Simulation results show that CoCo is a High Gain, High Impedance/High SWR Antenna.
Due to its high SWR, an impedance matching device is required to be incorporated in the feed coax (i.e. between CoCo and Receiver) to bring down SWR to 1.5 or less, in order to fully utilize the high gain of CoCo.

The simulation is for CoCo alone, and does not include affect of feed coax.

As you have already pointed out, adding feed coax will change performance of CoCo, unless some feed isolation arrangement such as sleeve balun is provided. After adding sleeve balun at the feed point, the affect of feed coax becomes very small, and the antenna performs almost as the stimulation shows.

The addition of isolating arrangement however does NOT improve SWR / reduce impedance. An impedance matching arrangement will still be required to get good SWR (1.5 or less) and a good performance.

Above simulations were for for antenna in free space.
Now I have modified the simulation model (4-element and 8-element coco) for antenna at 7 meters (23 feet) above real ground.

This has affected the radiation pattern and the gain, but the SWR/Impedance did not change. It remained high at same values as those for antenna in free space, and still require impedance matching arrangement to bring down SWR to a decent value (1.5 and less).

There are various antenna impedance matching techniques, and this is an elaborate and detailed subject.

Test equipment like Antenna Analyzer or VNA are required for proper impedance matching.

To know about these techniques:

(A) Please refer to ARRL Antenna Handbook.
From the links given below, you can download:
(1) Chapter 18 “VHF and UHF Antenna Systems” http://www.qrz.ru/schemes/contribute/arrl/chap18.pdf
(2) Chater 26 “Coupling the Line to the Antenna” http://www.qrz.ru/schemes/contribute/arrl/chap26.pdf
This is not the latest edition of ARRL Book, rather few years old edition, but contains good enough info about antenna impedance matching.

Hi ab cd,
I’m watching this thread with interest as my best home-made antenna is a CoCo. If I can improve it that will be great.

Thanks for all your hard work on this.

Have you actually built a CoCo and tested theory against your analyser?

[Edit]

I’ve looked back at the charts in the first post and noted that SWR is getting smaller the more elements that are used. If you went to 18 or 20 elements, does the SWR come down below 2?

No, not yet, as I dont have any coco on hand to test.
All previous builds have ended up in the trash bin because of their poor performance.

Ok, I will make a 4-elements and an 8-elements coco, and test Impedance/SWR by Antenna Analyzer, possibly this weekend.
Lets see what the measurements tell.

Ok, I will model and simulate 18 element coco, possibly this weekend.

Higher the number of elements, higher are the number of segments. This results in consumption of higher computer resources, and higher simulation time.

For 12 element coco, it took my desktop’s 49% memory and about 20 minutes to execute the simulation. I dont know how long it will take for larger number of elements. Also, there is a limit of number of segments a model can have. By increasing elements, number of segments may cross this limit.

We build and use lots of CoCo’s anywhere from 10 to 22 element with something like 30 of them running right now

Like them because they are sturdy and survive bad weather conditions.

RG6 cabling, a satellite tv amp, and power injector (our standard install) makes them = or better than any of the commercial antennas we have tested (long cable runs).

Good performance of your CoCos shows that you have built all these CoCos meeting following conditions:
(1) Element length is determined using correct and accurate VF of coax used.
(2) Elements are cut accurately, and are assembled accurately & neatly.

The simulated models also meets these requirements (digitally). These should also perform good.
Now the big question:
How come an antenna performs good if it has SWR 4.6 (8-elements) or 4.2 (12-elements)?

The answer is:
If the antenna has such a big gain like 8.4 dBi (8-elements) or 10.4 dBi (12-elements), it can.
But how?
Well, lets see what happens when there is an impedance mismatch.

(1) Perfect Match (SWR=1)
With perfect match (Zant = Zrecvr, SWR=1), there is zero reflection, and full power available at antenna is transferred to the receiver.

(2) Decent Match (SWR=1.5)
With decent match (Zant=75 ohm Zrecvr=50 ohm, SWR =1.5), there is some reflection, but very little. This will result in slightly less than full power transfer between antenna and receiver. The exact value of this mismatch attenuation is 0.177 dB.

(3) 8-elements CoCo (SWR=4.6, Gain=8.4 dBi)
With high mismatch (SWR=4.6 dBi), the mismatch attenuation is 2.3 dB (see calculations below).
The net gain of antenna is 8.4 dBi - 2.3 dB = 6.1 dBi, STILL VERY GOOD

(4) 12-elements CoCo (SWR=4.2, Gain=10.4 dBi)
With high mismatch (SWR=4.2 dBi), the mismatch attenuation is 2.1 dB (see calculations below).
The net gain of antenna is 10.4 dBi - 2.1 dB = 8.3 dBi, STILL VERY GOOD

*CALCULATION OF MISMATCH ATTENUATION:

Formulae
Attenuation due to impedance mismatch = - 10 log { 1 - Γ² } dB, where Γ is Reflection Coefficient
Also Γ = (SWR-1)/(SWR+1)
Hence attenuation due to impedance mismatch = - 10 log { 1 - (SWR-1)/(SWR+1) ]² } dB

CASE-1: SWR = 1.5
Attenuation due to impedance mismatch
= - 10 log { 1 - (1.5-1)/(1.5+1) ]² } dB
= - 10 log { 1 - [0.5/2.5]² } dB
= - 10 log {1 - 0.04} dB
= 0.177 dB

CASE-2: SWR = 4.6
Attenuation due to impedance mismatch
= - 10 log { 1 - (4.6-1)/(4.6+1) ]² } dB
= - 10 log { 1 - [3.6/5.6]² } dB
= - 10 log {1 - 0.413} dB
= 2.3 dB

CASE-3: SWR = 4.2
Attenuation due to impedance mismatch
= - 10 log { 1 - (4.2-1)/(4.2+1) ]² } dB
= - 10 log { 1 - [3.2/5.2]² } dB
= - 10 log {1 - 0.378} dB
= 2.1 dB*

One factor that should be taken into account is the beamwidth Although the net gain is high, due to the narrower beamwidth you’ll receive less aircraft/positions than an equivalent net gain with good matching.

Obviously it’s a remarkable result if you don’t have any better solution, but it’ll never replace a properly matched antenna

Many thanks for the simulation. It looks like there is an optimum number of elements. Probably not worth going much above 12 elements for ease of construction and stability.

I’ve ordered the N1201 analyser so I can check the CoCo I have.

I’m still playing with directional antennas but the beekeeping season has started so time is short…

If your CoCo is already performing good, then improvement of reception will not be large by improving SWR.
If you dont have a VNA or Antenna Analyzer, attempts to improve SWR will be just trial-and-error and a shot-in-dark.

Benefit of SWR improvement is substantial if the CoCo is a poor performer due to use of inaccurate or assumed VF, or there are inaccuracies in construction.