Need a dock/cable that can charge through AC while connected to USB [I'm an iPhone newbie, I hope the question isn't too stupid]

I want to be able to put my iPhone 4 in a dock and have it connected to my computer for syncing, but I want it to charge from an AC adapter so that it will continue charging when I turn my computer off at night.

Does anyone know of a dock with an AC power input that's separate from the USB connection, or a spliced cable that inserts 5V power from an AC adapter instead of from the computer's USB port?

Looking around online it seems that most docks and cables allow you to either charge from AC, or charge and sync from the USB while the computer is on, but I want to be able to turn the computer off and still charge without switching cables.  I could probably hack two USB cables together, but I'd rather buy a product that's designed for this.
I have an old Belkin TuneSync Charging dock, which also is a 5-port powered USB hub, that does the trick. The specs don't say that it works with iPhones, but mine worked just fine with both my iPhone 3G and now with my iPhone 4. I think the spec was just written before iPhones were available, as the unit was introduced back in 2005.

Belkin doesn't seem to still be making them, but they are still readily available. I just found it via Amazon:

http://www.amazon.com/Belkin-TuneSync-Charging-Dock-White/dp/B000BMVIQ2