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When you get your new cable modem, it does not know what frequency it's supposed to be running at.
When you plug in your modem, and it just sits there, it is actually going through the following steps:
(If your modem has indicator lights, you can look at the manual and determine which stage it is at by looking at the flashing LEDs.)
1.) Staring at a very low frequency (around 100MHz), the cable modem starts scanning for a cable modem signal. It will keep going higher and higher until it "hears" a cable modem stream. (Check your cable modem's documentation to see what frequencies it supports).
2.) Once it has found a cable modem signal, it listens for a few seconds for a broadcast from the cable company. This broadcast contains the information that the cable modem needs in order to talk back to the head end (a machine at the company which manages the cable modem network). If the cable modem does not hear this information after a while, it will just continue scanning listening for another cable modem signal (go back to 1.).
Part of this information is what frequency to talk back on (between 5 and 42Mhz on DOCSIS systems).
3.) Once the cable modem has learned how to talk back, it will actually start trying. The cable modem will start broadcasting at a very low signal level (usually around 8db). This is where the cable modem is ranging, or determining how hard it has to "yell" through all of your splitters in order for your provider to hear it. It will continue increasing it's broadcast power until it hears back from your provider. Usually this ends up being approximately 25 to 50db. If it turns out to be more than 56db, our system considers that to be too much.
4.) Once the CMTS (head end) has acknowledged the modem, the modem then identifies itself. The head end will then either grant or deny access to the network. If it is denied, the cable modem goes back to step 1.
The cable modem at this point will check and see if it needs to upgrade it's internal software (flash ROM).
4a.) If so, it will begin the software update from your provider (usually you'll have a flashing TEST light or something during this process), install it, and reset itself. Go back to step 1.
4b.) If the modem does not find an update, the headend will tell the modem to download a configuration file via TFTP from a server. This file contains the configuration for the cable modem, such as maximum speed, ip address (if any), and other data the cable modem needs to access the network properly. The modem will then load the configuration, and viola:
5.) You are now connected. (Cable/Link light goes solid.)
(Thanks to NoVA_CoxUser for a correction)
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