**Here are some comments relating to the subject of current distribution
through loading coils as rehashed on rec.radio.amateur.antennas news group:**

**Posting by Cecil, W5DXP shedding some light on
the "theoretical" (Kirchoff and Ohm laws) arguments and their
propriety to the case: **

*"Assume a transmission line with an SWR of 10:1. Put a series inductor *

in series with the transmission line. Assuming negligible losses, the

forward current is the same at each end of the coil and the reflected

current is the same at each end of the coil. The question is: Do the

superposed currents, Ifwd+Iref, remain constant? Of course not, because

of phase shifts. With a large enough coil, one could cause a current

maximum point on one side of the coil and a current minimum point on

the other side.

That same principle holds true for standing wave antennas which are

antennas with (surprise!) standing waves. The current is NOT the same

at each end of the coil (unless a current maximum or current minimum

occurs in the middle of the coil). However, for traveling wave antennas,

the current at each end of a loading coil would be close to equal.

--

73, Cecil http://www.qsl.net/w5dxp"

**More info from Cecil, W5DXP on the subject: **

*"Yuri Blanarovich wrote: *

> What I was looking for is to see 1. if anyone else MEASURED the current in

> loading coils, and what results they arrived at (and if we are wrong, then

> where did we go wrong). 2. If this is right than to have modeling software

> implement it with least error. I would like to use that for optimizing, say,

> loaded elements for receiving arrays on low bands, optimizing mobile antennas,

> loaded multielement beams, etc.

Hi Yuri,

try this out for your argument in the other group. Using EZNEC:

Example 1: 102' CF dipole with loading coils in the center of each arm

to cause the antenna to resonate on 3.76 MHz. I get XL=j335 ohms.

Example 2: Replace the above loading coils with series inductive stubs

hanging down. Ten foot stubs with six inch spacing between the wires is

what I used. What happens to the current across that six inch gap is obvious

from the current plot using EZNEC. Hint: There is a step function across

that six inch gap just as there will be with a six inch coil.

Then ask: Why doesn't EZNEC treat these two cases the same way?

--

73, Cecil http://www.qsl.net/w5dxp"

**and ... **

"

Yuri Blanarovich wrote:

> There is too much reliance now going on modeling program results, ignoring
some

> realities.

*Yuri, *

here is a modeling result that you might like. :-) I took a 102' dipole

and loaded it in the center of each leg with an inductive stub that made the

dipole resonant on 3.76 MHz. I added a one ohm series 'load' to each side of

the stub. Drawing one leg of the dipole, it looks like this:

----------R2-+ +-R1----------FP--- ... other half

| |

| | inductive

| | stub

+-+

EZNEC reports 0.85 amps through R1 and 0.57 amps through R2, a difference

of 33%. If one could model the inductive loading reactance as an actual

physical coil instead of a lumped single point impedance, results would

be similar to the above.

Now here is something that might blow some minds. The inductive stub

above is ten feet long. That's about 1/8WL on 20m. A 1/8WL shorted stub

equals +jZ0. The results of running the above antenna on 20m is that the

current through R1 is 185 degrees out of phase with the current through R2.

At the time when the current through R2 is flowing toward the end of the

antenna, the current through R1 is flowing toward the feedpoint. Wonder

what Kirchhoff would say about that. If you replace the stub with a coil

of the same reactance, not much changes.

**Tell W8JI to stop using lumped circuit analysis when he should be using **

distributed circuit analysis. :-)

--

73, Cecil http://www.qsl.net/w5dxp"

**W5DXP:**

Yuri, my latest posting sheds more light. Apparently, W8JI doesn't

realize that there are two superposing currents phasor-adding together

to get the net current and the phase distribution between those two

current waves are opposite because they are traveling in opposite

directions. This is a characteristic of standing-wave antennas.

See what happens when one tries to ignore the component waves?

Because the two currents are traveling in opposite directions, any phase

delay through the coil shifts the phase of the two currents IN OPPOSITE

DIRECTIONS. Thus the total relative phase shift effect through a 10 degree

coil is 20 degrees.

Mark, NM5K wrote:

> Dunno...I finally got up enuff courage to wade thru a bunch of that

> myself. Both had some decent points..But....Just using my built in

> "BS" filter only, which rarely seems to fails me, and ignoring all

> other influences, I still have to side with Tom. I still think the

> current is fairly constant.

W5DXP:

The key to understanding is to realize that the net current is the

phasor sum of the forward current and reflected current (on a standing-

wave antenna). Assume a 10 degree phase delay through the coil on the

frequency of operation. Ifwd-in and Iref-out are on the same side of

the coil. Ifwd-out and Iref-out are on the other side of the coil.

Ifwd-in--> coil Ifwd-out-->

-----------------------////////////-------------------------

<--Iref-out <--Iref-in

Assume that |Ifwd-in| = |Ifwd-out| which satisfies Kirchhoff

Assume that |Iref-in| = |Iref-out| which satisfies Kirchhoff

Ifwd-in + Iref-out = net current on left side of the coil

Ifwd-out + Iref-in = net current on right side of the coil

Ifwd-out lags Ifwd-in by 10 degrees

Iref-out lags Iref-in by 10 degrees (Iref-in leads Iref-out)

Now let's assume that Ifwd-in and Iref-out are in phase. So current

on the left side of the coil equals Ifwd-in at zero degrees plus

Iref-out at zero degrees which is a current maximum point.

Ask yourself: Can we have a current maximum point on both sides of

the coil? I trust that answer is obvious.

Ifwd-out lags Ifwd-in by 10 degrees. Iref-in leads Iref-out by 10 degrees.

So current on the right side of the coil equals Ifwd-out at -10 degrees

plus Iref-in at +10 degrees, NOT a current maximum point.

Therefore, in this example, net current on the left side of the coil

cannot possibly be equal to net current on the right side of the coil.

--

73, Cecil http://www.qsl.net/w5dxp

**and summarized by W4JLE:**

*If we
feed an antenna at the current point, the current decreases as the*

voltage increases along the antenna element from feed point to end..

That being said, a coil replacing a segment of an antenna (in order to

physically shorten it) will exhibit the same properties (relating to

currents) as the segment it replaced.

## Posted By W5DXP:

(> W8JI comments)

> Cecil,

>

> Apparently you have never taken time to read what I actually said,

> and what Barry Booth W9UCW and Yuri said.

I came in late on the thread and have not read all the postings except

for yours. Please don't assume that I agree with Barry and Yuri 100%.

Here is one of your assertions picked at random:

> In a normal mobile or home antenna with even a somewhat reasonable

> loading coil design, the current is immeasurably different at each end.

Besides your one special case toroidal coil example, every measured
configuration has

the currents *measurably different* at each end. Measure the delay through

your toroidal coil and I will calculate that difference for you since

you are unable to measure it. There is no such thing as a real-world

coil with a zero propagation delay! Your above statement is false as

are a number of your other statements. I hate to waste bandwidth quoting

your false statements, but here are some of them:

> ... compared to

> antennas with proper inductors like the Bugcatcher, which has

> almost perfectly equal currents at each end.

A Bugcatcher is not a toroidal coil. The magnitude and/or phase

of the two currents is NOT "almost perfectly equal".

> In a well-designed system, the current is almost perfectly uniform.

All "well-designed systems" use toroidal coils? :-)

> 2.) In a normal mobile or home antenna with even a somewhat reasonable

> loading coil design, the current is immeasurably different at each end.

> For all practical purposes, it is identical because a common properly

> working current meter would never resolve the difference.

Your "common properly working current meter" proves it is measurably

different except for one special case toroidal coil.

> It (current) is exactly equal in a two terminal component, and in a

> typical reasonably mounted and constructed loading coil there is only

> a modest current reduction at best.

The 180 degree phase-reversing coil in Kraus' phased array is a

two terminal component which is small compared to the 1.5WL of

the wire in the antenna. The currents have opposite phases. Is

Kraus wrong?

> Model an antenna with EZnec, and look at the load.

Note: EZNEC makes an assumption about lumped inductive loads that is

not valid for real-world coils. EZNEC cannot be used to prove anything

about real-world coils. It seems obvious that you didn't know that at

the time you posted the above.

> The rule is this:

> Coil current is essentially equal at both ends, as long as the coil

> is not long compared to the length of the antenna.

>

> THE VOLTAGE can be (and is) different on each end of the inductor,

> NOT the current.

>

> Unless the coil has

> considerable length compared to the antenna length, it has the

> essentially the same current in one terminal as out the other.

>

> The CORRECT current distribution is shown in the ARRL Antenna

> Handbook in 16-6 figure 9 of the 18th Edition.

Note that an earlier figure (Fig 7 in the 15th edition) contradicts

the above. There is always a current step-function across a real-

world loading coil used in a physically short 1/4WL antenna. Your

quoted figure is the one that is wrong and needs to be corrected.

> Displacement current over the length of a small fractional wavelength

> loading coil that is not operated near self-resonance is minimal to

> the point of being immeasurable.

You *measured* it on *every* configuration except the toroidal coil.

Roy even *measured* it on a toroidal coil.

> When it (inductor) is a series circuit, the voltage increases and

> current remains constant.

This is what you posted and apparently once believed. Your own measurements

prove this to be a false statement. The current remaining constant in both

magnitude and phase violates the laws of physics.

> Unlike some have claimed, Eznec and Spice models MUST calculate currents

> accurately or the results are grossly wrong.

As has been proven, EZNEC does not calculate currents accurately.

I have EZNEC files to prove that if anyone wants them. One simply

cannot model a phase-reversing coil using EZNEC's lumped inductance.

> The current flowing in must equal sum of currents out.

Nope, in a phase-reversing coil, the current flowing in can be

one amp into each end (zero current flowing out). This was your

original basic mistake - using lumped circuit theory on a distributed

network problem.

> In a properly designed system with the coil reasonably far from
self-resonance,

> the current would be essentially equal at both ends unless the coil was very

> long compared to antenna length.

In your measurements, your coils are NOT "very long" compared to the

antenna length. A Bugcatcher coil is NOT "very long" compared to the

antenna length.

> I never said the current couldn't be different, I simply said it has

> nothing to do with the "electrical degrees" as Yuri and you propose.

Apparently, you have never taken time to read what I actually said.

I said every real-world coil has a delay through it and that delay

affects the superposition of the forward and reflected currents. On

my web page, I give an example of a coil with a 45 degree delay. It

seems obvious to me that delay can be almost anything except zero.

Believing that the delay through a coil can be zero violates the

laws of physics. Please don't confuse what Yuri has said with what

I have said.

> Despite the fact the electrical length "replaced" by the loading coil is

> about 60 degrees, there was only about 3 percent difference in current going

> into the coil and current coming out in Roy's measurements and NONE in mine

> with a toroid.

I gave you the formula for calculating the degrees occupied by the coil.

ArcCos(0.97) is 14 degrees. I didn't say it would be 60 degrees. I said

the degrees occupied by the coil can be estimated using ArcCos(Iout/Iin).

Incidentally, if the magnitude and phase of the current into and the

current out of your toroid are equal, your toroid violates the laws

of physics.

If there is no difference in current going into and out of your coil,

then there is zero delay through the coil. But there is a delay through

*every* real-world coil. Whatever that delay is, it affects the sum of

the forward and reflected currents. If your feedpoint impedance is

slightly inductive, a current maximum point exists inside the toroid

and could explain your unusual measurements. In that case, the magnitude

of the currents could be equal but the phases would be opposite.

> With a conventional small coil, Roy and I both measured about the same taper.

> Still only a few percent.

You said: "... the current is immeasurably different at each end." Now you

admit that you and Roy MEASURED it. Both statements cannot be true.

> Frankly like Roy I am a little embarrassed to have to argue something as
simple

> as how an inductor works.

Frankly, I am embarrassed that a well educated and otherwise knowledgable

engineer once believed the following statement: "In a normal mobile or home
antenna

with even a somewhat reasonable loading coil design, the current is immeasurably

different at each end.", and now won't even admit that statement/belief was

false even though the currents have been proven to be measurable. The discussion

had to be diverted from a normal bugcatcher mobile loading coil to a
hardly-ever-

used-for-mobile toroidal coil to try to save face.

In short, for every real-world coil, there is a difference in the magnitude

and/or phase of the net current-in compared to the net current-out. To

maintain that the current-in is ever equal in magnitude and phase to the

current-out in a real-world Bugcatcher coil is simply wrong.

--

73, Cecil http://www.qsl.net/w5dxp