Amateur Radio (G3TXQ) - Twin Feed experiment
The HexBeam pages on this web site recommend that low impedance feedline be used for interconnecting the various wire elements of the antenna. 50 Ohm coax is the usual choice, although coaxial cable can be difficult for the novice constructor to terminate neatly. Twin Feed would make construction a little easier, but it is only available commercially with characteristic impedances (Zo) of 300 Ohms or 450 Ohms - too high for the HexBeam application. Hence my interest in home-constructed low-impedance Twin Feed transmission line.
The usually-quoted approximation for the characteristic impedance of twin-feed with air as the
Zo = 120 Ln( 2*b/a)
where b is the centre-to-centre spacing of the wires and a is their diameter. However this expression is only valid for Zo > 200 Ohms; for lower values of Zo the more-complete formula is required:
Zo = 120*ArcCosh(b/a)
or if you wish to avoid the inverse hyperbolic function:
Zo = 120*(2*Ln(Sqrt(b/a-1)+Sqrt(b/a+1))-Ln(2))
I have produced a simple spreadsheet which calculates Vf and Zo using this formula. Either formula shows that decreasing the ratio b/a will reduce Zo. This suggests that low impedance Twin Feed could be constructed by placing side-by-side 2 large diameter wires which have relatively thin insulation. Stripping the insulation from one of the wires would reduce the spacing even further. This approach is shown in the two photographs on the right, and is often quoted as a simple way of producing a low impedance line.
I searched the electrical section of my local DIY store for suitable cable. Standard 6mm² UK earth wire seemed to have a high ratio of conductor diameter (3mm) to insulation thickness (0.9mm), so I purchased a short length with which to experiment. One wire was stripped of insulation and tied closely to the insulated wire with plastic tie-wraps every 100mm. The resulting Twin Feed had a measured Zo of 88 Ohms - very close to the predicted value of 90 Ohms for a pair of wires with this spacing and an air dielectric. It might be expected that the dielectric constant of the insulation would reduce Zo significantly; it doesn't, because it forms a relatively small part of the total dielectic material in which the field is contained.
It is clear that producing a Zo as low as 50 Ohms is challenging - the ratio b/a needs to be 1.088. The obvious solution is to use even thicker wire, but this makes the Twin Feed difficult to handle because of its stiffness. At this point I realised that using the braid of coaxial cable such as RG-58 might provide a solution: compared to its jacket thickness, its braid diameter is large and yet it is easy to handle.
The predicted Zo for Twin Feed using lengths of RG-58 (3.3mm braid, 4.8mm jacket) is between 64 Ohms and 110 Ohms, depending on what proportion of the field is contained within the PVC jacket. I measured the Zo as 73 Ohms and the Velocity Factor as 0.66, suggesting that the effective Dielectric Constant is about 2.3 (compared to 3 for PVC alone). But RG-58 is not an ideal choice: PVC makes a relatively lossy RF dielectric, and there is some evidence that manufacturers load their PVC jackets with carbon to make them more UV stable. There are better choices.
A comment by KD7NM pointed me in the direction of RG-400. It is a similar size to RG-58 but its Flourinated Ethylene Propylene (FEP) jacket makes a better RF dielectric. It is much less lossy than PVC, and although its Dielectric Constant is lower at 2.1 this is offset by the jacket being thinner. The photograph on the right shows a cross section of an experimental length of Twin Feed formed by placing two lengths of RG-400 inside heatshrink tubing.
The predicted Zo for Twin Feed using lengths of RG-400 (3.9mm braid, 4.9mm jacket) is between 58 Ohms and 84 Ohms, depending on what proportion of the field is contained within the FEP jacket. I measured the Zo as 68 Ohms and the Velocity Factor as 0.79, suggesting that the effective Dielectric Constant is about 1.6 (compared to 2.1 for FEP alone). Interestingly the ratio of the effective Dielectric Constant to the jacket Dielectric Constant is exactly the same as for the RG-58 case - a result we might have anticipated because the geometries are very similar. Although the Zo is not as low as the target 50 Ohms, this Twin Feed would be acceptable for the HexBeam application. Stripping the jacket from one of the cables would further reduce the Zo to about 58 Ohms
Given that the air surrounding the jackets forms a significant part of the total dielectric, we might expect that any water on the jackets could affect the characteristics of the cable. I took a short length of the "twin RG-400", placed a load resistor across one end, and measured the input impedance with the cable dry: it was 104 Ohms. I then sprayed the cable with water. The impedance immediately dropped by 30 Ohms to 74 Ohms. As it dried out the impedance slowly climbed - after 5 hours it had reached 98 Ohms and it finally recovered to 104 Ohms after 12 hours.
We conclude that it is possible to fabricate low characteristic impedance Twin Feed, but:
- Cables must be chosen very carefully. They should have large diameter conductors and thin insulating jackets. Close attention should be paid to the RF characteristics of the jacket material - it should be low loss and have high dielectric strength if it is required to handle high powers. PVC is not a good choice.
- Steps should be taken to protect the Twin Feed from rain in applications where stability of the Characteristic Impedance is important.