Some years ago while I was dating the woman who would become my wife, I thought about setting up a station at her home in Nevada City, California, that I could use when I visited her. Talking with friends on the morning 75 meter net, one recommended that I install a full-wave 80 meter loop. Given her large lot and the pine trees in her back yard that could be used as supports, I thought, "Why not?"

I have a huge reel of phosphor-bronze antenna wire -- this is the same wire used to make portable wire antennas manufactured by such companies as TCI. From it I cut a 280 foot length (

*very*roughly 280 feet), added about 50 feet of 300 ohm ladder-line (which was all that I had), and put it up in the back yard with pine trees supporting the four corners in a very crude diamond shape.

The ladder-line was routed under the eaves along the back of the house to where a length of RG-142 B/U 50 ohm coax protruded through a hole in the wall. The ladder-line connected directly to the coax, and this coax then ran through the attic to my operating position.

I knew the SWR wasn't great, but my tuner could tune it and so I did not worry too much about it. And once tuned, the loop worked very well for the 75 meter morning net, and I was even able to make DX contacts on the higher bands. But I never looked very deeply into the antenna system's performance until I finally decided to bring my HP 3577A Vector Network Analyzer (VNA) up to the Nevada City QTH...

**What SWR did my transmitter really see?**Using the HP 3577A, I made an S11 measurement at the transmitter-end of the coax in my shack. Below is a capture over the range of 2 to 8 MHz.

Matlab vna_s11.m file provided by Dick Benson, W1QG

Matlab SViewer.m file provided by Dick Benson, W1QG

**Ouch! Not good -- the tuner was getting a workout !!!**Well, the obvious question now was, could I improve upon it?

Rather than guessing at how to improve the antenna, I decided to approach it analytically. And a good starting point would be to create an EZNEC model that I could then use to experiment at optimizing the antenna system.

__Creating an EZNEC Model of the Loop:__The big problem with creating a model, though, was that the antenna was already up in the trees, and I had zero desire to lower the whole thing down to the ground so that I could measure dimensions.

But I thought I could get close enough to the actual dimensions by measuring distances on the ground between supports and by estimating heights. Ditto for the length of the 300 ohm line.

Below is the model that I created, including the 300 ohm transmission line (which I projected horizontally from the antenna for ease of creating the model).

The EZNEC SWR plot of the impedance seen at the far end of ladder-line is:

Note resonances at 3.025, 4.7, and 7.525 MHz.

As one more check, I lugged the 3577A (and 35677A) outside (not easy, especially from a 2nd floor ham shack!) and made an S11 measurement at the end of the 300 ohm transmission line. Here's the SWR plot of that measurement:

Matlab SViewer.m file provided by Dick Benson, W1QG

So the frequencies of the resonance dips of the S11 measurement of the actual antenna with ladder-line are very close to those of EZNEC model -- confirmation that my model was, in my opinion, good enough.

The next step -- I couldn't easily measure the impedance at the actual loop's feedpoint, but I could use my EZNEC model to estimate it by shrinking the model's transmission line down to a very short length (e.g. 0.1 feet) and calculating SWR

Very nice! The resonances of the loop model are at 3.775 and 7.425 MHz. Just what I would expect to see for a loop cut to be resonant in the middle of the 80 meter band.

And here is SWR over the range of 3-30 MHz:

Note that the loop's resonances either hit or are very close to all ham bands (except 60 meters). But note, too, that the SWR at the higher frequency resonances worsens as frequency increases.

I had a 67 foot length of RG-8 (Belden 8237), terminated with N connectors, back at my home in the Bay Area, so I brought it up to Nevada City.

Next I needed a way to feed the loop that used a female N connector. Following a trip to the local hardware store...

(The B&W antenna feed at the upper right was used for temporary "proof of concept" testing, and then immediately retired!).

Raising the loop's feedpoint, with coax attached. Note the two 1:1 current baluns below the feedpoint. One consists of 5 turns through two FT-240 mix 43 and two FT-240 mix 31 cores, and the other is three turns through a mix 31 clamp-core.

__Measuring Performance:__The first thing I checked was the load that the transmitter would see. I measured S11 at the transmitter end of the coax (RG-8 from antenna plus RG-142 into the shack), with the reference plane set to be the 35677A's port 1 (i.e. 1-port calibration (short, open, 50 ohm load) done at the 35677A's Port 1):

**SWR at Transmitter**

Matlab vna_s11.m file provided by Dick Benson, W1QG

**with frequency, compared to the EZNEC model of the antenna's SWR at the loop feedpoint:**

*drops*Could this measured "improvement" in SWR at high frequencies be due to feed-line loss?

Fortunately, because the feed-line is now 50 ohm coax, it's pretty simple to measure the loop's feed-point impedance with the Vector Network Analyzer (VNA). It just requires that the VNA's reference plane be set to be the end of the coax that directly connects to the loop, itself.

But to do this, I needed to:

1. Lower the feed-point corner of the loop and disconnect the coax from the loop. It is this end of the coax that will become the VNA's new reference plane.

2. Perform a 1-port cal by sequentially attaching a short, an open, and a 50 ohm reference load to this end of the coax.

3. Re-attach the coax to the loop feed-point, raise it back into the air, and do an S11 measurement on the VNA!

Here's the result:

**SWR at Loop's Feed-point**

Matlab vna_s11.m file provided by Dick Benson, W1QG

The measured SWR minimum on 10 meters is about 4.5:1, while the EZNEC model shows 5.8:1. So not exactly the same, but it shows that my "eyeballing" of my loop's dimensions is pretty close.

The next obvious question was...

__How much power was I losing in my coax?__To calculate this I first needed to create a data file (.S2P file) of the coax cable (which consists of RG-8 and RG-142) based upon

*actual*measurements. This was done by measuring its four s-parameters (S11, S21, S12, S22):

Matlab vna_gui_1.m file provided by Dick Benson, W1QG

In this example, the frequency is 29 MHz, and the matching network to bring the SWR down to 1:1 is an LsCp network with an Lx of 425.5 nH and a Cp of 17.8 pF.

Total Loss is about 5 dB. Not very good, but an improvement over the 6.8 dB of loss that would occur if there were no matching network.

Note: to determine the matching network's values, above, I used the impedance-matching calculator at this website, as shown below:

**Loss with the original Ladder-line/Coax feedline:**For a comparison of performance, I also measured the four s-parameters (S11, S21, S12, S22) of the original ladder-line plus RG-142 coax feedline.

To do this, I had to bring the ladder-line end of the feedline into the shack...

...and attach it to the network analyzer!

The SimSmith Model which includes the resultant ladder-line/coax .s2p file:

I used the same .S1P file for the antenna as I had used when calculating power-loss with the coax feedline (no need to change that file because it is data for only the loop, itself, without any feedline).

Notice that the loss at 29 MHz is 2.9 dB, after matching. So at high frequencies the ladder-line/coax combo is

**than the coax-only feedline. (Even so, about half the power is being lost in the feedline).**

*better*

__Loss if add a 1:4 Impedance Transformer to Loop-end of Coax feed:__Dick, W1QG, mentioned that I should try the coax feedline with a 1:4 transformer connected to the loop at the loop feedpoint (i.e. 50 ohm port connected to coax, 200 ohm port connected to the loop, itself).

Here's the SimSmith model if an ideal, lossless, 1:4 transformer (turns ratio = 1:2)) is inserted between the antenna (L block in the diagram, below) and coax (A block in the diagram, below):

Note that the loss at 29 MHz (after matching) is now 2.5 dB. A significant improvement over the 5 dB loss without a transformer (but still, almost half the power is lost in the feedline at 29 MHz).

__Summary of Loss results:__The table, below, summarizes the loss results for the three different feedline versions (note, to save my time I skipped 160, 60, 30, and 12 meters, because I do not (yet) operate on these bands).

__Conclusions:__- The coax-only feedline beats the ladder-line/coax combination feedline on 80 through 20 meters.
- Above 17 meters, the ladder-line/coax combo beats the coax-only feedline.
- If we add a 1:4 transformer (in this case, lossless) to the coax-only feedline (attached at the loop), the coax-with-transformer combo beats all (although there can be an additional 0.4 to 0.5 dB loss on 80 and 40 meters, worst case).
- At the band edges on 10 meters, almost half the power is lost in the feedline, best case (with coax and 1:4 transformer)!

**So the next task is: build a 1:4 transformer (balun) and measure how well it performs!**

__W1QG's notes on measuring Feed Line Loss, using Matlab:__Dick is a tremendous MatLab enthusiast. Here are his thoughts on using MatLab to measure Feed Line Loss...

The SimSmith results seemed quite reasonable, but I have been fooled before.

What I wanted was an alternative method, and preferably one that did not require creating an LC matching network for each frequency of interest. Now, SimSmith may well do this, but it would require some digging.

I know MATLAB will do it, and it is a good check on the SimSmith results.

The key is the function called powergain:

Gp gives the powergain (note that it will be a LOSS for this work) given the:

1) s_parameters of the system (Coax in this case), including Zo that the S_parameters are based on.

2) Zl= the load impedance which is the antenna.

Note that Gp does NOT incorporate the source impedance.

The neat thing is the Gp result is what you would get if you conjugately match the input of the S parameter system. So creating the little LC match for each freq (a la SimSmith) is not needed.

Now, for the sake of completeness, and because it is trivial to do, Gt and Ga were also calculated.

Ga is what you would get if you just look at the line loss with Zs=50 ohms. Note that there is no Antenna information.

And Gt is what you get if you have a 50 ohm Zs, and the Antenna as a the load.

Here is the big picture.

The small discrepancy comes from the tiny but finite loss of the LC and inexact freq match of the 28.04 vs 28.01.

Here is a close up of 20 M:

Another interesting view is to plot Gp , Ga , and the Antenna SWR:

The only eye opener is how large the Feed Line loss can be a low frequencies where the *

**measured*** antenna SWR goes through the roof.
For further entertainment, the MATLAB "Publish" feature generated this html "report", and it is attached as well.

##
**Contents**

% Predicting Feed Line Loss with MATLAB

% Dick Benson

`clc`

clear all

close all

These are actual measurement data from K6JCA Loop Antenna

path=[pwd,'\'];

s= '180508 Nevada City Loop, Coax Fed, SOL CAL, 2-30MHz.s1p';

`[Antenna_Obj,Antenna_Notes,Antenna_State] = spar_read(path,s);`

s= '180508 Nevada City Loop Coax.s2p';

`[Coax_Obj,Coax_Notes,Coax_State] = spar_read(path,s);`

s= '180518 Nevada City Loop, Coax Fed, Two Choke baluns, 2-30MHz.s1p';

`[Composite_Obj,Composite_Notes,Composite_State] = spar_read(path,s);`

SWR will be the comparison metric.

Zo = Antenna_Obj.Z0; % assumed 50 ohms for all s-parameter files

FreqMHz= Antenna_Obj.Freq*1e-6; % AND assume Freq Vector is the same for all as well.

`Z_Antenna = gamma2z(Antenna_Obj.S_Parameters,Zo);`

`Gamma_Coax_Plus_Antenna= gammain(Coax_Obj.S_Parameters,Zo,Z_Antenna);`

`SWR_Measured = vswr( squeeze(Composite_Obj.S_Parameters));`

`SWR_Antenna = vswr( squeeze(Antenna_Obj.S_Parameters));`

`SWR_Predicted = vswr(Gamma_Coax_Plus_Antenna);`

`figure`

`plot(FreqMHz,SWR_Measured,FreqMHz,SWR_Predicted)`

legend('Measured Composite SWR','Predicted SWR by Separate Coax and Antenna Meas.')

title('Compare Prediction of Separate Coax, Antenna, to Single Composite SWR ');

xlabel('Freq in MHz');

ylabel('SWR');

text(7,12,'The agreement is VERY GOOD!')

`figure`

`h_lines = semilogy(FreqMHz,SWR_Measured,FreqMHz,SWR_Predicted,FreqMHz,SWR_Antenna);`

set(h_lines(3),'Color',[1 0 0],'Linewidth',1);

legend('Measured Composite','Predicted by Separate Coax and Antenna Meas.','Actual Antenna SWR')

title('Compare True SWR at the Antenna, to SWR at End of Feedline');

xlabel('Freq in MHz');

ylabel('SWR')

grid on

grid minor

text(7,130,['The actual antenna SWR is huge compared to what is ',char(10),...

' observed at the end of the coax.',char(10),' (NOTE:log Y axis)'])

`Zs=Zo;`

` `

Ga = powergain(Coax_Obj.S_Parameters,Zo,Zs,'Ga'); % Just Feed Line loss in the matched case.

Gt = powergain(Coax_Obj.S_Parameters,Zo,Zs,Z_Antenna,'Gt'); % System loss with 50 ohm Zsource.

Gp = powergain(Coax_Obj.S_Parameters,Zo,Z_Antenna,'Gp'); % This is the one we want !

% Note that Gp has no dependence on the source (Zs) impedance. It only depends on the

% S-Parameters (which need to have Zo spec'd) and the Load impedance (the

% Antenna)

%

`figure`

`h_lines= plot(FreqMHz,-10*log10(abs(Ga)),FreqMHz,-10*log10(abs(Gt)),FreqMHz,-10*log10(abs(Gp)));`

set(h_lines(1),'Linewidth',1,'Color',[1 0 0]);

set(h_lines(2),'Linewidth',1,'Color',[0 0 1]);

set(h_lines(3),'Linewidth',2,'Color',[0 1 0]);

xlabel('Freq in MHz');

ylabel('Loss in dB');

legend('Ga','Gt','Gp');

grid on

grid minor

text (7,16,['Ga=Available Power Gain',char(10),'Gt= Transducer Gain',char(10),'Gp=*Operating Power Gain*']);

`figure`

`[hAx,hLine1,hLine2]=plotyy(FreqMHz,[-10*log10(Gp),-10*log10(Ga)],FreqMHz,SWR_Antenna);`

set(hLine1(1),'Color',[0 1 0],'Linewidth',2);

set(hLine1(2),'Color',[1 0 0],'Linewidth',2);

set(hLine2,'Color',[0 0 1],'Linewidth',2);

legend('Operating Loss in dB','Matched Line Loss','Antenna SWR')

xlabel('Freq in MHz');

grid on

grid minor

ylabel(hAx(1),'Loss in dB');

ylabel(hAx(2),'Antenna SWR');

title('Loss and Antenna SWR vs Freq');

That's it for this post!

__MATLAB Scripts for Plotting VNA Data:__
Dick Benson's MATLAB scripts for capturing VNA data (e.g. from an HP 8753x) and displaying it (that I use above) can be downloaded from his page in the

**section: Dick Benson MATLAB files***MathWorks file exchange*

__Standard Caveat:__
Either I or Dick Benson (W1QG) might have made a mistake in our 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.

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