## Sunday, January 8, 2012

### Antenna experiment - Delta Loop for 7 Mhz band

I  had a 80 m dipole that was not performing too well because it was only at 25 ft  height due to physical constraints in my backyard.

Looking at my options I decided to re-use the antenna materials and make a delta loop for 7 Mhz band.

Using Kok Chen's (W7AY) CocoaNEC software  I created a NEC2 model for Delta Loop.
Using a programming language resembling C it is really easy to create these models  - see Fig 2. and code sample below:

model("deltaloop - corner feed ")
{
real h, dh, fr, l, vf;
element _e1, _e2, _e3;

vf = 0.95;      //velocity factor of wire
fr = 7.1;       //frequency in Mhz
l = c/fr/vf;     // length l = 44.44662 m @ 7.1 Mhz
h = 5;         // height of the bottom h = 5m, apex at h+dh = 17.8m

dh = sqrt((l/3*l/3) - (l/6)*(l/6));

// three elements are each L / 3 length - using #14 AWG wire // and 21 segments for each element in the model
_e1 = wire(0, -l/6,  h, 0, l/6, h, #14,  21) ;
_e2 = wire(0, -l/6,  h, 0, 0, h+dh, #14, 21) ;
_e3 = wire(0,  l/6,  h, 0, 0, h+dh, #14, 21) ;

voltageFeedAtSegment(_e3,1.000000,0.000000,1);
averageGround();
frequencySweep(6.9, 7.3, 40);
}

 Fig1. Delta Loop Current Magnitude

 Fig2.  Model dimensions
 Fig 3. SWR plot of NEC2 model
 Fig 4.  3D shape of radiation pattern

The NEC2 model above is designed for  SWR minimum  at 7.1 Mhz.

Fig 3. shows that Zmag at resonance is about 140 ohms making SWR at the minimum about 2.8 : 1  without any impedance matching.

By changing model parameters like feed point, height and ground quality you can influence the impedance.

In my back yard I have about 70 ft tall tree so having the loop apex pulled up at  ~ 60 ft is doable with a proper support rope going through the top branches of the tree.

The model also shows the 3D radiation pattern that has a weird looking indentation on one side. This is also visible on the azimuth graph Fig 5.  below.

 Fig 5. Azimuth      and      Elevation

The  antenna feed point (Delta-C Center Insulator) is at the bottom loop corner  very close to the house - see the picture below. I added two ferrite chokes to suppress common mode current and  also put some new self fusing silicone coax tape around the PL239 connector to prevent moisture entering the coaxial cable.

 Fig 6.  Antenna feed point
 Fig 7.  The apex of the delta loop

The apex is barely visible in the Fig 7.  Following the black support rope from left bottom corner (from apex of my 18 Mhz delta loop) towards middle of the photo you can see a gray insulator in the middle of the branches.

 Fig8.  The 7 Mhz delta loop - 145 feet total wire length

I wanted to get the resonance frequency at 7.1 Mhz.  After doing some measurements using AIMuhf antenna analyzer I  added 11 ft of wire to the existing 80 m half wave dipole to convert it to a full wavelength 7.1 Mhz loop antenna.

Original 80 m antenna was 134 feet, so the new length is 145 feet (44.196 meters). This corresponds to the NEC2 model fairly closely  (NEC2 model L = 44.44 meters).

From the delta loop articles in the internet  you can get all kind of formulas such as  L = 1005/f  for the wire length.

As the local environment influences the antenna it is better to  make the wire a bit longer and use an antenna analyzer to cut it to the resonance length.

The SWR minimum 1.33:1 was at 7.1 Mhz  after adjusting the wire length.  SWR is below 2.0 between 7.0 and 7.2 Mhz as demonstrated by the red line in Fig 9. below. To validate AIMUhf results I measured  SWR and it was around 1.5 also according to my other SWR meters.

From the NEC2 model  I expected that I would need a 2:1 balun or some other impedance matching network as the model did show 140 ohm impedance at the feed point.

However, the measured Zmag (green line) is  37.5 Ohm at  7.1 Mhz resonance frequency. This measurement was not done at the feed point but at the end of a 112 feet 50 Ohm coax line. The coax line usually impacts the complex impedance.  At 7.1 Mhz  the wavelength is L =  (300/7.1)*0.82 = 34.65 m (113.67 ft)   as  Belden RG8X  that I am using has  velocity factor of 82%.  This is within 1% the length of the coax so we can ignore the coax line as it is 2x half wavelength and $Z_\mathrm{in}=Z_L \,$   according the wikipedia in this special case.

It looks like I need to analyze this discrepancy between the model and real antenna a bit more.

 Fig 9. AIMuhf Antenna Analyzer output

I looked at my coax cables to find out where this discrepancy is coming from.  I turned out to be more complicated than I thought.  I had 25 ft RG8X coax from ham shack to my feedthrough panel. Then I had 37.5 ft of  RG8U connected to 50 ft of RG213/U coax that was feeding the antenna.  Total length was 112.5 ft  and all this coax is supposed to be 50 Ohm but one  problem was that all these coax cables have different velocity factors.

RG8X should be 82%  (I measured physical length 25ft  and using AIMuhf came to actual VF = 77%).
RG213/U  should be 66% and  RG8U should be 78% (foam).  I did not measure VF  of these two latter ones.

I decided to simplify this coaxial setup and use only one type of coaxial cable.  I had 20 ft and 50 ft RG213/U cables that was just enough to get to the antenna feed point. After re-cabling this setup I measured coax length using AIMuhf TDR function, see Fig 10. below. I was surprised to see a big variation between 30 - 42 Ohms on the coax impedance that should nominally be 50 Ohms.  I re-calibrated AIMuhf  but got the same results.

 Fig 10.  25ft + 50 ft of RG213/U coax cables

Using this newly installed 70 ft  RG213/U cable I measured the delta loop again. The SWR minimum has shifted 10 kHz lower to  7090 kHz.

 Fig 11. Delta loop SWR measurement.
Using  VK1OD.net RF transmission line calculator and taking Zmag 45.7 from above to Zin  I got the following results:

# RF Transmission Line Loss Calculator

 Parameters Transmission Line RG-213/U Code RG-213/U Data source DSE Frequency 7.100 MHz Length 70.000 ft Zin 45.70+j0.00 Ω Yin 0.021882+j0.000000 S Results Zo 50.00-j0.39 Ω Velocity Factor, VF -2 0.660, 2.296 Length 275.63 °, 0.766 λ, 21.336 m Line Loss (matched) 0.355 dB Line Loss 0.356 dB Efficiency 92.13 % Zload 55.12+j0.17 Ω Yload 0.018142-j0.000056 S VSWR(50)load 1.10

Once again  the  NEC2 model and reality seem to be far off  -- the Zload results above  55.12 Ohms +j0.17  does not seem to match with  140 Ohms predicted by NEC2 model.

Looks like this  investigation will continue.

In any case I did work several stations with this new delta loop antenna with good results.