How can I make cheap, smooth homemade Alfredo sauce? I've tried making Alfredo sauce several times based on a few online recipes.

It generally comes out pretty tasty, but also with one flaw: the sauce is grainy or gritty because the grated Parmesan cheese doesn't fully melt.  Doing searches online, most people seem to recommend starting with block Parmesan cheese and grating or shredding it at home.  However, at least at the stores around here, block Parmesan is much more expensive than the usual dried/grated stuff.

Does anyone have a technique for getting the cheaper stuff to melt smoothly into the sauce, or alternatively a cheaper source for the more suitable types of Parmesan?
The real stuff is expensive because it's still actually cheese. If you're gonna use the canned stuff, you're probably better off just leaving it out entirely (or sprinkling it on top at the table as-desired...)

It doesn't take a lot of cheese either - it's pretty strong stuff. You can probably get away with just a few ounces...