Cecil,

Interesting.

I am quite familiar with Kirchoff's equation in regard to voltages
around a loop and his equation about currents at a node. Did I miss a
third equation regarding currents around a loop?

Hint: Kirchoff would not be the slightest bit bothered by this problem.

Reg, as usual, has it completely correct.

73,
Gene
W4SZ

Cecil Moore wrote:
Reg Edwards wrote:

The whole business can be mathematically modelled.


The point is that it cannot successfully be modeled
with the lumped circuit model where the current is
constant everywhere in the circuit. What would
Kirchhoff have thought about a coil with 0.1 amp
at the bottom and 0.7 amps at the top? It certainly
doesn't mean that 0.6 amps is flowing sideways. All
it means is that the relative phase of the forward
current and reflected current changes through the
coil and therefore the distributed network model
needs to be used.

Gene Fuller wrote:
I am quite familiar with Kirchoff's equation in regard to voltages
around a loop and his equation about currents at a node. Did I miss a
third equation regarding currents around a loop?

Nope, you missed an implication of Kirchhoff's current law.
Unequal currents into and out of a passive black box implies
the existence of a node inside the box.
--
73, Cecil http://www.qsl.net/w5dxp

Cecil,

Your response makes no sense at all. Unequal currents into and out of a
passive black box implies charge storage, which generally means capacitance.

You cannot have it any other way, with or without waves or reflections.
Conservation of charge is one of the most fundamental laws in nature.

Reg was correct.

73,
Gene
W4SZ



Cecil Moore wrote:
Gene Fuller wrote:

I am quite familiar with Kirchoff's equation in regard to voltages
around a loop and his equation about currents at a node. Did I miss a
third equation regarding currents around a loop?


Nope, you missed an implication of Kirchhoff's current law.
Unequal currents into and out of a passive black box implies
the existence of a node inside the box.

Gene Fuller wrote:
Your response makes no sense at all. Unequal currents into and out of a
passive black box implies charge storage, which generally means
capacitance.

Boundary condition: There's nothing but wire inside the black box.
--
73, Cecil http://www.qsl.net/w5dxp

Cecil,

This is getting more interesting by the moment. Have you now removed
some of the well-known physical attributes of wire and transmission
lines? Specifically, what happened to the L and C of the wire?

I have no issue with the use of network theory, reflection coefficients,
standing waves, or any other commonly used descriptions. However, none
of these mathematical conveniences change the fundamental physical laws.
If current, and therefore charge, appears to be unbalanced, then there
must be charge storage somewhere.

As Reg pointed out, the charge is stored in the capacitance of the coil.
No need to invoke any magic incantations about networks and standing waves.

In principle any of these problems can be solved with very basic
equations found in any E&M text. In practice it is extremely cumbersome
to do so, and that is why all of the network formulations have been
developed. Just don't fall into the trap of thinking that any new
physical behavior is created by the reflections and standing waves. I
believe in previous messages you have referred to that thinking as
"seduced by the math models."

73,
Gene
W4SZ

Cecil Moore wrote:
Gene Fuller wrote:

Your response makes no sense at all. Unequal currents into and out of
a passive black box implies charge storage, which generally means
capacitance.


Boundary condition: There's nothing but wire inside the black box.

Gene Fuller wrote:
I have no issue with the use of network theory, reflection coefficients,
standing waves, or any other commonly used descriptions. However, none
of these mathematical conveniences change the fundamental physical laws.
If current, and therefore charge, appears to be unbalanced, then there
must be charge storage somewhere.

Gene, the flaw is in your misunderstanding of the
fundamental physical laws, not in those laws.

We measure the net current at one end of a coil at 0.1
amp and we measure net current at the other end of the
coil at 0.7 amps (my web page example). The net current
*APPEARS* to be unbalanced, but appearances can be
deceiving. THERE IS NO STEADY-STATE CHARGE STORAGE
ANYWHERE IN THE SYSTEM. Does this violate any fundamental
physical laws? Of course not. Here's why (neglecting losses):

V*I*cos(theta) equals the same power at both ends of the
coil. That proves there is no steady-state energy storage.

V1*(0.7)*cos(theta1) = V2*(0.1)*cos(theta2)

This is a distributed network. A lumped circuit analysis
fails miserably when you try to use it in a standing-
wave environment and you have just proved it. That is
also the same mistake that W8JI and W7EL have been
making.

The forward current at the 0.7 amp point is 0.4 amps at
zero deg. The reflected current at the 0.7 amp point is
0.3 amps at zero degrees. The net current is the phasor
sum of those two component currents.

Inet = (0.4 amps at zero deg) + (0.3 amps at zero deg)
Inet = 0.7 amps at zero deg

The forward current at the 0.1 amp point is 0.4 amps at
82 degrees. The reflected current at the 0.1 amp point is
0.3 amps at -82 degrees. The coil causes an 82 degree
phase shift in both forward and reflected currents and
since their phasors are rotating in opposite directions,
the sign of their phase shifts are opposite.

The net current at this end of the coil is:

Inet = Ifor + Iref
Inet = (0.4 amp at 82 deg) + (0.3 amp at -82 deg)
Inet = 0.057 amps + 0.043 amps = 0.1 amp at zero deg

The fundamental physical laws are perfectly valid as has
been demonstrated here. It is your understanding of them
that seems to be the problem. You seem to have been fooled
by appearances and as a result, you chose the wrong model
with which to try to solve the problem. The distributed
network analysis was developed because the lumped circuit
analysis falls apart under certain circumstances. One of
those circumstances is the presence of standing waves like
the ones that exist in a 75m mobile antenna.
--
73, Cecil http://www.qsl.net/w5dxp

Gene Fuller, W4SZ wrote:
"This is getting more interesting by the moment."

There are plenty of coils in boxes which have different currents into
and out of their two ends.

A coil in a box used to be a common way to resonate a too-short 1/4-wave
(90-degree) whip. A company I worked for had many Land Rovers, trucks,
boats, and ships on and around the Argentine side of the island of
Tierra del Fuego.These were equipped with H-F SSB tranceivers. Mobile
amntenna was a stainless whip mounted atop a substantial fiberglass box.
The box contained the loading coil which was accessible for preselecting
the right coil tap to resonate the whip with the vehicle for a
particular operating frequency. The box also contained a motor-driven
band-switch to automatically change taps on the coil when the frequency
was changed on the radio.

I am well aware of the ability to resonate a 90-degree whip with no more
than the proper coil in series with the short whip on a base insulator.
I tuned every one of those coils for each of the frequencies we used in
Argentina with my own hands.

ON4UN has a graph, Fig 9-22 on page 9-15 of "Low-Band DX-ing" which
shows current distribution of a base-loaded whip, In his example, the
whip is 45-degrees long.. The loading coil provides the extra 45-degrees
required for resonance.

Current at the base of ON4UN`s whip is one amp times the cosine of
45-degrees, or 0.707 amp. The loading coil has an input of one amp.

With 1 amp into the loading coil and 0.707 amp out of the loading coil,
the coil definitely does not have the same current at both ends.

Best regards, Richard Harrison, KB5WZI

Richard Harrison wrote:
ON4UN has a graph, Fig 9-22 on page 9-15 of "Low-Band DX-ing" which
shows current distribution of a base-loaded whip, In his example, the
whip is 45-degrees long.. The loading coil provides the extra 45-degrees
required for resonance.

Current at the base of ON4UN`s whip is one amp times the cosine of
45-degrees, or 0.707 amp. The loading coil has an input of one amp.

With 1 amp into the loading coil and 0.707 amp out of the loading coil,
the coil definitely does not have the same current at both ends.

It's not that perfect in the real world but the basic concept
still applies. The actual current at the top of the coil is
somewhat higher than 0.707 amp because the current inside
the coil is greater than 1 amp. EZNEC says the current about
1/3 of the way up from the bottom of the coil is about 1.15
amp. The inductance of the coil forces the phase between
the voltage and current to increase. To maintain the same
V*I*cos(theta) power, the current must also increase.

The high flux fields developed inside the coil somewhat distort
the perfect current cosine wave found in a thin wire dipole so
it is not quite as black and white as ON4UN indicates.
--
73, Cecil http://www.qsl.net/w5dxp

Richard Harrison wrote:

ON4UN has a graph, Fig 9-22 on page 9-15 of "Low-Band DX-ing" which
shows current distribution of a base-loaded whip, In his example, the
whip is 45-degrees long.. The loading coil provides the extra
45-degrees required for resonance.

Those diagrams were highly misleading, and have been withdrawn from the
current 4th edition. That whole introduction to short verticals has been
completely rewritten and revised.

The problem was that the current profiles of the full-size and loaded
quarter-wave antennas were both drawn against a linear vertical scale of
*phase*. This not only misrepresented the physical lengths of the lower
and upper sections, it also misrepresented the length and effect of the
coil. This presentation is highly misleading, and the first victim was
the person who drew it, and then overlaid current profiles on it.

(I don't think this was ON4UN. When someone sets out to produce a
500-page book, they have to quote some things on trust from other
people; and it may take a few editions to iron out all the kinks. Much
more to the point, ON4UN is right at the leading edge of his subject,
and each edition contains something new and important.)

The replacement diagrams in the 4th edition are much better. They show
current profiles against *physical* height, and help bring out what's
really happening.

Current at the base of ON4UN`s whip is one amp times the cosine of
45-degrees, or 0.707 amp. The loading coil has an input of one amp.

With 1 amp into the loading coil and 0.707 amp out of the loading coil,
the coil definitely does not have the same current at both ends.

You can't quite those figures in evidence, because they were never more
than a speculation based on misunderstandings. When ON4UN came to think
about it, he quite rightly changed his mind.



This brings up another point that hasn't been mentioned so far in this
discussion: there is an important difference between purely inductive
loading, and the kind of loading you can get from any practical
inductOR.

Note the difference. An inductOR is a real-life electronic component, a
coil of wire. InductANCE is its main electrical property - but it isn't
the only one.

When a shortened antenna is loaded by pure inductance, you find the
following:

1. The magnitude and phase of the current flowing into the loading
inductance are both the same as that of the current flowing out (this is
a fundamental property of pure inductANCE). This means the current
distributions in the sections above and below the loading inductance
join up in a sharp kink.

2. What does go through a step change is the *voltage* across the
inductance. This changes in both magnitude and phase. For a typical
centre-loaded whip, the RF voltage is low in all of the bottom section,
but above the loading inductance it's very high indeed.

To repeat: this is the situation for loading with pure inductANCE.

(Sorry to keep shouting "ANCE!" and "OR!" like that, but I'll bet
someone still comes back with a reply that proves they didn't read what
I actually wrote.)

The diagram in ON4UN's 4th edition (Fig 9-44) shows these effects much
better than I can describe them in words. The diagram came from an
article by W7XC in QST for March 1990. I strongly recommend everyone to
look at these diagrams... but please don't treat them as 'bible text'.
Do your own thinking about it.

A different viewpoint on loading inductANCE is given in an article by
Boyer in 'Ham Radio'. This uses the 'antenna-transmission line analog'
theory... and comes to exactly the same conclusions about the effects of
loading inductANCE: it is simply there to resonate the capacitive
reactance that arises from having physically shortened the antenna.
(Ironically, ON4UN's worked examples and computer programs to calculate
loading inductance have always been based on this approach; the
conceptual error in early editions was only in that one diagram.)

With a firm grip on the way that pure inductANCE loads an antenna, you
are then in a good position to look at the differences that appear when
you use a practical inductOR.

With a real-life inductOR, you don't have pure inductANCE any more. It
is embedded in a component that is made from some length of wire, wound
into a coil that has a physical length and diameter, has capacitance
between its own turns, and also has capacitance to the straight sections
of antenna above and below it. The effects of the coil's inductANCE will
still be there, but you can certainly expect to see a lot of detailed
differences.

But the practical differences can't possibly be understood without that
basic understanding about inductANCE as a foundation. Without it, you're
building your house on sand.



--
73 from Ian GM3SEK 'In Practice' columnist for RadCom (RSGB)
http://www.ifwtech.co.uk/g3sek

Gene Fuller weote:
"Conservation of charge is one of the most fundamental laws of nature."

Unequal currents into and out of a passive black box are very simple to
produce. Suppose the black box contains a simple transformer with a
ratio other than one to one? The power can be constant but the voltage
and current must be different on input and output. R-F is a-c, not d-c.

Best regards, Richard Harrison, KB5WZI