Here's another topic discovered from search engine referrals. I'm unclear whether the searcher is looking for information on how repeaters of any sort work, or the specific differences between ten meter repeaters and other types of repeater, so I'll cover both topics.
Just about anyone who's been involved in amateur radio for any time at all will have encountered a repeater, and for many hams (especially those in the US with Technician licenses) repeater operations are the majority of their activity, so it's probably safe to say that repeaters are at least somewhat important to hams. (They're also important to other radio services, but I won't get in to that in this article.) Fundamentally, a repeater is an automatically controlled station that receives a signal and immediately retransmits that same signal back out. The idea behind this is to enable two stations, each of which has relatively limited power, and more significantly, relatively limited antenna systems, to communicate with one another by way of the repeater station, which will typically have more power and, more importantly, a much better antenna system (where "better" in this situation means "installed at greater altitude").
As an example, a typical VHF mobile installation will have an antenna with center of radiation at perhaps six or eight feet above ground level and a power level of perhaps 50 watts. Two stations thus equipped will be able to communicate directly with one another at a range of about ten miles in relatively flat terrain. However, if the repeater is equipped with a 100 watt transmitter and an antenna installed at 200 feet above ground, it should be in range to mobile stations equipped as above within about 25 miles. Furthermore, any two mobile stations within this range will be able to communicate with one another via the repeater. This represents about a six-fold increase in the ability to communicate.
So how does the repeater accomplish this? Fundamentally, a repeater is a receiver connected to a transmitter, combined with various control circuits (e.g. to prevent the repeater from transmitting when there's nothing to transmit, and for other purposes, some obligatory, others not). Now, one of the things that confused me when I first heard about repeaters back in the early 90s is how the repeater could receive a signal and transmit it back out on the same frequency without interfering with itself. The simple answer to this is that repeater don't do this: virtually all repeaters receive on a different frequency than they transmit. (There are some "repeaters" that operate "simplex" by delaying the transmission until the receiver message is complete, but that's technically not a repeater; the definition of a repeater requires simultaneous retransmission. And there are other repeaters that do operate on the same frequency in and out by using separate antennas at well-separated locations; we'll come back to that later.) Because the receive frequency is different from the transmit frequency, the transmitter doesn't interfere with the receiver and both function can proceed simultaneously. The difference between the receive frequency (or "input") and the transmit frequency or ("output") is called the "offset". There are customary offsets for most repeater operations, which vary by region (for various reason). In the United States, the customary offset for two meters is 600 kHz, and for ten meters it typically 100 kHz.
And here's another aspect of repeaters I failed to get at first: most repeaters use the same antenna for both receive and transmit. Of course, this raises another question: how do you put a 100 watt signal onto an antenna to be sent out, and at the same time pull in a signal measuring often in the nanowatts without the receiver being overwhelmed by the transmitter's raw power even if it is on a (somewhat) different frequency? That was another one I didn't really get until I started studying for my Extra. The answer is, of course, filtering, and the two main techniques for doing this are the duplexer and the circulator.
A duplexer is a set of filters that are designed to pass signals on one frequency with very little loss, while at the same time rejecting signals on another (often nearby) frequency with very high attenuation. In the repeater case, you want a filter on the receiver side that passes the input frequency with as little loss as possible, and attenuates the output frequency as much as possible, while on the transmit side you want the exact opposite. Because of the very tight tolerances required (only 600 kilohertz separation for two meters), these filters have to be very tight, too tight to be built out of ordinary discrete components like capacitors and inductors, so for virtually all repeaters these are resonant cavity filters. Resonant cavities provide much tighter pass bands and reject bands than any discrete circuit could. Even so, two, three, or even four filter pairs are typically required to provide sufficient isolation.
The other component that is useful in providing this isolation is a little piece of electronic voodoo called a circulator. A circulator is a device, typically constructed out of ferrite disks, with three ports that allows a signal to pass from port 1 to port 2, from port 2 to port 3, and from port 3 to port 1, but not in any of the reverse directions. To be honest I still don't fully understand how they work; it has something to do with the signals setting up a rotating magnetic field in the ferrite disks that cancels the reverse signals; at this point I'm happy to call them "electronic voodoo" and leave it at that. In any case, connecting the transmitter's output to port 1, the antenna to port 2, and the receiver's input to port 3 will also provide a significant chunk of the signal isolation required to protect the receiver from the transmitter. Many stations use some combination of duplexing filters and circulators to achieve the required isolation (which is a mininum of at least 60 decibels, more if possible) between transmit and receive.
This is really the hard part of the repeater from an RF standpoint. The rest of the repeater is just a more or less ordinary receiver tuned to the receive frequency, a more or less ordinary transmitter tuned to the transmit frequency, a little bit of audio-frequency circuitry to ensure that the transmitted signal is well-balanced, and some control circuitry to do things like transmit the station's callsign periodically, and turn the transmitter on and off as required. Of course, nearly endless features can be added to a repeater, but these are ancillary functions, not the core of the repeater functionality.
Now, on to the more specific question of ten meter repeaters. One of the characteristics of resonant filters is that one of the factors that determines their size is the wavelength of the pass frequency (the other, of course, is the filter sharpness, or Q, required). This is why two meter "cans" (as they're called, as they really do look like cans) are typically about the size of two paint cans stacked on top of one another, while cans for 70 centimeters are much smaller, about the size of a can of spray paint. This is because 70 cm is a third the wavelength of 2 meters, and in addition the customary offset in 70 cm is 5 megahertz, instead of the much smaller 600 kilohertz used in 2 meters. As a result, 70 cm machines (hams often refer to repeaters as "machines") can use physically much smaller cans. For ten meters, this goes the other way: ten meters has five times the wavelength of two meters, and the customary offset of only 100 kHz is even more demanding than the 600 kHz of two meters. A set of cans for ten meters capable of providing a reasonable degree of isolation would be at least the size of hot water heater tanks. If you read the article I linked above you'll note that the designer of those filters silver-plated the interior of the cavity filters to minimize loss; the cost of silver-plating that much surface would be quite substantial. Also, the very narrow offset would necessitate very finicky tuning.
Mainly because of this, it's more practical for 10 meter repeaters to use "diversity antennas" instead of filtering to achieve the necessary isolation. Separating the antennas by a mile or so will achieve as much signal isolation as would even the best possible filtering arrangement. In this approach, the receiver and the transmitter are at different locations, and the audio received at the receiver is conveyed to the transmitter's location either by a landline link (a physical hardline cable, a dedicated telephone circuit, or some other non-radio connection including possibly a VoIP circuit), or alternatively by transmitting the audio via a radio link operating in some other band. Typically these links are in the 70cm band and use very directional antennas that are carefully aimed at one another. (The same approach is use for multi-input repeater systems, but that's beyond the scope of this article.)
This same approach can be used in any band, but using diversity receive in any band other than ten meters (and perhaps six meters, where it is also occasionally seen) creates the problem that the coverage area where the repeater can be heard (which is based on transmitter location) may not correspond well to the area where the repeater can hear remote stations (which is based on receiver location). This is less of a problem for ten meters because ten meters has much broader propagation, due to skywave propagation modes including near-vertical incidence skywave (NVIS), and so the nonoverlap areas are likely to be smaller.