Cecil, et al:

I think the real key to this mystery is to consider the
wave velocity in the loading coil. Admittedly at the
beginning of this debate (I have been following the
debate since the big W8JI / K3BU shootout on the
Topband email reflector) I was squarely in the lumped
element camp, but Cecil Moore's thought provoking
arguments have begun to give me reason for pause.
Here's why:

Under the lumped circuit view of things, there is no
delay between current going into the inductor and the
current coming out the other terminal. There is a 90
deg phase shift between the inductor current
and its terminal voltage, but there is no need to introduce
the notion of a delay between the input and output currents
in order to account for an inductor doing inductor like
things. All one needs to get inductor like behavior is a
two-terminal black box whose terminal voltage is equal
to L times the derivative of the current passing thru it
(e.g. L = di/dt). If one could build such a black box
(unfortunately, I am afraid it is akin to building an isotropic
radiator), it could be used in place of a real inductor in all
manner of tuned circuits and impedance matching
applications. In fact, we routinely use such a black box to
simulate real inductors in programs like Spice, EZNEC,
Touchstone, etc. And in many of these applications, the
ideal inductor is a reliable proxy for a real inductor.

Now let's consider a parallel two-wire transmission line.
If I have such a line with a Zo of say 450 ohms, and I
open circuit one end of the line and drive the other
end with an RF generator, I will get a nice sinusoidal
standing wave pattern along the length of the line that
bears a striking resemblance to the current distribution
on a linear antenna element. At 1/4 wavelength from the
open end of this line, I will be at a current maximum where
the input impedance is very close to a short circuit (
I am assuming a low-loss line with minimal radiation).
If I now break this 1/4 wavelength long line in the middle
and remove a section of line and replace it with a pair
of my black box ideal inductors (one ideal inductor
in series with each leg of the transmission line), I should
be able to adjust the value of the inductors such that I
can replace the missing section of line and achieve a
current maximum/short circuit condition at the input of
the line (e.g. resonance).

At this point, I should look at the knobs on my two black
box ideal inductors, read off the inductance values, and
note the readings for future reference. Now, given that my
inductors are ideal, there will be no current taper across
them as there was in the transmission line section
that they replaced. You can verify this with a circuit
simulator, like Serenade, Touchstone, or Superstar. This
derives from the fact that there is no propagation delay
through an ideal inductor. The current going into an ideal
inductor is always in-phase (and of equal magnitude) with
the current leaving it.

Okay now that we have dealt with the ideal case,
let's remove the black boxes and replace them with a
pair of parallel ganged roller inductors (actual real parts
you can buy on Ebay!). As with the black box case, I
should be able to adjust the inductance values of the
ganged inductors until I achieve resonance (maximum
current/minimum impedance) at the input to the parallel
wire transmission line. Again, I will note and record the
readings on the calibrated turns counters for future
reference. Now let's take a close look at the setup. I now
have two roller inductors with their axis parallel to the
longitudinal axis of the transmission line. The centerlines
of the two roller inductors are some distance "d" apart
from each other. If I just consider the 4 terminal
network formed by these two inductors, it begins to
look an awful lot like a parallel two-wire delay line of
length, L and some unknown characteristic impedance,
Zd and unknown velocity of propagation, Vp.

Uh oh!! now we have some delay associated with our
"loading coils". A TEM mode wave impinging on the
input to this 4 terminal "delay line" network will propagate
at some finite Vp. Thus if I terminate the output of the
real inductor network with the proper Zo, the input current
will be equal to the output current, but with some finite
delay between the input current and the output current.

Now if I reinsert this delay contraption back into my
450 ohm two-wire line, it will still produce the same
resonant condition as before (I didn't change the
inductance settings), but now that I know it has some
delay associated with it, I should expect to see some
taper in the current along its length. Of course, the fact
that the Zd of the "delay line" doesn't necessarily match
the Zo of the 450 ohm line probably complicates
matters. I'll most likely generate reflections at the
input to the inductor assembly, and re-reflections at
the output (reward traveling wave). Still, I have satisfied
the condition for generating a taper across these real
inductors. After all, borrowing from Cecil Moore's
argument, the delay along a linear mismatched
transmission line is what is responsible for the
observed taper in the current (e.g. standing wave).

Now for the $64,000 dollar question. What is the Zd
and Vp of the ganged roller inductor assembly. Will
the Vp necessarily bear some fixed relationship to
the inductive reactance of the inductors, or will this
depend on the form factor of the inductor assembly.
Will the length of the inductor assembly divided by
the wave velocity, Vp be equal to the delay of the line
section that it replaced, or will this delay depend on
the form factor of the inductor assembly (using ferrites
versus air core inductors, I can easily envision two
pairs of parallel inductors with the same inductive
reactance, but very different form factors). Will the
value of inductive reactance needed to "resonate" my
loaded transmission line vary with the delay and or
form factor of the parallel loading inductors, or will
this value be fixed and equal to the value of inductive
reactance required when I was using the ideal "black
box" inductors?

Hopefully you alll see where I am going with
this. What say, Gents?

73 de Mike, W4EF.....................................

"Cecil Moore" wrote in message

Jimmy wrote:
lumped inductance = lumped change in current.

Actually, I think the assertion was that
lumped inductance = no change in current.
--
73, Cecil http://www.qsl.net/w5dxp

Michael Tope wrote:
Will the
value of inductive reactance needed to "resonate" my
loaded transmission line vary with the delay and or
form factor of the parallel loading inductors, or will
this value be fixed and equal to the value of inductive
reactance required when I was using the ideal "black
box" inductors?

Hopefully you alll see where I am going with
this. What say, Gents?

Hi Mike, good posting. I admire open, questioning minds. I
just added some information on this subject to my web page.
Although there is some relationship between inductance and
delay, I hardly had to mention inductance at all. The phases
of the forward current and reflected current are changing in
opposite directions. Given any delay at all, the magnitude of
the net current will change through the coil (given a typical
mobile antenna coil). The electrical length of a mobile antenna
loading coil can be approximated by finding the angle whose
cosine is (net top current)/(net bottom current). Note that this
estimate works for loading coils installed in electrical 1/4WL
monopoles or electrical 1/2WL dipoles, not for the general case.
--
73, Cecil http://www.qsl.net/w5dxp



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Michael, W4EF wrote:
"Cecil Moore`s thought provoking arguments have begun to give me reasonn
for pause."

It`s been said the key to enlightnent is repetition, repetition, and
repetition.. It must be so.

A series resonant circuit is the usual form of a standing-wave antenna.
Inductance, capacitance, and resistances due to radiation and heat
conversion are unevenly distributed along the antenna. As King, Mimno,
and Wing say in "Transmission Lines, Antennas, and Wave Guides" on page
86:

"Inductance and capacitance as used for near-zone circuits with uniform
current cannot be defined, and ordinary circuit analysis does not
apply."

Best regards, Richard Harrison, KB5WZI

Cecil, W5DXP wrote:
"I hardly had to mention inductance at all."

Imductance equals delay. That`s why inductors are called retardation
coils.

In a resistor, current varies exactly in the same way and at the same
time as the applied voltage. Volts and amps are in-phase.

In an inductor, current is delayed and builds from the time that voltage
appears across the inductor. In a lossless (pure) inductance, current
lags the applied a-c voltage by 90-degrees. When the voltage is maximum,
current is zero, and when the voltage is zero, current is maximum.

90-degrees represents some fraction of a second, depending on cycles per
second as 90-degrees is the time required for 1/4-cycle. The higher the
frequency, the shorter the time represented by 90-degrees.

Loss in an inductance makes an impedance composed of inductive reactance
and resistance. As current is delayed in reactance by 90-degrees, but is
in-synch in a resistance,
Pythagoras gives us the total impedance, and the phase angle of the
resultant impedance is an "operational vector", not a "field vector".
The angle of current in the impure inductance which is made with the
applied voltage is easily determined with trigonometry or graphical
methods. An operational vector is also called a phasor. Delay can vary
from 0 in a pure resistance to 90-degrees in a purely reactive circuit.

Inductance makes current lag by 90-degrees. Capacitance makes current
lead by 90-degrees.

Broadcasters use a T-network called a 90-degree phase shifter. All three
reactances have the same impedance as the input and output impedance.

For example, two 50-ohm reactance coils are connected in series in the
signal path. A 50-ohm capacitive reactance is connected between the
junction of the two coils and the other side of the circuit (ground).

One of the coils cancels the capacitive reactance, leaving a pure
inductive reactance of 50-ohms in series with the circuit to cause a
90-degree phase lag. Often ganged variable inductors are used in the
90-degree phase shifter to produce the exact delay required and this has
almost no effect, less than 1%, on output current magnitude from the
phase shifter over a plus or minus 15-degree phase adjustment range.
It`s simple trigonometry.

Best regards, Richard Harrison, KB5WZI

On Tue, 2 Dec 2003 09:24:17 -0600 (CST),
(Richard Harrison) wrote:
"Inductance and capacitance as used for near-zone circuits with uniform
current cannot be defined, and ordinary circuit analysis does not
apply."

Hi Richard,

I thought this was dead long ago. Your statement is true of course,
but it seems - like the custom of putting a coin in the mouth of the
recently deceased - arguments have to be invented to push us all on
across the Styx.

73's
Richard Clark, KB7QHC

Richard Clark wrote:
"I thought this was dead long ago."

So did I. This recent posting is a repetition for me, but sometimes
repetition is needed for those who weren`t there in whole or in part for
the earlier postings.

I don`t expect anyone to accept a statement without proof from me that
ordinary circuit analysis does not apply to antennas, but from 3 E.E.
Sc. D.`s who were at the time they made the statement giving their very
best for victory in WW-2, I would expect some serious consideration and
at least a first assumption that the opinion is correct.

Best regards, Richard Harrison, KB5WZI

Richard Harrison wrote:
It`s been said the key to enlightnent is repetition, repetition, and
repetition.. It must be so.

Drops of water can wear away a rock.
Drops of truth can wear away sacred cows,
even when embedded in granite brains.
--
73, Cecil http://www.qsl.net/w5dxp



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On Tue, 02 Dec 2003 16:45:34 -0600, Cecil Moore
wrote:

Richard Harrison wrote:
It`s been said the key to enlightnent is repetition, repetition, and
repetition.. It must be so.

Drops of water can wear away a rock.
Drops of truth can wear away sacred cows,
even when embedded in granite brains.

And there are some who **** on your leg and try to convince you its
the rain - Judge Judy

Gentleman,

The point of my post was not to point out the obvious
fact that lumped circuit analysis has some limitations
when used in the context of antenna loading coils. The
debate (at least the one I am familiar with), was whether
or not the current magnitude across an antenna loading
coil varied as the current would vary in a linear section
of antenna having same physical length as the loading
coil, or whether the current magnitude would vary as the
current would vary in a linear section of antenna have
the same physical length as the section of antenna that
the loading coil replaced.

In either case, distributed effects not accounted for
in simple lumped element models are recognized to be
at work. For the former scenario to be true, the current
retardation through the loading coil is presumed to be
roughly equal to that observed in a linear section having
the same physical length as the loading coil. In this case
the retardation would be Tau = length physical/Vp. This
scenario recognizes that distributed effects are at work
(hence the small, but finite current taper), but suggests
that the dominant factor responsible for the loading of
the antenna is the phase shift between the inductor
current and the voltage across it.

The latter case also suggests that distributed effects are
at work, but to a much greater degree than in the former.
In this case, the loading of the antenna is presumed to
be the result of the large current retardation introduced by
the loading coil. In this case, the retardation is presumed
to be Tau = length effective/Vp or Tau = length replaced/Vp.
In this scenario, the effect of the phase shift between the
loading coil current and the voltage across its terminals
seems to be considered incidental and is largely ignored.

The point of my loaded transmission line example was
to show that under either set of assumptions, the
loading coil will produce the desired result. That is to
say that it will load the physically short structure (in the
case of my example, a transmission line) thus bringing
it into so-called resonance. Thus the fact that the loading
coil produces the desired result (e.g. input impedance
match) can't be pointed to as proof that one physical
mechanism is dominate and the other is not. The
transmission line stub loading network doesn't have to
behave the same way as the lumped inductor loading
coil to produce the same desired result (e.g. input
impedance match, resonance, or whatever you want to
call it).

What I am getting at, is that both camps may be
wrong. The answer may lie somewhere in between
these two extremes (e.g. taper equivalent to physical
length vs taper equivalent to electrical length), but this
isn't attractive because its ambiguous and doesn't make
for nice diagrams that can be placed on websites, in
textbooks, or in antenna handbooks (not to mention
all of the accompanying self-righteous chest beating).

73 de Mike, W4EF.................................

P.S. for those of you who have already heard all this
please accept my apologies as I missed out on last
months debate.


"Richard Harrison" wrote in message
...
Richard Clark wrote:
"I thought this was dead long ago."

So did I. This recent posting is a repetition for me, but sometimes
repetition is needed for those who weren`t there in whole or in part for
the earlier postings.

I don`t expect anyone to accept a statement without proof from me that
ordinary circuit analysis does not apply to antennas, but from 3 E.E.
Sc. D.`s who were at the time they made the statement giving their very
best for victory in WW-2, I would expect some serious consideration and
at least a first assumption that the opinion is correct.

Best regards, Richard Harrison, KB5WZI

Michael Tope wrote:
What I am getting at, is that both camps may be
wrong. The answer may lie somewhere in between
these two extremes ...

As I understood it, there is an extreme on only one side. One side
says the current through a loading coil doesn't change. The other
side says that the current through a loading coil does change.
You can look at the decrease in the feedpoint impedance of a loaded
antenna Vs a wire antenna and prove that the coil doesn't exactly
replace that length of antenna. The coil is a more efficient inductor
and less efficient radiator than the wire it replaces which results
in a higher net current at the feedpoint. To the best of my knowledge,
no one has said there is an exact 1:1 correspondence between the coil
and the wire it replaces. The correspondence is only approximate.
--
73, Cecil http://www.qsl.net/w5dxp



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