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I'm trying to install an 8-way coaxial splitter in the roof of my apartment building. This will then have one WiFi input signal and split out to many coaxial cables which have a wifi aerial at the end of them.

Given that on average, there is 1 dB loss per meter across your standard 75 Ohms coaxial, plus each apartment has two splitters which could potentially be adding more loss, plus the exposed ends (which will have POE filters), is it possible to cover a building five to six stories high by adjusting the input power (or using an amplifier)?

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@BillP3rd storey is British, it's not a spelling mistake. –  slhck Mar 4 '12 at 19:06
    
Yes, but since the British spelling for metre wasn't used... –  BillP3rd Mar 5 '12 at 0:08
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No. Whatever it is you're trying to do would be better accomplished by keeping the Wi-Fi radio (the AP) as close as possible to the antennas, and distributing the network via data cables (Ethernet, MoCa, HomePNA-over-coax, or even 10BASE-2/thinnet/cheapernet), not RF (antenna) cables.

If you want to provide Wi-Fi access throughout a multi-story building, you have to place APs throughout the building, with Ethernet (or something like it) connecting them together on the back end.

Also, Wi-Fi antenna cable is usually 50-ohm cable, not 75-ohm TV antenna cable. So if you were planning on repurposing existing TV antenna cable instead of pulling new cable, your plans are probably already dashed. Also be sure to you know the loss rating of your cable and splitters at the frequency range you're dealing with. Cables and splitters are often optimized for performance at different frequency ranges, so you probably want gear specifically designed to perform well from 2.4 to 6 GHz.

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That coax had better be 50 Ohm RG-142 or RG-400 if you're going any distance (30 feet or less) Losses are pretty high at these frequencies (2.4GHz, 5.0GHz is hardline/waveguide territory for distance). Run of the mill RG-58 isn't going to cut it and as pointed out, 75 Ohm tv cable is an impedance mismatch to the radio and antenna, you could do just as well soldering a resistor across the plug. Decibels are a logarithmic scale. On your calculation, at 3 decibels loss (3 meters), you have half the power, at 20 meters, you are 20db down or only 1/100 of the original power. –  Fiasco Labs Mar 4 '12 at 18:33
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