Another good choice, a bit cheaper, they don't like to get as cute with their firmware as D-Link does, also bcm chipset. Same interface as your 8816 or close enough to it. Warning: The only other TP-Link modems worth buying are the 8950 and the 8960 and they've been disco'd in favour of inferior devices.
The 8840T is Trendchip same as the 8816 but with 4 ports. The old 8840 without the T was broadcom based.
Thanks for the warning, they slipped that one past me. Ok, so there's only one choice on the market now (reasonably priced BCM modem). -- If you have an apple and I have an apple and we exchange these apples then you and I will still each have one apple. But if you have an idea and I have an idea and we exchange these ideas, then each of us will have two ideas. George Bernard Shaw