A pure ADSL modem
An ADSL connection holds frames of data in a point-to-point protocol like PPPoA. A pure ADSL modem converts back and forth between PPPoA frames conveyed over the analogue tones of ADSL and the same frames of data conveyed over an ethernet cable. Other than the transmission medium changing the frame data is left untouched. Old school dial-up modems operated much the same way.
Almost all ADSL modems however do more than just forward raw data, they are also a router. By analogy they act like a postal sorting office. PPPoA frames get unbundled and the internet packets within examined, then forwarded to the appropriate computer or device on the home network matching the address on the packet. When an ADSL modem holds username/password login details for the ISP account, that's the sure-fire sign it is acting as a router.
There are scenarios however where you want a modem to just pass on PPPoA frames untouched. I had such a need where I already had a device entrusted with performing all my home network needs - an Airport Extreme basestation. I didn't want a modem to duplicate this functionality.
My previous setup was a kludge - I had an ADSL router providing a home network but to just one device - my Airport Extreme. The Airport then provided my actual home network to everything else. All my traffic was therefore going through two networks which was unnecessary.
So I got myself a pure ADSL2+ modem, a DrayTek Vigor 120:
This just outputs raw PPPoA frames over ethernet. If I connect this modem to my laptop for example, in Windows I can configure a dial-up networking connection, type in my ISP login details and then connect to the internet. There is no router my computer is hiding behind; my computer is the single device assigned the public IP address my ISP gives me.
To provide a home network I connect the Airport basestation in the same way. An ethernet cable connects the modem to the WAN port of the Airport. The Airport configuration holds the ISP login details, the Airport does its own dial-up networking and logs into my ISP, so the Airport becomes the device exposed on the internet with an external IP address. The Airport then separately provides a home network over wifi and ethernet and shares that internet connection with this network.
Setting up the Vigor 120 with the Airport Extreme
This was pretty much just entering my ISP login details in the Airport utility software, connecting an ethernet cable from the modem to the WAN port of the Airport, and that was it.
One issue was out of the box the modem does provide a DHCP server used just to access the modem admin webpage. This caused a conflict with the Airport, which refused to act as a DHCP server itself because it could see this other DHCP server on the WAN port. As soon as I disabled the modem DHCP server, the Airport was then happy to be a DHCP server for my internal network.
My internal network is on the 10.0.1.x to 10.0.1.200 address range. I set the static address of the modem to 10.0.1.201. When the internet connection is active the Airport is expecting only PPPoA frames over the ethernet cable from the modem and does not expect any other kind of network traffic, so the admin webpage is inaccessible. To work around this I temporarily unplug the ethernet cable from the WAN port and plug it into any of the 4 ethernet ports on the Airport instead. The router can then be accessed from the home network on any web browser by browsing to 10.0.1.201. Once I finish configuring, I plug the cable back into the WAN port and the internet comes back up pretty much immediately.
Other ADSL only modems
The Vigor 120 is the only one I'm aware of that is just a modem and not a router. However you can configure some other routers and switch them to 'PPPoA bridging mode' or some equivalent phrase, which disables all the router functionality and gets the router to act as a pure modem. If you use another device to provide your home network and that device supports a PPPoA input I can recommend setting things up in this manner. Avoid setting up multiple TCP/IP home networks just to chain devices together.



