What does PLL voltage do?

[CoW]8(0)]

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.

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'.

Take a wave, then superimpose a wave on top of that such that the they both begin and end on zero, that is all you need.

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.