This implementation is adapted to rebroadcast the output of a CD player, television receiver, or radio receiver. I use it so that I can move about the house and listen to my favorite programs without disturbing others. Within and the house, I find that I can get 10 to 20 meters away from the transmitter with the small pocket FM receiver I carry in my shirt pocket. Your mileage may vary. The transmitter as built and pictured below (the transmitter is in the blob of hot melt glue on the end of the battery holder) does not have an on-off switch. I put a 1.5 AA cell that was run down too far to run my CD player in this transmitter and it ran for over a month before I replaced it. The one in the transmitter at this moment has been running it continuously for over three months. Current draw is only about a milliamp with a new battery (assuming you don't have a super-high beta transistor in which case the theoretical limit is about 2.5 ma). An on-off swich is not necessary, though it may satisfy an emotional need.
Tips to get it working: Wind the coil on a 4 or 5 mm diameter Philips blade screwdriver or similar form then slip it off. I used some vinyl insulated #24 hookup wire as well as #30 enameled wire. In both cases, I played with the length of the coil to tune the transmitter to a dead spot on the FM band. The coil is held in place with hot melt glue. If you don't have a spectrum analyzer or frequency meter, use a good-quality FM receiver to make sure its tuned where you think it is. While adjusting the coil, keep in mind that all superheterodyne receivers have images. If you find that two or more adjustments make the transmitter show up on the same spot on the receiver, it might be necessary to take a short walk and find out which adjustment drops out first -this would be the image, because the receiver's front end (if it has a tuned front end) will reduce its sensitivity to the image.
Many kinds of transistors will work fine in this application. After all, its only an oscillator (frequency modulation is obtained my modulating the base-collector voltage, thereby modulating the depth of the depletion layer of the reverse-biased base-collector junction, which results in a change in capacitance at the collector, which results in a change the resonant frequency of the collector circuit.). I used an 2N4401 because I have a lot of them. I like 2N3904 and MPSH34 for this too.
Variations The objective of this design is to provide a simple, appliance-like low-power transmitter to rebroadcast audio. This transmitter does not have pre-emphesies, so it is not high-fidelity. It has sort of an "AM" sound for music and is fine for speech. Since there is no audio level control on the input, the audio level out of the CD player (or whatever you are driving it with) needs to be adjusted. Or, you can just add a 10k to 50k as an input level control, its no big deal. This transmitter, as built is not tunable once assembled, the coil tweaked to the desired frequency, and everything glued down. If you want to make one that's tunable, it might be easiest to reduce the 18 pf capacitor and put a small trimmer capacitor in parallel with the inductor (across the reduced value capacitor). Voltage variable capacitors would be an nice alternative to a mechanical variable capacitor but they don't offer much tuning range with only a 1.5V power supply.
Notice: Before operating a radio transmitter, find out what kind of transmitter operation, if any, is permitted in your locality. Radio transmitter operation is a serious legal matter. In the United States, operation of unlicensed intentional radiators is covered by Part 15 of Title 47 of the Code of Federal Regulations. This design can be readily adapted to different frequencies and different power levels. If you choose to build and operate the transmitter described here, you do so at your own risk. I'm only publishing this as an example of what can be done.