"Larry W4CSC" wrote
I've never seen 20 watts produce a corona in air over 8" long....

Awww .... my buddy's 4-watt CB does it all the time. Of course he had it
peaked up at the truck stop but ... (c;

73, K3DWW

"Gary Schafer" wrote in message
...
On Tue, 04 May 2004 15:08:08 -0000, Larry W4CSC

...The 650 W amp melted the solder joints on the core ....


So about 97% of your power is going up in heat in the coils.

If Gary's right then 97% of 650 Watts otta get the coil so hot it melts
solder and ... OY!

That sounds dangerous to me, Larry. I think you otta send the whole rig to
me so I can check it out. With a DD degree I may be the best qualified (c:

On 2004-05-05, Gary Schafer wrote:

Well I don't profess to be any kind of expert either.

You claimed to be expert enough to tell that Larry doesn't
know what he's talking about, and to be able to distinguish
the "right" material from the "wrong" as published by ARRL.
That *sounds* like a claim...

Yes, the series resistance is the "real part". However it is not just
the DC resistance of the material in the coil. It is the AC resistance
of the material known as skin effect, which will be greater than the
DC resistance at radio frequencies. The higher the frequency the
greater the skin effect. The voltage applied is irrelevant.

Bzzt. The voltage applied is irrelevant only for linear components.
But if you want to assume that antennas (and/or coils) are linear
over the range of frequencies and voltages you're considering, I'm
willing to go with that.

Now I'll rephrase the last half of what you wrote:

Every component has an impedance that may be frequency-dependent.
We'll be working at a single frequency, f. The real part
of the impedance of a coil at frequency f will be called
the "series resistance."


Series resistance = Real ( Impedance(f))

There's an equation. It DEFINES the term on the left in terms
of two things on the right -- the "real part" function, which
was known to Cauchy for instance, and the Impedance, which you
can find in Horowitz and Hill, for instance. Write some
more things like that, and I'll be running right along with you.

3. Do you understand the difference between Radiation resistance and
feed point resistance? This is an important one!

I'm just a farmer from the country, but where I come from, there's
just impedance. I don't know how you split the real part of that
complex number into two parts. Maybe where you come from, there's
"carbon resistor" resistance and "thin-film" resistance, too, but
I'm not sure how the electrons can tell the difference.


A Google search doesn't yield any real information on "feed point
resistance," so I guess that answering for myself, I can say
"sure...radiation resistance is the real part of the impedance of an
antenna; feed point resistance is an undefined term."

There *does* seem to be widespread use of the term "feedpoint
resistance," although definitions seem to be scarce as hen's
teeth. Just being the ignorant sorta guy I am, I tend to
gravitate towards the ones that define "feedpoint impedance;"
one could then say that feedpoint resistance is the real part
of that complex impedance. But that seems strikingly similar
to the definition of "radiation resistance." How very odd.

This is the very reason I pose the question! By making presumptions
you get yourself into trouble in understanding. Don't feel alone
though, because this is probably one of the most misunderstood terms
with antennas.

I don't think I was making any assumptions. The only term I
found DEFINED was "feedpoint impedance"; I would HOPE that
the definition of feedpoint resistance would be "real part of
feedpoint impedance," but not all engineering is consistent
in its terminology.

Again, I don't claim to be any sort of expert here. If you read the
original post in this thread it attempts to explain it with some
references too.

Uh...I read the originals. No equations, no definitions, and
the websites pointed to had the same sort of blather.


But in a nut shell, "radiation resistance" is an imaginary term when
dealing with antenna radiation. It is the amount of resistance that it
would take to dissipate the same amount of power that actually is
being radiated. It is pure resistance. No reactance involved.

Uh...I'm going to sound stupid here, but how do you measure "power
dissipated?" And does it include, for instance, the heat generated
by the wiring, etc.? Certainly that's power dissipated, but
somehow it doesn't seem to capture the sense of the thing you
describe above. Perhaps you could give me a definition of THAT
term as well.



FEED POINT RESISTANCE, on the other hand is the resistance (assuming a
vertical whip antenna here) seen at the base of the antenna , the
feed point.

Hunh? All I know about is impedance, I'm afraid, when talking
about AC signals. Can you express this thing in terms of
impedance? All I want is a simple equation...

It includes the radiation resistance of the antenna, the
loss resistance of any coil involved and the ground resistance. They
are all in series. This is with the reactance tuned out so the feed
point is purely resistive. Feed point impedance would be the same
thing but it may have reactance. In other words not purely resistive.

Ah...so now we have a circuit. It looks something like this:


AC+ -----###---%%%%------%%%%%%----AC-

where the first set of "%%%" signs represent a component
with the (presumed) linear behavior of the atmosphere
and the second resistor (it was all I could draw) represents
the (presumed) linear behaviour of the earth. And the ###
is some coil at the bottom of the antenna perhaps.

Maybe I've got this circuit wrong -- please correct me
if this isn't the model you're using. But if it IS the model
you're using, then each of the three components above has
a reactance at frequency f, and you can start writing out
the equations. [I should say "One could start writing out
the equations"; I'm getting the sense that you cannot.]

5. Do you know that the same amount of current that flows at the feed
point of the antenna is the same amount that flows in the radiation
resistance of the antenna? They are in series you know.

"Flows in the radiation resistance?" I don't honestly know whether
Larry knows more or less than you do, but at least I've never seen him
write something like this.

Me either that's why I ask the question. But first you must understand
what radiation resistance is. See above.

Now that I "understand" that radiation resistance is a resistance
that could be substituted for some part of the circuit and would
dissipate the same power as the replaced part did, BUT is
not actually a resistance of any part of the circuit, I cannot
see how any current flows in it.

6. I assume that you know ohms law and that if the same amount of
current flows in two series resistors that the larger resistance will
dissipate more power than the lower value resistor?

Um...Ohm's law tells me, if I recall correctly, that for certain
materials, the current flowing through them varies linearly with the
applied (DC) voltage; in these cases, the ratio of the two is called
the "resistance." If you think I'm being overly pedantic here, you can
ask "what's the resistance of a diode?" The answer is, of course,
"the current through a diode does not vary linearly as a function
of the applied voltage, so it does not have a resistance."
So you have to be careful about applying Ohm's law...

Oh the diode has resistance all right but in its case you have to
define what point on the curve you are looking at. Irrelevant here
though. Here we are talking about two linear resistors. Nothing
complicated.

No. A diode doesn't have resistance per se. It's true that the
voltage/current curve is (probably) differentiable at most points,
so one could speak of a "local resistance," but that doesn't
mean that you can say anything relevant with Ohm's law, except
if you're talking about very very tiny changes in voltage and
the corresponding tiny changes in current.

I *don't* believe we're talking about two linear resistors. I know
I must be stupid, but if antennas were just pairs of resistors,
no one could make a living designing them. I *do* suspect we're
talking about some sort of collection of impedances, but
I've lost any hope that you know anything about them.

7. Do you understand that there is a phase shift between current and
voltage across a coil in an AC circuit.

I would say "an inductor has a complex impedance that happens not to
be a real number, but rather one that has an imaginary part as well."

Also true. But it also has a real phase shift.

Uh...are you telling me that there are two different ways to
express a complex number, one of them in terms of the real
and imaginary parts that sum up to give the number, and the
other in terms of a magnitude and an argument? If so, deMoivre
beat you to it by a few years.


8. Do you understand that the radiation resistance gets very low in a
short antenna?

Uh...I guess I don't "understand" that. But if you'd write
out an equation or two, I might know what you meant by it.

Rr = 395 x (h/lambda) squared

Where Rr = radiation resistance
h = radiator height in meters
lambda = wavelength in meters

OK. It's an equation. THIS I can work with. Presumably since you
said so above, this is an equation for a vertical whip antenna.
And it's certainly true that in this equation, the term Rr increases
with the square of the height. I'm going to guess that one
of two things is true:

(a) This is your a DEFINITION of the symbol Rr, in which case
your conclusion in statement 8 is true, but not interesting, or

(b) You got this equation from somewhere where it is either
(i) empirically observed for a wide range of values of h and lambda,
and where Rr is actually defined so that it can be measured, or
(ii) proved, based on some assumptions about the circuit in question
(does it include a loading coil, for instance???) and a clear
definition of Rr,

In case b, I'd love to see the data and/or proof, but even more,
I'd love to see the definition of the thing being measured (or
appearing in the proof, as the case may be).

(referenced from the ARRL antenna handbook) like it or not. :)

Ah. Excellent. Forgive me for not having it with me; I'm in
France. But if you'd type in, verbatim, their definition (NOT
description) of radiation resistance, that would be great...

I am not going to say it again. Please READ the former posts. I have
shown the references many times and explained what the errors were.
And please, don't take my word for it if you have any doubts.

OK. I read 'em. The "explanations" are blather, and so I
guess I'm not gonna take your word for it.


If you are really interested in learning please read the original post
in this thread and go look at the web site of W8JI that I posted
there. He explains this very subject very well in detail. He even
throws in a little math for you.

I've read the original post. I think I grasped every germ
of truth in it.

And I've looked at W8JI's web page. The discussion in his
radiation_and_fields.htm page is particularly entertaining.
It's true that it ignores just a few things (like, say, Maxwell's
equations, and the relativistic relationship between the electric
and magnetic fields, and a few other things you can read about
in, say, Purcell's lovely book on Electricty and Magnetism,
semester 2 of the Berkeley Physics series; but what the hell
does Purcell know? After all, he's only got a Nobel prize in
physics, not a radio license...) but the gist is not uniformly
awful. The part where he says that there are electric fields,
magnetic fields, and electromagnetic fields is a pleasure to
look at. When *I* look at Maxwell's equations, I see phi,
the electric potential, and E, the electric field, and B, the
magnetic field. (And if you feel giggly, you can add, say,
zeta, the magnetic potential, and then declare it to be zero
everywhere). No mention of a THIRD field. Live and learn,
I always say. But I don't think that I want to live and
learn from that particular source...

By the way, he mentions a formula for radiation resistance,
too (claims it's a definition, but since he's given other
definitions above, this must certainly NOT be the definition.
Or maybe he's just a crappy writer. Anyhow, his formula
(for which he provides no proof) looks like yours. But
the constant differs by a factor of five. Go figure!

--John

"Vito" wrote in
:

"Larry W4CSC" wrote
I've never seen 20 watts produce a corona in air over 8" long....

Awww .... my buddy's 4-watt CB does it all the time. Of course he had it
peaked up at the truck stop but ... (c;

73, K3DWW

FINALLY, someone in this thread with some common sense....(c;

73, larry W4CSC

"Vito" wrote in
:

"Larry W4CSC" wrote
I've never seen 20 watts produce a corona in air over 8" long....

Awww .... my buddy's 4-watt CB does it all the time. Of course he had it
peaked up at the truck stop but ... (c;

73, K3DWW



Many of my older ham friends, who have now passed on to that great DX site
in the sky, I hope, could remember the days when the engineers told the
government any frequency over 2 Mhz was useless, so they gave it to the
hams.

The hams were too stupid to know it was useless, so went ahead anyways
making DX contacts on UHF (over 2 Mhz in those days). Damned engineers
have been stealing OUR frequency bands back ever since.....(c;

Gary's trolling got quite a few bites, today.....

Larry W4CSC

"Vito" wrote in
:

"Gary Schafer" wrote in message
...
On Tue, 04 May 2004 15:08:08 -0000, Larry W4CSC

...The 650 W amp melted the solder joints on the core ....


So about 97% of your power is going up in heat in the coils.

If Gary's right then 97% of 650 Watts otta get the coil so hot it
melts solder and ... OY!

That sounds dangerous to me, Larry. I think you otta send the whole
rig to me so I can check it out. With a DD degree I may be the best
qualified (c:


Many hams have made drawings of my little mobile antenna after feeling the
brunt of its force in an all-out horserace between their mobiles and mine.
For having only 20 watts output and being able to shed 630 watts of heat
without glowing red, it does quite well for itself....(c;

The coils get warm to the touch, but not as hot as our expert portends them
to be.....

Below 7 Mhz, where my car chassis groundplane becomes very inefficient,
it's best NOT to lean against the car when the transmitter goes off. A
friend of mine was leaning into the starboard window to see the dash lights
glowing with RF barefoot and got quite a HOT FOOT!.....(c;

Larry W4CSC
QRP means any power under 1KW, right?

-----------------------------------------------------------------
On Wed, 5 May 2004 22:38:54 +0000 (UTC), "John F. Hughes"
wrote:

On 2004-05-05, Gary Schafer wrote:

Well I don't profess to be any kind of expert either.

You claimed to be expert enough to tell that Larry doesn't
know what he's talking about, and to be able to distinguish
the "right" material from the "wrong" as published by ARRL.
That *sounds* like a claim...

Your definition of an expert is obviously different than mine.

Yes, the series resistance is the "real part". However it is not just
the DC resistance of the material in the coil. It is the AC resistance
of the material known as skin effect, which will be greater than the
DC resistance at radio frequencies. The higher the frequency the
greater the skin effect. The voltage applied is irrelevant.

Bzzt. The voltage applied is irrelevant only for linear components.
But if you want to assume that antennas (and/or coils) are linear
over the range of frequencies and voltages you're considering, I'm
willing to go with that.

Old debating tactic. Tell me I'm wrong, then agree.


Now I'll rephrase the last half of what you wrote:

Every component has an impedance that may be frequency-dependent.
We'll be working at a single frequency, f. The real part
of the impedance of a coil at frequency f will be called
the "series resistance."


Series resistance = Real ( Impedance(f))

There's an equation. It DEFINES the term on the left in terms
of two things on the right -- the "real part" function, which
was known to Cauchy for instance, and the Impedance, which you
can find in Horowitz and Hill, for instance. Write some
more things like that, and I'll be running right along with you.

Thanks but I'll stick with my definition.


3. Do you understand the difference between Radiation resistance and
feed point resistance? This is an important one!

I'm just a farmer from the country, but where I come from, there's
just impedance. I don't know how you split the real part of that
complex number into two parts. Maybe where you come from, there's
"carbon resistor" resistance and "thin-film" resistance, too, but
I'm not sure how the electrons can tell the difference.


A Google search doesn't yield any real information on "feed point
resistance," so I guess that answering for myself, I can say
"sure...radiation resistance is the real part of the impedance of an
antenna; feed point resistance is an undefined term."

There *does* seem to be widespread use of the term "feedpoint
resistance," although definitions seem to be scarce as hen's
teeth. Just being the ignorant sorta guy I am, I tend to
gravitate towards the ones that define "feedpoint impedance;"
one could then say that feedpoint resistance is the real part
of that complex impedance. But that seems strikingly similar
to the definition of "radiation resistance." How very odd.

This is the very reason I pose the question! By making presumptions
you get yourself into trouble in understanding. Don't feel alone
though, because this is probably one of the most misunderstood terms
with antennas.

I don't think I was making any assumptions. The only term I
found DEFINED was "feedpoint impedance"; I would HOPE that
the definition of feedpoint resistance would be "real part of
feedpoint impedance," but not all engineering is consistent
in its terminology.

Again, I don't claim to be any sort of expert here. If you read the
original post in this thread it attempts to explain it with some
references too.

Uh...I read the originals. No equations, no definitions, and
the websites pointed to had the same sort of blather.

I suppose it seems so when you have little understanding on the
subject and have a closed mind to such. But then I see your main
interest is to try and display your debating skill.



But in a nut shell, "radiation resistance" is an imaginary term when
dealing with antenna radiation. It is the amount of resistance that it
would take to dissipate the same amount of power that actually is
being radiated. It is pure resistance. No reactance involved.

Uh...I'm going to sound stupid here, but how do you measure "power
dissipated?" And does it include, for instance, the heat generated
by the wiring, etc.? Certainly that's power dissipated, but
somehow it doesn't seem to capture the sense of the thing you
describe above. Perhaps you could give me a definition of THAT
term as well.

Reread the above definition of radiation resistance carefully.




FEED POINT RESISTANCE, on the other hand is the resistance (assuming a
vertical whip antenna here) seen at the base of the antenna , the
feed point.

Hunh? All I know about is impedance, I'm afraid, when talking
about AC signals. Can you express this thing in terms of
impedance? All I want is a simple equation...

Keep reading.


It includes the radiation resistance of the antenna, the
loss resistance of any coil involved and the ground resistance. They
are all in series. This is with the reactance tuned out so the feed
point is purely resistive. Feed point impedance would be the same
thing but it may have reactance. In other words not purely resistive.

Ah...so now we have a circuit. It looks something like this:


AC+ -----###---%%%%------%%%%%%----AC-

where the first set of "%%%" signs represent a component
with the (presumed) linear behavior of the atmosphere
and the second resistor (it was all I could draw) represents
the (presumed) linear behaviour of the earth. And the ###
is some coil at the bottom of the antenna perhaps.

Maybe I've got this circuit wrong -- please correct me
if this isn't the model you're using. But if it IS the model
you're using, then each of the three components above has
a reactance at frequency f, and you can start writing out
the equations. [I should say "One could start writing out
the equations"; I'm getting the sense that you cannot.]

Yes by golly you have it! I think anyway, if I understand your
writing.
Yes each component has reactance as well as resistance. But when the
circuit is at resonance the reactance is tuned out. It is then a pure
resistive load containing only the resistive elements.
Resonance is when the capacitive reactance is equal to the inductive
reactance in the circuit. But then you knew that.
And it doesn't matter whether I can or can't write out any formula.


5. Do you know that the same amount of current that flows at the feed
point of the antenna is the same amount that flows in the radiation
resistance of the antenna? They are in series you know.

"Flows in the radiation resistance?" I don't honestly know whether
Larry knows more or less than you do, but at least I've never seen him
write something like this.

Me either that's why I ask the question. But first you must understand
what radiation resistance is. See above.

Now that I "understand" that radiation resistance is a resistance
that could be substituted for some part of the circuit and would
dissipate the same power as the replaced part did, BUT is
not actually a resistance of any part of the circuit, I cannot
see how any current flows in it.

No imagination? :)
It is part of the circuit in the form of the antenna that radiates the
equivalent amount of power.


6. I assume that you know ohms law and that if the same amount of
current flows in two series resistors that the larger resistance will
dissipate more power than the lower value resistor?

Um...Ohm's law tells me, if I recall correctly, that for certain
materials, the current flowing through them varies linearly with the
applied (DC) voltage; in these cases, the ratio of the two is called
the "resistance." If you think I'm being overly pedantic here, you can
ask "what's the resistance of a diode?" The answer is, of course,
"the current through a diode does not vary linearly as a function
of the applied voltage, so it does not have a resistance."
So you have to be careful about applying Ohm's law...

Oh the diode has resistance all right but in its case you have to
define what point on the curve you are looking at. Irrelevant here
though. Here we are talking about two linear resistors. Nothing
complicated.

No. A diode doesn't have resistance per se. It's true that the
voltage/current curve is (probably) differentiable at most points,
so one could speak of a "local resistance," but that doesn't
mean that you can say anything relevant with Ohm's law, except
if you're talking about very very tiny changes in voltage and
the corresponding tiny changes in current.

I *don't* believe we're talking about two linear resistors. I know
I must be stupid, but if antennas were just pairs of resistors,
no one could make a living designing them. I *do* suspect we're
talking about some sort of collection of impedances, but
I've lost any hope that you know anything about them.

In simple terms, any time you have a voltage applied to something that
does not conduct infinite current that something is said to have
resistance. It's resistance may not be stable and may change with
amounts of applied voltage but it is still resistance and good old
ohms law still applies for each static point. But then again this is
completely irrelevant to the rest of this.
Nice diversion attempt though.

You seemed to have formed your opinion long ago of how things work.
More debate tactics.


7. Do you understand that there is a phase shift between current and
voltage across a coil in an AC circuit.

I would say "an inductor has a complex impedance that happens not to
be a real number, but rather one that has an imaginary part as well."

Also true. But it also has a real phase shift.

Uh...are you telling me that there are two different ways to
express a complex number, one of them in terms of the real
and imaginary parts that sum up to give the number, and the
other in terms of a magnitude and an argument? If so, deMoivre
beat you to it by a few years.

Running low on tactics?


8. Do you understand that the radiation resistance gets very low in a
short antenna?

Uh...I guess I don't "understand" that. But if you'd write
out an equation or two, I might know what you meant by it.

Rr = 395 x (h/lambda) squared

Where Rr = radiation resistance
h = radiator height in meters
lambda = wavelength in meters

OK. It's an equation. THIS I can work with. Presumably since you
said so above, this is an equation for a vertical whip antenna.
And it's certainly true that in this equation, the term Rr increases
with the square of the height. I'm going to guess that one
of two things is true:

(a) This is your a DEFINITION of the symbol Rr, in which case
your conclusion in statement 8 is true, but not interesting, or

(b) You got this equation from somewhere where it is either
(i) empirically observed for a wide range of values of h and lambda,
and where Rr is actually defined so that it can be measured, or
(ii) proved, based on some assumptions about the circuit in question
(does it include a loading coil, for instance???) and a clear
definition of Rr,

In case b, I'd love to see the data and/or proof, but even more,
I'd love to see the definition of the thing being measured (or
appearing in the proof, as the case may be).

(referenced from the ARRL antenna handbook) like it or not. :)

Ah. Excellent. Forgive me for not having it with me; I'm in
France. But if you'd type in, verbatim, their definition (NOT
description) of radiation resistance, that would be great...

Being in France is a lame excuse. I am sure if you wanted to you could
find a copy there but I am sure that you can also find it in many
other books that deal with antenna theory. But then that would end
the argument too easily wouldn't it.

Already done several times.


I am not going to say it again. Please READ the former posts. I have
shown the references many times and explained what the errors were.
And please, don't take my word for it if you have any doubts.

OK. I read 'em. The "explanations" are blather, and so I
guess I'm not gonna take your word for it.

Meaning you don't understand them.



If you are really interested in learning please read the original post
in this thread and go look at the web site of W8JI that I posted
there. He explains this very subject very well in detail. He even
throws in a little math for you.

I've read the original post. I think I grasped every germ
of truth in it.

Careful you don't get infected by it.
Truth can be an awful thing to deal with.


And I've looked at W8JI's web page. The discussion in his
radiation_and_fields.htm page is particularly entertaining.
It's true that it ignores just a few things (like, say, Maxwell's
equations, and the relativistic relationship between the electric
and magnetic fields, and a few other things you can read about
in, say, Purcell's lovely book on Electricty and Magnetism,
semester 2 of the Berkeley Physics series; but what the hell
does Purcell know? After all, he's only got a Nobel prize in
physics, not a radio license...) but the gist is not uniformly
awful. The part where he says that there are electric fields,
magnetic fields, and electromagnetic fields is a pleasure to
look at. When *I* look at Maxwell's equations, I see phi,
the electric potential, and E, the electric field, and B, the
magnetic field. (And if you feel giggly, you can add, say,
zeta, the magnetic potential, and then declare it to be zero
everywhere). No mention of a THIRD field. Live and learn,
I always say. But I don't think that I want to live and
learn from that particular source...

I see you are trying hard to sneak in some of your credentials without
trying to make it obvious but you have failed. Are they imaginary or
real?

By the way, he mentions a formula for radiation resistance,
too (claims it's a definition, but since he's given other
definitions above, this must certainly NOT be the definition.
Or maybe he's just a crappy writer. Anyhow, his formula
(for which he provides no proof) looks like yours. But
the constant differs by a factor of five. Go figure!

I think that he has quoted well known antenna professors in his
definition. Ones you may not be familiar with since RF and antennas
are foreign to you as you have stated.
Are you now the new expert?


You have written many words and have said little of any substance.
Only to try and twist and turn statements to make them seem
unscientific.
You tell me that I am wrong in my explanation and go on to say in
the same paragraph you agree with me. (debate 101)

Maybe you view the discussion as a contest but I don't. I am only here
to try and help others understand a little about antennas.
You seem more interested in winning a debate rather than providing any
useful information to others.

Forgive some of my seemingly snide remarks. However I think they are
fitting with some of the amateur debating tactics you have presented
which add nothing to the discussion of antennas.
There is an entertainment value though.

Regards
Gary


--John

On 2004-05-06, Gary Schafer wrote:

Uh...I read the originals. No equations, no definitions, and
the websites pointed to had the same sort of blather.

I suppose it seems so when you have little understanding on the
subject and have a closed mind to such.

Nah. I think that it's pretty clear that the original posts had no
equations. I happen to think that mathematics is the language of
science, and so when words get vague and ambiguous, I ask for
mathematics. That's just my idiosyncracy.

In simple terms, any time you have a voltage applied to something that
does not conduct infinite current that something is said to have
resistance.

Ah. Now I can throw away my copy of Horowitz and Hill.

[description of website vs. E&M book by Purcell]

I see you are trying hard to sneak in some of your credentials without
trying to make it obvious but you have failed. Are they imaginary or
real?

Nah. I don't have any credentials here. Just an interest in
science. *Purcell* has credentials. I'm just a guy who likes
equations. You apparently don't. That's OK. We'll go about
understanding phenomena differently. It's a big world.

I have no idea whether you're right, Larry's right, or both
are wrong about loaded antennas. But I do know that you're
the wrong person for me to try to learn from, because you
aren't willing to write definitions or equations, and those
are what I use to understand science.

Fortunately, there are other sources of information out
there...

-John