------50.1
Mhz examples:
A four port coax cable power divider is made of two pieces one-quarter
wavelength long and with a 'T' in the middle and at each end. Theory: on
each side, you bring two 50 Ohm lines together in parallel bringing the
impedance to 25 ohms. 25 ohms passes through one-quarter wavelength of 50
Ohm cable and becomes 100 ohms at the other end. The same thing happens on
the other side so at the center 'T' you have two 100 Ohm impedances coming
together in parallel and you are back to 50 ohms. This system uses no 75
Ohm cable.
Your other question was how long the 50 Ohm phasing lines should be with
the antennas configured in a collinear fashion. The simplest way to do it
is to keep the lines in one wavelength multiples. Like the inner two Yagis
might be fed with 2.5 wavelength cables and the outer Yagis would then be
fed with 3.5, 4.5 or 5.5 wavelength sections of coax.
Here is your formula.
11802.8/ freq in MHz = 1 wavelength
in inches in free space. So 11802.8 / 50.2 = 235.116 inches. For
one-quarter wavelength you divide that number by 4. 235.116 / 4 = 58.779
inches.
When using coax you must multiply this 58.779 times the velocity factor of
the coax. Let's say you are using LMR 400 for all your lines like I do.
LMR 400 velocity factor is 0.85 so 58.779 x 0.85 = 49.962". When we build
this 4-port divider, we put an 'N' connector on one end of about 51" of
LMR 400 and using a sweeper and scope we trim the cable until it is a
one-half wavelength resonant cable at 50.2 x 2 or 100.4 MHz. Now in actual
practice, we trim about one inch off this final length to compensate for
the length of one-half of the center 'T' connector. This system is several
MHz wide to the 1.2:1 VSWR point,s so if you miss by 0.5 MHz it won't
matter at all in the big picture. The most important thing is that both
pieces are the same electrical length (i.e. they are resonant at the same
frequency).
Use the same basic formula when cutting the phasing lines. One wavelength
is 235.116" x 0.85 = 199.85 inches. Put that number in your calculator
memory. After you have the minimum length of the cable required to reach
from the center power divider to the outer and inner Yagi feed points,
divide this 199.85 into the length you have come up with. Let's say the
outer length needs to be 65 feet or 780 inches. So 780 / 199.85 = 3.902
wavelengths. This tells you to make the cable just a bit longer or 4
wavelengths 4 x 119.85 = 799.39" or about 67 feet to start before trimming
to exactly four wavelengths at 50.2 MHz.
You can use an MFJ antenna analyzer to trim your cables. Put a 'T' on the
MFJ. On one side you terminate with a 50 Ohm load. Connect your cable with
one connector on the other side of the 'T' and 'sweep' the MFJ tuning for
the best match at around 50 MHz. Now go down in frequency until the VSWR
is 1.5:1 and note that frequency. Now go up in frequency until the VSWR if
1.5:1 and note that frequency. The midpoint between the two 1.5:1 VSWR
frequencies is your cable's exact one-half wavelength multiple point.
At each one-half wavelength multiple
an open cable reflects an open back to the 'T' on the MFJ, so the MFJ only
sees the 50 Ohm load. At any other frequency other than a multiple of the
first, the cable introduces every other impedance all the way up to a
short which occurs on an odd one-quarter wavelength long cable. To
summarize, an open one-quarter wavelength section reflects an RF "short"
back to the 'T' on the MFJ and an open one-half wavelength section
reflects that same open back at the 'T'. The MFJ does not like to 'see' a
short, so we go to twice the frequency where that cable is now one-half
wavelength long and it now reflects an "open" at the 'T' as if it were not
even there and the MFJ just 'sees' the 50 Ohm load again.
Phasing two 50 Ohm antennas together is done the same way as before, but
you must use two one-quarter wavelengths of 75 Ohm cable like RG-11 on
either side of the center 'T'. Barrels go at the outer end of the
one-quarter wavelength sections to couple to the two equal length 50 Ohm
phasing lines.
I should mention that you do not need to be in one wavelength multiples
for the phasing lines in this setup; just two equal lengths. Back to the
4-port system we discussed yesterday. If you had a classic configuration,
where four equal length phasing lines could be used, you would not have to
make them any particular wavelength multiple. You could just cut them all
equal and be done with it. We like to do things at one-half and one
wavelength multiples, so we can be sure they are all "electrically " the
same length. Another small advantage of using one-half and one wavelength
multiples is that the true impedance of the antenna feedpoint is mirrored
at each one-half wavelength down the line so when you look up each
individual phasing line you see the real antenna except for some slight
improvement due to feedline loss. In a good quality phasing line this
effect is is minimal.