Forty referees have officiated in Championship games so far this season. There is no specific rotation but nor is it completely random. For instance referees do not do the matches of their local clubs or clubs which they have said that they support - Kevin Friend will therefore never get a City game, just as Peter Jones never got one when he was still reffing.
MJ Jones (some referees seem not to have first names nowadays) and Richard Beeby have taken Championship games more than anybody else this season - 6 each. Steve Bennett, Mike Dean, Chris Foy and Mike Halsey, who are all on the Premier League list have taken just one Championship game each - Bennett has also taken one in the Conference League North! There are also refs who are primarily from the lower divisions who have taken a Championship game.