I am sure that most, if not all, amateur radio operators have used a repeater at some point. For most the process is reasonably simple. On a modern transceiver you enable repeater mode and set your radio to the frequency of the repeater. Much of the time you also have to set a tone so that the repeater will respond to your input. If you have ever watched your radio while you are transmitting to a repeater, you probably noticed that your radio display switched to a different frequency while transmitting. The reason for this is the fact that the transceiver at the repeater site cannot receive and simultaneously transmit on the same frequency. To get around this issue we tell the repeater to listen on one frequency and transmit on a separate frequency. This is all information that is covered in the knowledge base for the Technician license.
What about the antenna though? Can an antenna receive and transmit simultaneously? Think about your answer carefully.
The fact is, that an antenna has no problem listening and resonating at the same time. The caveat is that you need to transmit on a frequency different from the one you are going to transmit on. If you did have your repeater set to transmit on the same frequency that it was set to receive on bad things would happen. At the very least you are going to end up with a feedback loop where every signal the repeater transmits on the output side is fed right back into the receive side. You may have heard this happen when you hold a microphone up to a speaker that is connected to the microphone via an amplifier.
Now that we know that we need to use separate frequencies, how do we keep those signals from interfering with each other? We need to direct the input signal to the receiver side of the repeater transceiver and keep the output signal from transmit side of the receiver from mixing with the input signal. This is done in one of two ways. A Duplexer or a Diplexer. Diplexers are simple devices and relatively easy to build, however they are not a good solution for repeater use due to limitations of the filters used. Duplexers are capable of high powered continuous usage and are regularly used in repeater installations. Duplexers can be broken down into two types, band-pass and band-reject.
Band-pass duplexers work by only allowing the input and output frequencies being used to pass through the filters. This means that the only frequency passed through the input filters it the input frequency and the only frequency to pass through the output filters is the output frequency.
Band-reject duplexers work by notching out or blocking the input and output frequencies from reaching the opposite side of the transceiver. On the transmit side, the filters notch out or block the input frequency. On the input side, the filters notch out or block the output frequency.