At the time, the only band saw that I had was a Ryobi 9" table-top saw. This jig was built as an extension for the band saw table. It stands 12 ½" tall and extends out 24" from the side of the blade. The top is scrap ½" plywood and the legs and base are made from 2" x 4" scraps. There is a ½" dado running down the center of the table away from the blade. In this dado there is a 1/8" slot going all the way through the top. A small bolt sticks up through the slot from the underside. The dado is wide enough to accept the nut so that the bolt can be tightened down at any distance from the blade within the slot. The slot begins at 2 ¾" from the edge of the blade and extends to 22" from the blade. So, I can cut any circle with a radius between those two dimensions.
I do have to drill a small pilot hole in the underside of the wood I'm cutting to accept the end of the bolt. Then I just turn the wood on the bolt and as it feeds into the blade a perfect circle is cut.
One drawback to this design, however, is that one edge of the wood must be cut to the proper radius of the circle before you start using this jig. Otherwise, the workpiece won't fit onto the jig. For the circles I have made I just used the band saw to cut one side of the wood right to the circle's outer edge. Then, that side of the work goes against the blade first. After that, the rest is easy.