I saw this instructable as well as the "cat jet", but both are really giant and intrusive. I figured I could make a little fan+filter out of just a computer fan and some type of carbon/charcoal air filter, so I did.
The result is small and unintrusive, and only requires periodic air filter changes (the package says every 3 months but I'm not sure if that holds up in this case). No hose running to a window, no big loud fans, no complex motion detection system. Just a small quiet fan running 24/7 at low speed, using little power (less than a watt).
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Step 1: Parts & Tools
1. A computer fan (the bigger the better)
2. Some sort of 12 volt DC "wall wart" (lower voltage will work too, but the fan will run slower)
4. Wire nuts, or solder, or something
5. Small bungee cord, or rubber band, or zip ties, or something
6. Electrical tape or heat shrink
7. An activated carbon filter (cost me $10 at home depot)
2. Knife or dremel or something to cut the litter box with
3. (recommended) Wire stripper
4. (optional) Soldering iron
Step 2: Put It All Together
The filter is very large, 4 feet by 1+ feet. Cut out a square that's a bit bigger than the fan, so you can wrap it around the sides and secure with your bungee cord/whatever. Save the rest for future filter replacements. A bungee cord or rubber band are ideal since you can easily take them on/off when it's time to replace the filter.
(note: it might be a good idea to use 2 or more layers of the filter, I'm not sure yet)
Now wire the fan to the power supply. Test the polarity by seeing whether the fan turns. If your fan has three wires, ignore the white wire. It's for RPM monitoring, used by computer motherboards.
I used wire nuts and electrical tape to keep the connection together but solder and heat shrink would be nicer. I also used an 80mm fan and a 7.5 volt power supply, where a 120mm fan and 12v power supply would be ideal. I'm not yet sure how much these factors matter.
Also make sure that you use a fan with a sound level you're comfortable with. If you're stuck with a loud one, you can use a lower voltage supply to quiet (and slow) it down. If you have a fast fan, make sure to put a grille or other protection over it to keep the cat from being hurt.
One last thing about the fan: run the wires under the bungee so that the strain is relieved from the point at which the wires are soldered into the motor. If those solder points take too much of a beating, they or the wire will probably break there eventually.
Cut the appropriate holes in the litter box, one large one with four surrounding screw holes, preferably in an area that's at the opposite end from the door. This will keep the air flowing through in a straight path and hopefully do a good job of keeping the odor from leaking out the door.
I did a really sloppy job of cutting the holes, but it doesn't really matter as the whole thing is on the back of the litter box and is out of view.
Now plug it in and watch it go.