I apologize if I'm being too indirect. This should clear things up.
The blue line is sin(t) while the green line is sin(1.5t + pi). sin(1.5t + pi) has a frequency 1.5 times larger than that of sin(t), hence the frequency multiplier of 1.5. At the node (where t = 0 and t = 2*pi), the values of both waves do match and according to you are in 'phase lock'.
But at t = 0, the waves are going in opposite directions and are exactly pi out of phase (hence the + pi). I guess the main issue is the way you're describing what it is to be 'in-phase' and and 'phase-lock'. The semantics you're using are inconsistent. I think describing the the PLL in terms of frequency rather than periods would simplify it drastically. You're describing it as if you're adding 1/2 a period (ie: pi) to the input to get the output.
And all that's really saying is you're increasing the frequency of the output 1.5 times the input. And this is all that really needs to be said, all the results you describe about 'going in opposite directions' and other characteristics will be a result of that statement. The 1/2 value is of frequency, not of periods or phasing.




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