As far as I know there are no HDTV PCI tuners that also have hardware encoding for analog broadcasts, whether OTA or via video input. (I wish there were such.) There is only one external USB HDTV tuner that has such capability, the OnAir Solution (formerly, Sasem). See:
http://www.copperbox.com/lite/onair.php
Their new version (with LG's 5th generation tuner, good if you have multi-path problems) is $250.00 while clearance on older models is $200.00 so there is a bit of a price premium to pay. I don't recall if they are certified to work with BTV.