A repeater site is two paths. The RF path carries signal from the antenna through the feed line and duplexer to a receiver and a transmitter. The power path keeps all of it running. The blocks are introduced in Repeaters and controllers; here is how they fit together and what goes wrong.
Two paths, one ground. Failure usually starts at the edges: antenna and feed line, or the AC supply.
A 50 W transmitter is +47 dBm. The receiver beside it must hear signals around -120 dBm. That is a gap of about 170 dB (see Decibels), and the two frequencies may be only 600 kHz apart. Sharing one antenna makes it worse, for two reasons.
The carrier overloads the receiver. A strong signal at the transmit frequency drives the receiver front end into nonlinearity.
Transmitter noise lands on the receive frequency. Every transmitter has faint wideband noise (sidebands). It is tiny next to the carrier, yet it falls in the receiver's channel and raises its noise floor, so weak signals vanish. This is desense, and it is usually the harder problem; see Noise and signal-to-noise ratio.
A duplexer fixes both with high-Q cavity filters. A pass cavity lets one frequency through; a notch (reject) cavity blocks one. A transmit-side notch tuned to the receive frequency rejects the transmitter's noise there; a receive-side notch tuned to the transmit frequency rejects its carrier.
Three things set how many cavities a site needs:
Frequency separation. The closer the pair, relative to the band, the sharper the filter. One manufacturer's VHF data sheet lists two pass-reject cavities per side for spacings of 600 kHz or more, and three per side for 400 kHz or more.
The band. Lower frequency means physically larger cavities.
Insertion loss. Every cavity attenuates the wanted signal too, typically around a dB or two per direction in total. That loss cuts both transmit power and receiver sensitivity, so more cavities are not automatically better.
An alternative is two antennas, one for each side, separated vertically so little energy couples between them.
Worked example (all numbers illustrative)
Transmitter noise in the receive channelnoise (dBm) = carrier (dBm) + noise density (dBc/Hz) + 10 log₁₀(bandwidth in Hz)
Carrier: 10 log₁₀(50 W ÷ 1 mW) = +47 dBm.
Assume the transmitter's noise 600 kHz away is -130 dBc/Hz. In a 12.5 kHz channel that adds 10 log₁₀(12 500) = 41 dB: -130 + 41 = -89 dBc, so the noise is 47 - 89 = -42 dBm.
Noise that arrives 6 dB below the floor adds about 1 dB to it. So it must reach the receiver at about -134 dBm.
Isolation needed: -42 - (-134) = about 92 dB.
Slide the isolation down to see desense appear.
Illustrative numbers: 12.5 kHz receiver, 5 dB noise figure, adjustable transmitter noise. Levels are in dBm, higher is stronger.
Desense1.0dB
Isolation needed for 1 dB92dB
The controller
The controller sits between receiver and transmitter and does the housekeeping:
Carrier and tone detect. It opens the transmitter only for a valid signal. If the repeater requires a CTCSS or DCS tone, the controller checks it; Part 97 permits limiting a repeater to certain users (97.205(e)). See Squelch, CTCSS and DCS.
Identification. Part 97 requires the call sign at the end of each communication and at least every 10 minutes during one (97.119(a)); the controller sends it by CW or voice automatically.
Time-out timer, courtesy tone and tail. The timer drops the transmitter if someone holds the key too long or a stuck signal appears. The courtesy tone signals that it is safe to talk.