N slices), although it's symmetric, M12 =
M21. If you put a changing current through an inductor that has some
mutual inductance with another, then some current is induced in the
other. However, since the antenna is a significant fraction of a
wavelength long, there's also a time delay involved, so that current
occurs a bit later. That is, the change in current in segment 1
induces a current in segment 2, but delayed by the distance from 1 to
2. Segment 1 also induces a current in segment 3, but it's delayed
even more.

So, rather than some simple model of a single L & C, or even a simple
distributed LC transmission line, you really have a model that has
lots of pieces, each connected more or less to all the other pieces by
some factor (which includes a time delay).

ANd this is what programs like NEC do. They actually divide the
antenna up into a bunch of segments, calculate the interaction between
every possible pair of segments (making some speed up assumptions for
segments that are very far apart), and then solve the system of linear
equations that results. You can get an arbitrarily accurate model by
making the segments ever smaller and more numerous, restricted only by
numerical precision and computing time. NEC does make some
simplifying assumptions. It assumes that the current along the segment
is represented by a simple model (a basis function), a constant plus
two sinusoids. I believe MiniNEC simplifies even further by assuming
constant current in the segment. The tradeoff is that for the same
accuracy, the rectangular basis function will require more segments
than the NEC basis function, but, it's easier to compute.




I'm still left with the increased bandwidth phenomenon. None of the
above would seem to account for this.


You're right.. it doesn't, because the simple models don't account for
ALL the interactions between subpieces of the antenna. The formula for
the inductance of a rod above ground doesn't know about propagation
speed, so it deals with the mutual interaction of one piece of the rod
with another, but not the time delay.

Think of it like the breakdown of the DC formula for resistance of a
round conductor as you start running AC through it. The DC formula
(resistivity * length/cross sectional area) doesn't account for
inductance, so when you run AC through, the inductance of one current
filament relative to another starts to have an effect.
I've been working with mobile antennas for the past several months, and
I might be going astray, because I keep thinking about increased
bandwidth as a partner of lowered efficiency. Not likely the case here.

No.. Bandwidth does not necessarily go with lower efficiency. That
statement is often the result of misinterpreting the statement about
size and Q and gain being related. A big fat antenna will have high
efficiency AND wide bandwidth.

Jim, W6RMK