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REPEATERS:  Consist of 2 radios connected so that when you transmit a signal on the receive frequency the repeater will repeat it by transmitting it on another frequency.

For VHF repeaters the transmit frequency is up or down from the receive frequency by 600 KHz. This is the offset, and is displayed on the radio by the "+" or "-" symbols for UHF repeaters the offset is 5 MHz

some radios will have a "ARS" setting or function which will automatically set the repeater offset for you

some repeaters may require a Continuous Tone-Coded Squelch System( CTCSS ) tone to open the squelch on the radio and allow you to be hear this CTCSS tone is a "sub audible tone" which you can select and program in your radio
most radio manuals will give you the list of tones so ask your local operators if a tone is required on the repeater you want to use.

There is also a DCS or Digital Coded Squelch  that can also be employed. you can google DCS to find more about the digital nature of this code.

these codes are usually used if the repeater is co-located with other transmitters where they maybe experiencing minor interference,

you can google many sites to get a list of repeaters. Here is one example below

notice the Frequency has a "-" sign so you would transmit 600KHz down or at 146.310 also note there is no tone required and also note at the very end "OPEN" which means any licensed  amature radio operator can use the repeater. if it is not "OPEN" then you must get permission to use the repeater from its owner.

Frequency Offset Tone  Location County St/Pr Call Use Operational status
146.910 -0.6 MHz   Barragada Heights Guam GU AH2G OPEN ON-AIR

IRLP    Internet Radio Linking Protocol

see  www.irlp.net    for a full explanation

simply put if you have an IRLP node connected to a repeater then by entering a DTMF 4 digit code

you can be talking to another ham in another city through their node.

the call is from your radio to the repeater which then sends audio to the node. after dialing a valid 4 digit code the first nodes audio is passed over the internet to the 2nd node . the 2nd node relays the audio to a repeater, then the ham who hears can respond.
the return audio is via the same path.

DTMF (dual tone multi frequency ) tones are are the same tones you hear on a telephone or cell phone and can be transmitted from you transceiver. most hand held radios are equipped with a number pad, and most mobile radios can accommodate a mic with  a number pad (some may need to be purchased separately)

a couple of things to remember

before talking wait a few seconds to see if there is a conversation in progress at the far end
the internet has inherent delay, so wait about 3 seconds after you push the talk button to start talking.
when done don't forget to bring the link down by dialing "73"