One question I had -- how can I use EZNEC to model feedline radiation of a coax-cable feeding an antenna?

Let start by looking at a dipole fed with coax...

__Feedline Radiation, Example 1: Coax-fed 80 Meter Dipole.__I'm going to start with an explanation that is also discussed elsewhere in excellent articles by the following authors (click on a callsign to be routed to their link): W0IVJ, W7EL, W2DU.

Let's take a look a a standard half-wave dipole up in the air, fed via coax from a grounded transmitter. Like this:

(Note: dipole and coax drawn sideways for convenience)

The tight coupling between coax shield and coax center conductor forces the currents to and from the source to be equal and opposite while they are within the coax, with the current returning to the source flowing on the inner surface of the shield.

In other words, the coax

*itself*acts as a very good common-mode choke (in the sense that it forces differential currents to return via the coax, rather than via a less desirable path). (For more information, please refer to: Noise Reduction Techniques in Electronic Systems, 2nd Ed., by Henry W Ott, page 51.)

*outside*surface of the coax, as shown below.

Note that I1 on the inner-surface of the coax (returning to the source) is composed of I2, the

*desired*current-path in the dipole element, and I3, the

*undesired*path on the coax shield's outer surface. And note, too, that I1 flowing on the

*inner*-surface of the coax shield is equal and opposite I1 flowing on the coax center conductor.

Given the currents, as drawn, above no current flows from ground directly to the source. This lets us redraw the model

*without*the source tied directly to ground:

Now the source only connects to the coax, and I have added a conductor (representing the

*outer-surface*of the coax shield, with the shield's length and dimensions) that runs from the antenna-feedpoint end of the coax to back to ground near the source.

*As long as we do not change the length of this conductor*(representing the coax shield), we can move the source towards or away from the antenna feedpoint with no change in performance (assuming ideal, lossless, coax). Like this:

Reducing the length of the coax in the above illustration to zero, our model reduces to:

Let's add our currents back in...

To minimize feedline radiation, we want to minimize I3, and the best way to do this is to add an impedance in the coax-shield-to-ground path at the source,

*which is actually the antenna feedpoint*, not the original location of the source (at the other end of the coax), as shown below:

Let's assume we are inserting a large resistance as a choke (rather than a reactance, which could worsen I3 current if it series-resonates with the impedance of the coax-shield-to-ground). How large does this resistance need to be to reduce I3 to an acceptable level?

Let's look at a worst-case model using EZNEC...

__Feedline Radiation, EZNEC Model, 80-meter Dipole Fed with 1/2 Lambda Length of Coax:__This dipole's elements has been tuned to resonate at 3.5 MHz. I will examine its currents and choking requirements at resonance (3.5 MHz) and at the other end of the 80-meter band (4.0 MHz).

The feedline length is 144 feet which, when represented by a conductor connecting one end of the dipole's feedpoint to ground (wire 5 in the EZNEC model, representing the coax shield's

*outer*surface), results in maximum current flowing on this conductor.

(I did mention that this was a worst-case model, didn't I?)

Let's look more closely at the model. Here's how the antenna is driven, at ground level:

...and here is how its feedpoint looks:

Notes:

- The transmission line (ideal, Zo = 50 ohms, Vf = 0.66) runs from the center of wire 4 to the center of wire 2).
- Note that one side of wire 4 connects to ground (via wire 7). This will let me check if any currents flow from ground back to the source.
- Wire 5 (and wire 6, which is in series with it down at the ground-end) represents the outer-surface of the coax shield (and thus the unwanted radiating path).
- The little red square in wire 5 (up near wire 2) represents a choke in wire 5 at the dipole's feedpoint whose impedance I can vary to model its effect upon current in wire 5, as well as its power dissipation.

Here are the antenna's currents:

Not good!

But we can improve upon this by inserting a choke (represented by a resistance-only impedance) into wire 5 up at the antenna's feedpoint (near wire 2).

Here's the impedance I will insert:

And here is its effect on the antenna system's currents:

Much better!

(

**A quick sidebar...**

What would happen if we were to place a choke at the

*source-end*of a feedline, when the feedline is 1/4 lambda long?

First, let's examine the currents with

*choke:*

**no**Looks good! (Note that the current for wire 7 (from one end of the source to ground) is shown to demonstrate that, within the limits of the EZNEC model, essentially no current flows from ground to the source)

Now let's add the choke (5000 ohms in wire 6)...

Now we have feedline radiation!

So the point is:

**When in doubt, with an antenna system in which the antenna is fed with coax, choke**

__at the antenna's feedpoint, NOT at the transmitter__.**...end of sidebar**).

Let's look at how different values of choking resistance affect wire 5's current, and how much power is dissipated by this resistance.

Here is a table summarizing the results of different choke impedances at 3.5 MHz:

Note that if I have an ineffective choke (e.g. 20 ohms, resistive), it could dissipate quite a bit of power!

__What happens to currents if we tune our transmitter to the other band edge at 4.0 MHz?__

Without any CM choke inserted, here are the antenna system's currents at 4 MHz:

There is some feedline radiation, but not as bad as the antenna system at 3.5 MHz. But this isn't surprising, because the feedline length is no longer 1/2 lambda long, so the impedance it presents at the antenna's feedpoint will be higher.

But, my goal is to look at currents in the worst-case scenario. So let's say that we were to add, at the dipole feedpoint, a choke whose reactance series-resonates with wire 5's reactance.

Also -- to more easily determine when the common-mode current is 30 dB down from the source current, I'm going to move the source up to wire 2 (the antenna's feedpoint) and eliminate the transmission line. We can do this because EZNEC's transmission line is perfect and does not radiate -- we are using wire 5 to represent the "imperfect" part of the transmission line which radiates. To illustrate this point, note that the current distribution of the "source-at-top" (i.e. in wire 2) antenna system, shown below, is essentially the same as the current distribution of the "source-at-ground" (i.e. in wire 4) antenna system, shown above.

With the source now at the top (wire 2), the source's current at that point is 1.0 A, rather than some other value with a phase angle. And so to meet the G3TXQ criteria, I simply need to increase the choke's resistance in wire 5 until the current through the choke is 30 dB down from the source's current in wire 2.

But first, let's force the current in wire 5 (representing the radiating feedline) to be

**maximum**(it's a worst-case analysis, after all).

If I add some reactance (-j350 ohms) as the series-load in wire 5 and adjust its value for maximum feedline current, the current through the choke is maximized, and the antenna currents become:

Here's a summary of different choke impedances for the off-resonance dipole:

__Notes:__

- 90 ohms resistance exhibits max power dissipation. And it is a LOT of power!
- Even at 1000 ohms of resistance, 14 percent of the transmitter power is dissipated in the choke. That is a lot.
- The choke's resistance must be at least 4000 ohms to reduce the unwanted feedline current to 30 dB below the transmit current. At this level, the power dissipated in the choke is 4.2 percent of the total power.

And again, I want to stress --

**I am looking at worst-case scenarios!**

Next, let's look at a full-wave coax-fed loop...

__Feedline Radiation, Example 2: 80 Meter Full-Wave Loop.__Let's look at a Full-Wave 80 meter loop, cut to be resonant at 3.5 MHz and again (like the dipole) feed from a grounded source with 144 feet of coax.

From my discussion, above, the source itself is effectively isolated from ground due to the common-mode choke behavior of the coax cable, itself. So I can simplify my model (just as I did when examining dipole currents at 4 MHz, above), and move my source to wire 6 at the loop's feedpoint.

Below is the loop. Note that wire 5 simulates the coax shield's outer-surface that connects one side of the loop feedpoint to ground, below:

Here's a closeup of the feedpoint, as well as data on the source and data on the series-load (which will be used to mimic a choke) in the first segment of wire 5.

And here are the currents:

Note the huge difference in at-resonance (3.5 MHz) currents from the dipole (earlier, above). Even though this loop has the

*same*feedline path to ground as the dipole (simulated by the 144 foot conductor to ground), it has

__very little feedline current__.

You can see that this feedline current is already 34 dB below the source's current (compared to 1 Amp), so: no choke is needed when the loop is

**operated at resonance**.

__What happens to currents if we tune our transmitter to the other band edge at 4.0 MHz?__

*are*common-mode currents:

The magnitude of the current on the coax shield, near where it attaches to the feedpoint (and at the point where I will insert a choke), is 1.44A.

I can simulate

**worst-case**feedline current by inserting +j110 ohms (inductive) in series into the feedline common-mode current path (inserted close to the loop's feedpoint). In this case, the current is 1.716 Amps.

To continue examining this worst-case scenario, let's keep this reactance of +j110 ohms, and add to it different values of resistance while examining how this resistance lowers the common-mode current as well as its power dissipation.

This table summarizes the results:

__Notes:__

1. When operated off-resonance, the choke's resistance

**must be 10,000 ohms**to reduce the worst-case common-mode current down to a level at least 30 dB below the transmit current of 1 amp (per G3TXQ criteria).

2. Significant power dissipation can occur even at fairly large values of resistance. Note that with a choke resistance of 4000 ohms, the power dissipation is 10 percent of total power.

__So my conclusions, comparing__

**worst-case**Common-Mode radiation scenarios on Dipole and Loop coax feedlines, are:1. An 80 meter loop, at resonance, requires little common-mode choking. The 80 meter dipole will require a choke.

2. A loop, off resonance, can require significantly more common-mode choking (at least twice as much) than a dipole fed with the same length of coax.

3. More power dissipation will occur in a loop's choke compared to a dipole's choke of similar resistance and worst-case reactance values.

__My Balun (and 80-Meter Loop) posts:__
80 Meter Loop, Part 1: http://k6jca.blogspot.com/2018/05/adventures-with-80-meter-loop-antenna.html

80 Meter Loop, Part 2: http://k6jca.blogspot.com/2018/05/adventures-with-80-meter-loop-antenna_30.html

Notes on 1:1 Baluns: http://k6jca.blogspot.com/2018/06/transmit-common-mode-chokes-11-current.html

Notes on Common-Mode Currents: http://k6jca.blogspot.com/2018/07/thoughts-and-notes-common-mode-current.html

__Standard Caveat:__I might have made a mistake in my designs, equations, schematics, models, etc. If anything looks confusing or wrong to you, please feel free to comment below or send me an email.

Also, I will note:

This design and any associated information is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.