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I'm looking for a simple way to impedance match an array of two 50 Ω antennas so that when they are combined they appear as one 50 Ω load.

Assume that both antennas are identically constructed, are in phase with one another, and have the same VSWR very close to 1. The frequency the antennas are tuned to is 2.4 GHz.

Is there a simple “rule of thumb” method that I could use that requires little equipment?

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  • $\begingroup$ I'm Marthien I'm interesting for this answer make me have a some idea. my question is what if the combine antena is different, like the antena cable delta loop 40m and dipole tubing aluminum 40m ? and what if i must combine three antena with the different band like 20m + 15m + 10M ? thanks before for the answer. best regard YB1BBW-Marthien $\endgroup$ Oct 4, 2022 at 1:08
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    $\begingroup$ @marthientarihoran It's the feedpoint impedance of the antenna that matters, so if they are each a good 50Ω match separately at the same frequency it shouldn't matter if they are different in other ways. As to your three-antenna question that's discussed a bit in the comments below ham.stackexchange.com/questions/1764/… but the antennas you ask about are not used at the same frequency. You should open a new question e.g. "can I feed multiple different band antennas with one coax?" $\endgroup$ Oct 4, 2022 at 20:04

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The canonical solution to this problem is a Wilkinson power divider. There are of course other power dividers, but the Wilkinson is easy to fabricate, provides good isolation between the output ports, and is lossless when the output ports are equal and in phase, which is true for an ideal antenna array.

If you were to make one of these yourself, you'd probably do it with coax. However, it's easier to illustrate with microstrip:

microstrip power divider

P1 would be connected to your transmitter, and P2 and P3 to your antennas.

Between P1 and P2, and also between P1 and P3, are quarter-wavelength transmission lines having an impedance of $\sqrt 2 \cdot Z_0$. For your case that works out to $\sqrt 2 \cdot 50 \Omega = 70.7\Omega $. 75 ohm coax is close enough and easier to find.

Between P2 and P3 is a resistor that's twice the characteristic impedance. For your case, that's $100\Omega$.

Made with coax, it looks something like this (click for bigger version):

coax power divider

Although it's not impossible to fabricate this sort of thing yourself, doing so at 2.4 GHz is a bit of a trick, especially if you don't have test equipment. 2.4 GHz is a very popular band, and this is a very common device, so you won't have any difficulty finding a pre-made solution for purchase.

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  • $\begingroup$ Looks ideal for the scratch builder, can it be used to combine greater than 2 antennas so long as they are all of the same impedance and phase? $\endgroup$
    – Ben
    May 7, 2014 at 18:48
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    $\begingroup$ @Ben It can, in two ways. You can cascade them together, ie, power dividers feeding power dividers. This works great when the number of outputs is a power of 2. Somewhat less commonly, Wilkinson dividers can be constructed with an arbitrary number of output ports. The resulting layout gets pretty hairy though, and can't be realized in two dimensions, so cascading dividers can be the simpler approach. $\endgroup$ May 7, 2014 at 22:21
  • $\begingroup$ @PhilFrost-W8II: Thank you for the link. Alas, it's apparently moved to N-way Wilkinson splitters. $\endgroup$
    – David Cary
    Oct 14, 2022 at 18:12

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