The impedance of free space is around 377 ohms. This derives from transmission line concepts and the speed of light (C). Google it if you're interested.

All (functional) antennas match the cable to free space. That's what they do. You can see this is true when you realize that the antenna accepts power at it's feed point impedance (50 ohms or whatever) and (if eveything is working perfectly) couples ALL the power into free space.

I advisedly used the term 'feed point impedance' above to help you realize that the impedance of an antenna varies along its length. This may help you to break the false link between the antenna's feed point Z and the Z of free space.

An antenna with a feed point Z of 20 ohms (for example) can be very nearly perfectly 100% efficient if it is built right. It's hard to improve on 100%. So there's no inherent advantage to an antenna that happens to have a feed point Z of (for example) 377 ohms.

(Antennas with very low Z can be hard to feed efficiently, but that's just IR losses at work. It can be overcome with thicker wires.)

If you're trying to rebroadcast an FM station into a mine or into an office building, then you need to realize that a little 10dB amplifier from Radio Shack isn't going to provide much transmit power. The 'boosting' concept that your attempting works if you use an illegally powerful transmitter (as opposed to a puny 10dB in line amp).

It might be better to use the outside antenna and a receiver and then rebroadcast using an FM modulator on a different frequency. Or instead, maybe hand out 900 MHz wireless headphones to everyone.

... and by the way, re-transmittting at broadcast frequencies without a license is bound to be illegal.

"I am doing a project that involves the following.  Signal recieved on 93 Mhz antenna , from here it goes into an amplifier, this then goes down a cable to a dipole antenna of some sort."
____________

Radiating an amplified 93 MHz signal being received at the same site would require extremely good isolation between the transmit and receive antennas to prevent system oscillation and blocking.

Also, in Canada and the US -- unlicensed radiation in the 88-108 MHz band must not exceed 250 uV/m in any direction from the transmit antenna.  See 47 CFR Part 15 (FCC Rules).

How does that affect the legality or otherwise of things that are designed to allow you to receive the output of your Ipod or cd or whatever on your car radio in the fm band?

I don't doubt for a moment that they are illegal to use in the UK (just like almost anything else you care to think of), but there is presumably a market where they can be used legally.

First, let me add the rest of the spec to what I posted earlier (sorry): ...unlicensed radiation in the 88-108 MHz band must not exceed 250 uV/m at a distance of 3 meters in any direction from the transmit antenna.  See 47 CFR Part 15 (FCC Rules).
 
zeitghost (Computer) 30 Oct 05 10:57 posted
"How does that affect the legality or otherwise of things that are designed to allow you to receive the output of your Ipod or cd or whatever on your car radio in the fm band?"

It doesn't, as long as they meet the "Part 15" field strength limit, which they must in order to be offered for sale to the general public (at least, in the US).
 

Yukondan,
You have two antennas, an amp and a cable.
These are either 50 ohm or 75 ohm impedance.
Your antenna may be 300 ohm input. If it has a connector on it, it's 50 or 75 ohms (probably 75 ohms). If you don't see a connector, and just two wing nuts, then it's 300 ohms.
Either way, you'll probably need to get a 300-75 ohm transfomer.

Describe your antenna, amp and cable a bit more regarding impedance and connectors.  

kch