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has following statement: "The “two in series, two in parallel” connection maintains 300 ohms. "
This statement is fully obsolete. Series junction of transmission lines do not exist.
Author of this statement, probably assumed, that T-joint of out-of-phase signal is "series junction" which add voltages (hence increase impedance).
T-junction follow superposition rules, which are described good in 1st paragraph.
According to this superposition rules, if two out-of-phase (opposite phase) signals come to T-joint, 100% reflection occurs (zero energy is dissipated on load after T-junction).
Thats why from forward direction such phased antenna array will have deep null (theoretically infinite supression).
But when incoming wave come from different azimuth, out-of-phase (180 degree) lag is not mantained any more on T-junction termninals and it work good.
Radiation pattern of such stack has 2 strong side lobes and deep null.
Stacking of any arrays have 3 possible approaches:
1) Star topology
2) Tree leaf topology
3) bus topology
To stack 4 antennas one possible solution is 4 equal length transmission lines (no matter twin lead or coax) coming to T-joint (N=4). That's "star" topology.
Star topology has couple drawbacks:
1) with higher frequencies (microwave) it's getting harder and harder to mantain equal length in T-joint.
2) total transmission lines length (and associated losses) is overkill
3) impedance transformers with high trans ratio are hard to manufacture, you have to deal with insanely low impedances. High tr ratio also mean less bandwidth. Lambda/4 transformer 1:4 has less BW than 1:2 transformer. With high-power (TX) applications big ratios mean big reactances, big currents or voltages (high risk of failures).
With N=4 and UHF frequencies, star is fine, but if N>4 or f>1 GHz, star is not good choice.
Tree topology (2:1, 2:1, 2:1...) doesn't have this drawbacks. But number of bridges/couplers increase.
for N=4 you need 3 spliiters with "1:2" ratio.
Bus topology is not practical, as it require directional couplers with desired amount of energy to be "sucked" from main bus. That is extremely hard for R&D and production. The only benefit is single transmission line (minumum possible total length)
Tree topology is very often used in ham applications (Yagi arrays), in patch antennas (printed) and professional high-power applications, because it perfectly work with Wilkinson power divider (1:1 impedance ratio), which has some benefits over Lambda/4 transformer + T-junction.
Star topology with coax and N=4 is very easy (up to 1 GHz).
But I cannot imagine how to do N=4 with Zo=300 Ohm twinlead.
How geometrically 4 open (non shielded) lines can come in 1 point?