Here’s a good basic primer on how to improve your odds of a DNA Circle forming on Ancestry – https://support.ancestry.com/s/article/How-DNA-Circles-are-created-1460089695851. However, I didn’t see clear-cut limitations on some things that have been reported as preventing formation of a DNA Circle. Also, you need to have a paid subscription to Ancestry to actually get to view the DNA Circles. I don’t have a paid account, but I do have a number of DNA Circles. In most cases, I know about where the common ancestor is likely to be in these Circles so not having paid access to view the Circle doesn’t hurt me as much as it would if I didn’t have enough information. As an alternative, you can get tree only access by contacting Ancestry since they don’t usually show the tree only access as an option when you go to subscribe.
For starters, your AncestryDNA needs to be attached to a public tree on Ancestry. If it’s not attached to a tree or not attached to a public tree, you aren’t going to get any DNA Circles. Note: many people who have public trees haven’t seen a DNA Circle in the several years their results have been on Ancestry.
Next, you need three (3) people that meet the public tree requirement, but they also must be at least second cousin or more distant in relationship. It’s important to understand that closer relationships than second cousin won’t count towards the three (3) person minimum to form a DNA Circle. They may show up in a DNA Circle provided you have enough other people showing up that are second cousin or more distant. As an example, you have three second cousins who are siblings and have tested with Ancestry and are attached to public tree(s). If these are your only close matches who have the same common ancestor that is in your tree, you won’t have a DNA Circle since the second cousins only count as one family unit towards the three person limit and you would only make the second family unit.
According to numerous reports, you need to have pretty much the same information on the estimated common ancestor on your tree as the others have on their trees. The smallest deviation can often prevent a Circle from forming.
A huge thing to watch out for is when somebody attaches the DNA to the wrong person. This is usually done to try and determine where the match is. Frequently called a Mirror Tree and here’s a good description of Mirror Trees – https://dna-explained.com/2017/07/29/concepts-mirror-trees/. Another problem with Mirror Trees is how long it can take Ancestry to reset its system after you move somebody’s DNA from Person A to Person B. Numerous people have reported it can take up to two (2) months before Ancestry’s servers catch up with your Mirror Tree DNA switch.
Here’s a good example by Kitty Cooper on the topic of DNA Circles – http://blog.kittycooper.com/2017/03/the-power-of-ancestry-dna-circles/. Another good example of a case where a person doesn’t have Circles: https://genealogyadventures.wordpress.com/2015/06/14/ancestrydna-so-what-does-it-take-to-get-a-dna-circle/. This article is a bit older, but still relevant https://dna-explained.com/2015/04/09/dissecting-ancestrydna-circles-and-new-ancestors/ and it makes a good point about the Circles not being proof. This last point is a key factor. Even if you and I have the same common ancestor, there is no guarantee that is where the DNA connection lies if it’s only somewhat far back. It could be a sibling of the ancestor, an aunt or uncle, or a grandparent’s sibling, etc. Short of actually testing the individuals and their descendants, you won’t know with certainty in most cases.