Using NEC2 for Antenna Feed Design

When I jumped into the radio game with my new old Icom IC-745 transceiver, I really had no idea what I was doing.  I knew I needed an antenna, so I went to a 1990 ARRL Handbook and found the “Loop Skywire” antenna which seemed like the one for me.  The one resource I have is tall Douglas Fir trees, and I thought that a “Skywire” made sense hung from those trees.  The ARRL article gave the impression that it was hard to go wrong, so I spent a couple of days figuring out how to hang wire in trees and get the feed line down to my radio.  Turns out, the unused chimney was perfect for both supporting one corner of the loop and as a cable feed-through into the new “radio room” in the house.  So I strung the wire, connected it all up and then went to try it out.  To my chagrin, the transmitter balked at the arrangement and would not allow me to plow through the standing waves that were on my antenna feed.  The SWR meter on my transceiver indicated SWR > 3, at which point the output circuit would refuse to give more power.  So much for “hard to go wrong!”

The solution was clear — I needed an antenna tuner that would make the impedance match to the antenna feed line.  I found an old Heath Kit tuner which fit the bill and solved the problem.  But it irked me that I didn’t understand enough to avoid this issue in the first place.

I recently decided I wanted to compare signals from my two rigs on two antennas, and having only one tuner, I was stuck again with how to match that loop.  In the last couple of months I’ve become proficient using the NEC antenna codes, so I decided to see if they could provide guidance.  I use the 4NEC2 implementation by Aire Voors which is a very nice version of these venerable programs.  The code has the ability to model transmission lines as well as radiating elements; it seemed it should work to figure out the feed line.

Whenever trying to use a modeling program, the first thing I do is make sure I can get the program to give me answers to a problem to which I already know the answer.  That gives me confidence that I am not wasting my time doing something wrong.  For the transmission line problem, I set up a very simple line with a variable termination resistance and nothing else.

You set this up in NEC with a pair of “wires” that are the ends of the transmission line and not connected to one another.  The transmission line definition includes the line impedance and its length.  One end was fed with a voltage source; the other end included two more short segments to complete the circuit, one of which included a load resistance.

I know that if this line is terminated with a resistance that same as the characteristic impedance of the line, I should see no reflections; power should all go from source to load and the standing wave ratio (SWR) should be one.  If I run a frequency sweep in NEC, that is pretty much what I see.

The short wires I used to connect the load show up as reactance at the higher frequencies, but that is to be expected.  The model shows SWR close to one with everything close to the 50 ohms I specified for the line impedance and the load resistance.

Now we are ready to have fun.  In real life I expect the antenna to have about 150 ohms radiation resistance, and the big spool of co-ax I have is 75 ohm CATV cable.  So lets run that simulation with line that is 3/4 wavelength long at 14MHz.  (We will get into why I picked that length shortly.)

The cable is no longer matched to a 50 ohm source, so the SWR is no longer 1.  But as you can see it is closer to 1 at some frequencies than at others.  The impedance seen at by the source is now complex, with the real part varying between 150 and 37 ohms, depending upon the frequency.

Let’s back up and recall the physics of the anti-reflective lens coatings.  This idea is simply that if you have a coating that is exactly 1/4 of a wavelength thick, then the reflections from the two sides of the 1/4 wave coating will be exactly 180 degrees out of phase with each other and will tend to cancel, so reflection from the surface will be diminished because of the coating.  Any odd integer multiple of 1/4 wavelength will have this effect.

We want to do the same thing with our feed line, minimize reflections by making the feed line an odd integer multiple of 1/4 of the wavelength.  I chose the length of the line to be 3/4 of a wavelength at 14 MHz – the 20m band that is arguably the most important ham band.  My antenna is too far away to use just a 1/4 wavelength line.  If my antenna impedance really was 150 ohms, using the 3/4 wavelength 75 ohm line would bring the SWR down from 3 to a more tolerable 1.3 by just cutting the feed cable the right length.

But what about the other bands?  In general an odd integer quarter wavelength multiple for one band will not be  and odd integer multiple on another band.  The antenna resonances, and the feed line resonances are likely to interact in ways that are hard to predict.  This is where using the NEC model really helps to extend our design beyond the single band case.

First, let us look at a square 40m loop antenna with NEC.   The rendition on the right is produced by the very nice 3D viewer in 4NEC2.  We can look at the impedance sweep for this geometry and get an idea of what to expect when we build something like this.  The curves shown below are the SWR for a 50 ohm driver and the antenna impedance versus frequency.  The resonances at the loop fundamental, 7MHZ, and its harmonics, 14, 21, & 28 MHz, are clear to see.

It is also clear why my first attempt to get this antenna to work failed.  No-where does the 50 ohm SWR drop below 3.  The advice to just “connect it up and go” from the ARRL article was just plain wrong.  At the time, I also read some advice about making the feed line an integer number of half-wavelenghts in order to perfectly transfer the impedance characteristics at the antenna back to the other end of the line.  If you put those two pieces of advice together, you get the following SWR sweep – much like my antenna behaved when first I connected it to my transceiver.

The curve above was generated with the model, shown in the figure to the right that includes both the loop antenna and the transmission line feed.  The feed line is modeled as a radiating wire (the outside of the coax cannot be neglected) as well as the ideal transmission line.  If you look at the resonances at 7, 14, 21, and 28 MHz, you will see that indeed the half-wavelength feed (also half-wave harmonic to the antenna harmonics) does transfer the SWR at the antenna to the other end of the line.  Both the model for the antenna alone and the model that includes the half-wave feed line have SWR-50 of ~3.5 at 7 MHz and ~5 for the higher bands.  The antenna impedance is just too high to match well, so we are back at square one.

We’ve recreated the problem I was having with the model.  Now let’s see what happens when we use the odd quarter-wave line length instead of the half-wave length.

Low and behold, we have tolerable SWR on all of the main harmonic bands with nothing more than chopping the feed line in the right place!  Note that doing the arithmetic for all of the other bands gets complicated quickly with the interacting sets of harmonics.  The simulations come into their own as the complexity exceeds your intuition about what should be happening.

So modeling and simulation are one thing.  Proof is in the pudding!  I put this together and measured SWR of 1.5 at 7 MHz, 2.2 at 14 MHz, and about 3 at 21 MHz, so I can easily operate on the 20 and 40m bands.  However, after I went through the excercise to write this up for this blog post, I also realized how it should be done.

If you look back at the 40m Loop impedance plot, you will notice that at the antenna resonances, the real part of the impedance is between ~150 ohms and ~240 ohms for the upper bands.  The best solution is to use a 4:1 impedance transformer at the antenna and 50 ohm cable to the transmitter.  The reflected 200 ohm impedance will match admirably on all of the resonant bands without resorting to tricks with a quarter-wave feed as shown in the simulation below.

But back to the 1990 ARRL handbook where the construction directions for the Loop Skywire state, “connect the coaxial feed line ends directly to the wire ends.  Don’t do anything else.  Baluns or choke coils at the feed point are unnecessary.  Don’t let anyone talk you into using them.”

What can I say — I just plain disagree!  The model results don’t support such a statement nor does my experience.  Using a 4:1 current balun I manged to get SWR of <1.4 on all of the resonant ham bands on the antenna.  That’s the way it is supposed to work!

Update:  After a few more years of experience with antenna modeling, the reader that has made it this far might well find useful my descriptions of how to model feed lines with 4NEC2 in my slide presentation, Practical Antenna Modeling, and the explicit descriptions of Modeling Baluns and Transformers with NEC Codes in the linked article.