I'm using a TP-Link WR740N router flashed with DD-WRT as a wi-fi repeater. However, in divisions where the signal from the main router is weaker than the signal from the repeater, the Internet speed (as measured with http://www.speedtest.net/) is about a 10 Mbps if directly connected to the repeater, whereas if connected to the main router (with a weaker wi-fi signal) I get about 30 Mpbs. What could be limting the internet speeds, seeing that the signal strength is extended with the repeater?
I believe if DD-WRT is acting as a repeater, it has to switch rapidly between AP and client mode and therefore the speed is reduced. To do AP and client mode at the same time you need two radios in the unit and most hardware DD-WRT runs on only has one.
One workaround is to get a second DD-WRT unit. One needs to be a client on your main wireless network. The second needs to be a DHCP-less/router-less (disable both DHCP and routing in the DD-WRT control panel) AP. The AP can get Internet via a short cable to the first, client router. Try to assign them to different channel bands (i.e. put your main AP and "repeater" client on channel 1 and the "repeater" AP on channel 6 or 11).