Translators can rebroadcast a regular FM station, an AM station, or an HD radio station.
When used to relay a regular FM station, they're used to extend the range of the parent station.
Translators for HD radio stations give listeners without HD receivers a way to listen to an HD station (or, more cynically / accurately, a way for station owners at the cap limit to add a freebie FM signal!).
In the latest round of translators for AM stations, they give the AM station an FM repeater so they can reach listeners who either don't have an AM receiver or who don't like the sound quality on AM and won't listen to AM radio.
Translators are typically low powered: maximum power for translators is 250 watts, compared to 50,000 watts maximum in this area for other FM stations. There are, however, loopholes that can give some translators large coverage areas despite the relatively low power. For example, even though WKQX, as an FCC Class B FM station could run 50,000 watts, that's 50kw at a reference height of 150m. But WKQX's transmitting antenna is 425m up, atop the Hancock Tower, so they have to reduce power to 5,700 watts. But translators don't have a specific reference height. One example here is the translator on 97.5, running the full 250 watts from atop the AON tower, at 349m.
All translators are not created equal, though. The Clubsteppin translator at 95.1 FM on Willis Tower is running just 60 watts. I haven't looked that closely, but would guess there are more stations nearby on 95.1 than on 97.5, thus the lower power for the 95.1 translators, who -- and this is another key fact about translators -- cannot interfere with full-powered FM stations.
A Chicago example: if the owners of WIIL (95.1 FM, from the WI/IL border) can show that they have listeners dealing with interference from Clubsteppin's translator on 95.1 in Chicago, they can get the 95.1 translator(s) in Chicago shut down.
Here's a Wikipedia article about translators:
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