Today I started to get the parts for my phasing harness for stacking two of the 4el 2m WA5VJB Cheap Yagis. Basically this is planned as follows:
First, rather than attaching the cable directly to the elements this time (which are aluminium – as I'm building two more from aluminium that are planned to be identical) I plan to mechanically attach N sockets to the DE. Therefore today I grabbed the N connectors, and will soon also grab some aluminium strapping to bend into the shape required.
Then I need to organise the harness bit. Now the basic theory is, that when you connect two antennas in parallel they appear simply as two impedances in parallel. This means if both yagis are tuned correctly to an SWR of 1:1 and thereby appear as a 50 Ohm Zload (when connected with 50 Ohm cable), then if they were both simply connected we'd have the following:
Zin = (R1 x R2) / (R1 + R1)
Zin = (50 x 50) / (50 + 50)
Zin = 2500 / 100
Zin = 25 Ohm
So rather than having a SWR of 1:1 it'd be up near 2:1!!
Instead, we need R1 and R2 to appear as though they're 100 Ohm each. One way to do this is through the application of an impedance transformer. The impedance transformer I've gone with is to use a 1/4 wavelength (or odd multiple thereof – ie. 3/4, 5/4) of coax with a 75 Ohm cable. When this is then attached to a Zload of 50 Ohm, the Zin will appear as 100 Ohm. There by we'd end up with:
Zin = (R1 x R2) / (R1 + R1)
Zin = (100 x 100) / (100 + 100)
Zin = 10000 / 200
Zin = 50 Ohm
And there we'd have the SWR 1:1 we're all after. The basic setup would then be:
Two 4el 2m WA5VJB Yagis tuned to a SWR of 1:1, each connected to a length of an odd multiple of 1/4wl 75 Ohm cable (I've chosen RG-6). These two lengths can then connect into some kind of junction (still to determine) which can then be connected to with normal 50 Ohm cable – maybe some RG-213 or RG-8 – back to the radio.
(But keeping in mind that the lengths have to be the SAME odd multiple – so both 1/4wl or both 3/4wl – otherwise the phase will be out and potentially cancel or something.)
So the other item I grabbed today is some Belden 1189A (RG-6/U). That, combined with my N sockets puts me about half way along on the harness front. Still need some N connectors that will work with RG-6/U and also to decide what I'll do with the junction point – I'd love a nice simple N connector T Junction (but does such a thing exist??).
And one last thing I've learnt… Where I say 1/4 wavelength above, I mean ELECTRICAL wavelength – not mechanical. So you _don't_ simply do:
(300 / f) / 4
ie. for 144 MHz you don't do:
(300 / 144) / 4 =
2.083 / 4 =
You HAVE to factor in the Velocity Factor (VF) of the cable chosen. Now ideally this should be measured, but the starting point is the manufacturers data. For Belden 1189A this has a VF listed as 0.82, so we work it out like this:
((300 / f) * VF) / 4
ie. for 144 MHz we should do:
((300 / 144) * 0.82) / 4 =
(2.083 * 0.82) / 4 =
1.708 / 4 =
Once you've got that (which you can see is definitely different to the first calculation) you can start measuring it. I plan to do this with a dummy load and SWR meter; and the help of VK1OD's TLLC (http://www.vk1od.net/calc/tl/tllc.php). In theory if I hook up my planned piece of cable and all is correct I should get an SWR of 2.2:1.
Anyway, there you have it. My current understandings of a basic phasing harness and how far I've got. Could be wrong, and I've still got a bit to go, so I'll keep you posted. 😉
(Ohh, and I've used 300 in my calcs above, but maybe I should use the 299.8 – as in the Speed of Light – but I reckon that'll do. Actually, I do wonder how accurate I can really aim for. Hopefully I can get it fairly accurate, I just wonder what process W5UN used when doing the harness for his massive EME array – linked to earlier. The errors there would definitely compound until it was unusable I'd think….)