Do you mean the following formula?

(a&!b) & G( ((a&!b)->X(!a&b)) & ((!a&b)->X(a&!b)) ) ?

For structures with a single cycle that is not that difficult, there is such a pattern. In general, however, there is the problem that LTL is not as powerful as automata are, so there is no algorithm that could translate any automaton to an LTL formula.