What does PLL voltage do?

[JumpingJack]

Thanks for the plots, but now plot sin(t) vs sin(1.5t + pi) and you'll see what's wrong with that statement.

1.5t + pi just shift it over... by pi (180 degrees) with a multipler now of 1.5, this has nothing to do with mulitplying or phase locking. At the node, the waves will be out of phase, not the same frequency, but out of phase for 1/2 multipliers in 1 period of the input wave form... this is not hard.

I.e. sin(2.5t) != sin(1.5t+pi) != sin(t)

Look you are stuck on a semantic ...

At the node where the wave locks, for 1/2 multipliers, one end the waves are instantaneously in phase and on the other end out of phase. If you prefer, forget the term 'phase' althgether .. and simple say x out put waves in 2 periods of the input wave, or x/2, when X is odd it will be non-integer 1/2 multpliers. Not quite how the circuit works, but you can say it.