Power dividers and gain

Let's say you have an antenna with 5 dB gain. If you wanted to stack this in a 2 bay the theory is that gain would be increased by 3 dB totalling 8 dB of gain (or 4 bay with 11 dB gain).

But isn't there an insertion loss of 3 dB in a 2 way splitter (and 6 dB in a 4 way splitter) since input power is equally divided between the ports? Wouldn't that mean that the total amount of ERP don't increase? Am I missing something here?

The "gain" comes from resulting radiation pattern which is more directional as you add more and more elements.

If these were yagis and you were to turn each antenna in its own direction so the signals would go separate ways than there would indeed be 3dB reduction for each of the two signals.

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