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How many watts would be needed to cover a 10 mile radius with good sound for music on the 88-108 MHz FM broadcast band? I am an amateur and for fun only.

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    $\begingroup$ Do you mean the 88-108 MHz FM broadcast band? The transmission of music is prohibited on any amateur band. Legal issues aside, the antenna will make a lot of difference with a given power. $\endgroup$ – Mike Waters Jan 26 '17 at 19:56
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    $\begingroup$ Since this is now neither about general radio theory nor about amateur radio, it's become off-topic. $\endgroup$ – Marcus Müller Jan 27 '17 at 0:14
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    $\begingroup$ @MarcusMüller Non-profit radio is not amateur radio? "amateur ˈamətə,ˈamətʃə,ˈamətʃʊə,ˌaməˈtəː/ noun 1. a person who engages in a pursuit, especially a sport, on an unpaid basis. "it takes five years for a top amateur to become a real Tour de France rider" synonyms: non-professional." Please let this question stand, I am interested in the answers. $\endgroup$ – user400344 Feb 7 '17 at 21:27
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    $\begingroup$ @user400344 no, it isn't. Please don't try to argue about the meaning of "amateur radio" on the ham stack exchange. Not every non-profit radio is amateur radio. That's not how language works. $\endgroup$ – Marcus Müller Feb 7 '17 at 21:31
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    $\begingroup$ @Mike Waters: In my country, transmission of music on some amateur band but only for test transmissions is allowed. $\endgroup$ – Tom Kuschel Feb 8 '17 at 17:49
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This depends in your intended communication. Are you trying to hit a fixed receiver, in which case you can aim an antenna to that receiver? or are you trying to communicate with a handheld or other portable system? Are you on a portable system? Is the target system on a hill? The gain on the receive antenna, as well as the radiation pattern of your antenna makes a huge difference.

Additionally, the actual band used may make a difference. Many different bands permit FM operation, and some have unique properties that increase propagation distance.

Often, a 5w handheld with a rubber duck can hit a repeater ~10-20 miles away, but this is one particular example of possible communication.

Edit:

As you mentioned that you want good quality for music, you'll really need a more powerful transmitter. Unfortunately, FCC part 97 (Amateur) rules disallow music through the amateur radio bands, so you'll likely need a commercial FM broadcast license to do that sort of thing.

I'm not qualified to talk at length about the particulars of antenna design, but there are other resources online. For broadcast FM radio, you'll need an antenna (a) in a high location, so receivers can clearly receive your signal; (b) high power, usually on the order of kilowatts. (WCBN-FM, a student radio station in Ann Arbor MI, uses a 200W transmitter, but has an effective range of around 10 miles).

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    $\begingroup$ Notice he said "good sound for music". $\endgroup$ – Mike Waters Jan 26 '17 at 20:01
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    $\begingroup$ @MikeWaters The music bit was added after my answer was made. $\endgroup$ – Tyzoid Jan 26 '17 at 21:08
  • $\begingroup$ Not 100% on-topic, but in the EU a lot of FM signals are moved to DAB+. That leaves a lot of good FM radios as garbage. Would like to keep mine in use. $\endgroup$ – user400344 Feb 7 '17 at 21:30
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This is a link budget question. Transmit power is just one factor: others are terrain, antennas, frequency, quality, noise, and so on.

If we restrict the variables to typical values for FM commercial broadcast stations, we can use the FCC's rules to make some estimations. By that reckoning, you need a transmitter of around 50kW with an antenna 150 meters high to achieve your goal of high-quality coverage over a 20 mile radius.

Unfortunately, that's a very expensive transmitter. And you need a commercial license.

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