K7ITM wrote:
On Oct 23, 10:35 am, (Richard Harrison)
wrote:
Mike, N3LI wrote:

"I thought that the inductance tends donward as the diameter of the wire
increases. I can understand your calculation after the wavelength part,
but don`t quite get the increased inductance part."

Good observation.

Wire inductance decreases with the circumference increase as this
effectively places more parallel inductors in place along the surface of
the wire.

Wire capacitance increases proportionally with the square of the
circunference of the wire as it is proportional to the wire`s surface
area.

The fatter wire grows capacitance faster than it changes inductance.

Reactance along a wire antenna element varies quickly near resonant and
antiresonant points so is not uniformly distributed. This complicates
calculations and requires average values for some. Bailey says of surge
impedance: "Nevertheless, this variation in theoretical surge impedance
shall not deter us from setting uup practical "average" values of surge
impedance.
Best regards, Richard Harrison, KB5WZI

I know we're talking about linear antennas here, but even in that
case, it's surely not true that capacitance increases as the square of
the wire diameter (or radius or circumference); nor inductance
proportional to 1/diameter. Consider that if both those were true,
doubling the wire diameter would quadruple the capacitance and halve
the inductance, and the propagation velocity along that wire would be
1/sqrt(4*0.5) or about .707 times as great as with the thinner wire.
Clearly things change much more gradually than that.

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.

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

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.


Thanks to everyone for the help, while I'm happy to accept the obvious
real results, It is even better if I can understand what is going on.


- 73 de Mike N3LI -

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

On Oct 24, 1:29*pm, wrote:
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.


so as the wire gets thicker the C per unit length goes up at some rate
and the L per unit length goes down at some other rate, fine so that
reduces the characteistic Z by some rate....but none of that changes
the wave velocity as was pointed out above in the coax example.

I think the shortening effect may all be due to the extra C of the end
surface, i.e it iss end effect. For a thick wire, the end is a circle
that has C and this is all extra C that is not present for the thin
wire. Is this extra C alone enough to create the shortening effect?

Mark

On Oct 24, 11:01 am, Mark wrote:
On Oct 24, 1:29 pm, wrote: 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.

so as the wire gets thicker the C per unit length goes up at some rate
and the L per unit length goes down at some other rate, fine so that
reduces the characteistic Z by some rate....but none of that changes
the wave velocity as was pointed out above in the coax example.

I think the shortening effect may all be due to the extra C of the end
surface, i.e it iss end effect. For a thick wire, the end is a circle
that has C and this is all extra C that is not present for the thin
wire. Is this extra C alone enough to create the shortening effect?

Mark


No.
And, "end capacitance effect" is a poor model for what's really going
on. It's been used as an "explanation" for the observation that an
antenna that is slightly shorter than half a wavelength is resonant(as
in has no reactive component at the feedpoint). The problem is that an
infinitely thin dipole is resonant at less than 1/2 wavelength, and in
that case, there's no real "end" to have an effect.

On Oct 24, 12:11*pm, wrote:
On Oct 24, 11:01 am, Mark wrote:



On Oct 24, 1:29 pm, wrote: 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.

so as the wire gets thicker the C per unit length goes up at some rate
and the L per unit length goes down at some other rate, fine so that
reduces the characteistic Z *by some rate....but none of that changes
the wave velocity as was pointed out above in the coax example.

I think the shortening effect may all be due to the extra C of the end
surface, i.e it iss end effect. *For a thick wire, the end is a circle
that has C and this is all extra C that is not present for the thin
wire. *Is this extra C alone enough to create the shortening effect?

Mark

No.
And, "end capacitance effect" is a poor model for what's really going
on. It's been used as an "explanation" for the observation that an
antenna that is slightly shorter than half a wavelength is resonant(as
in has no reactive component at the feedpoint). The problem is that an
infinitely thin dipole is resonant at less than 1/2 wavelength, and in
that case, there's no real "end" to have an effect.

?? I have been under the impression that in the limit as the
conductor radius goes to zero, the resonance does go to a freespace
half wavelength. You have to make the antenna _really_ thin to get
anywhere near that, though. Even a million to one length to diameter
ratio won't do it.

There's another empirical point, though, that may be worthwhile
considering to convince folk that Jim's exactly right that you can NOT
just figure things from "capacitance" and "inductance" and the
resultant propagation velocity. For the resonance of a nominally half-
wave dipole in freespace, the resonance changes by only a small amount
as the wire becomes thicker. With the wire length/diameter ratio at
10,000:1, resonance is about 2.5% below freespace half wave. For l/d
= 1,000:1, it's about 3.7%. At l/d = 100:1, it's about 6.1%. But for
the same l/d ratios operated at full-wave (anti)resonance, the factors
are respectively 7%, 9.3% and 17.5%. It would be tough to reconcile
that difference using the simple L and C per unit length model.

Ronold King made a career out of developing the theory of linear
antennas. I find the "Antennas" chapter he wrote for "Transmission
Lines, Antennas and Waveguides" to be a valuable source of insight
about antennas. It's presentation is more empirical than theoretical,
but I've found that his explanations there pretty much always give me
better insights into what's going on. It can be tough to find the
book, but I do have a PDF photocopy... If you want to get seriously
into the theory and math, one of his other books might be just the
ticket. Though I like the way he presents the material, I know of
others who are turned off by it, so "ymmv" as they say.

Cheers,
Tom

K7ITM wrote:

Ronold King made a career out of developing the theory of linear
antennas. I find the "Antennas" chapter he wrote for "Transmission
Lines, Antennas and Waveguides" to be a valuable source of insight
about antennas. It's presentation is more empirical than theoretical,
but I've found that his explanations there pretty much always give me
better insights into what's going on. It can be tough to find the
book, but I do have a PDF photocopy...

Not too tough. Amazon has 7 copies from $9.96 -
http://www.amazon.com/gp/offer-listi...4901677&sr=1-8
They appear to be the original 1945 hardcover book. Mine is a soft cover
Dover reprint published in 1965. Alibris has 17 copies, for $7.00 up -
http://www.alibris.com/search/books/...ave%20gu ides.

The quick web search that found these also found others. I picked mine
up at Powell's some time ago for $15.00.

I also highly recommend this book.

Roy Lewallen, W7EL

On Oct 24, 4:31 pm, K7ITM wrote:
On Oct 24, 12:11 pm, wrote:

And, "end capacitance effect" is a poor model for what's really going
on. It's been used as an "explanation" for the observation that an
antenna that is slightly shorter than half a wavelength is resonant(as
in has no reactive component at the feedpoint). The problem is that an
infinitely thin dipole is resonant at less than 1/2 wavelength, and in
that case, there's no real "end" to have an effect.

?? I have been under the impression that in the limit as the
conductor radius goes to zero, the resonance does go to a freespace
half wavelength. You have to make the antenna _really_ thin to get
anywhere near that, though. Even a million to one length to diameter
ratio won't do it.


Half wavelength of zero radius has a feedpoint impedance of about
73.1+j42.5 ohms
(see, e.g. page 639 of Orfanidis's online electromagnetics book
(chapter 16), which gives a one page derivation)
(http://www.ece.rutgers.edu/~orfanidi/ewa/)

Roy's right about the spiral not converging to 377+j0.. I misread the
graph.

Jim

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

The reactance of a conductor with a relatively large cross-section changes
slower with a change in frequency than one having a small cross-section.

Therefore its impedance bandwidth remains below a given limit over a greater
frequency span than one of a smaller cross-section.

RF

On Oct 24, 11:53 am, "R. Fry" wrote:
"Michael Coslo" I'm still left with the increased bandwidth phenomenon. None of the above
would seem to account for this.

____________

The reactance of a conductor with a relatively large cross-section changes
slower with a change in frequency than one having a small cross-section.

Therefore its impedance bandwidth remains below a given limit over a greater
frequency span than one of a smaller cross-section.

RF

If you plot the feedpoint Z over frequency as R and X on a
rectangular scale (not a Smith chart), you get a spiral. thin
antennas have a big spiral crossing the R axis at X=0 very steeply
(implying narrow match bandwidth), while fat antennas have a smaller
diameter spiral.

As someone else has pointed out, the spiral eventually converges to
something like R=377 when frequency is very high.

The "why" for all of this does not admit of a simple explanation.
(thereby providing nice grist for EM textbook writers, and brain
bending work for EM students)
It's the trying to understand why (the actual measured data has been
around for at least a century) is what prompted the work of folks like
Schelkunoff, Hallen, King, and others. They came up with good answers
for very specialized cases (inifinitely thin wires, conical antennas,
etc.). The fact that "real" antennas tend not to look like the
idealized ones with the analytical models led to the development of
finite element methods, in particular, the Method of Moments, which
NEC and it's ilk are based on. The idea had been around for a while,
but fast computers made it possible to do for interesting non-trivial
cases.

There are similar analytic models that are "pretty close" for Yagis,
for instance.

wrote:

If you plot the feedpoint Z over frequency as R and X on a
rectangular scale (not a Smith chart), you get a spiral. thin
antennas have a big spiral crossing the R axis at X=0 very steeply
(implying narrow match bandwidth), while fat antennas have a smaller
diameter spiral.

As someone else has pointed out, the spiral eventually converges to
something like R=377 when frequency is very high.
. . .

377 ohms is the impedance of free space, which is the ratio of E to H
fields of a planar TEM wave. People keep looking for this value when
dealing with antenna impedances, apparently due to the common
misconception that antennas are "transformers" of some sort to "match"
the impedance of free space (an E/H ratio) to a transmitter impedance (a
V/I ratio).

Quite a few people have tackled the problem of the impedance of an
infinitely long dipole. In _Antennas and Waves_, King & Harrison
conclude (p. 234) that the impedance is approximately 214 - j189 ohms.
However, this requires extrapolation from calculated and measured
results, since convergence is extremely slow. In _Antennas_, Kraus's
analysis doesn't show convergence, but it's based on a simpler theory
which I don't believe is as complete. Because it's not of much practical
interest, most of the analyses appear in academic papers rather than
antenna textbooks. It's not at all a trivial problem.

Roy Lewallen, W7EL