laplace representation of phase

[Debdut]

Hello all,
I am currently doing a phase-locked loop where the system transfer function is evaluated in laplace (s) domain. I have understood that part. I have attached a figure that I got from google.



Now there is a frequency divider in the feedback path. That can be added to the system by a block having transfer function 1/M, where M is the divider modulus.
What I am doing is a multiphase divider that needs various phases of the oscillator frequency. Now to create the block diagram of the considered pll I have taken several outputs from the VCO, added phases to them, multiplied them by rectangular pulses time shifted by required amounts, added all of them together and applied to the divider.

Bolded part is my question. Since the system is in laplace domain, how do I add phases, suppose I have to add a phase of 45 degrees, how do I represent it in the block diagram keeping correct dimensions and such...

 

[FvM]

I doubt that the signal annotation in the diagram corresponds to a formally correct laplace domain representation. If you are interested to figure it out, I suggest to read chapter two of Roland E. Best, Phase Locked Loops.

 

[CataM]

Here are some good notes as well about Phase Locked Loops by Analog Devices
https://www.analog.com/media/en/training-seminars/tutorials/MT-086.pdf

However, books always are better for a better building of knowledge.

 

[Debdut]

Thank you all,
However can you give insight to phase representation in laplace domain...

 

[LvW]

The drawing in post#1 shows a linearized PLL model which is applicable under locked condidtions only - and for a "moderate" phase difference between input and output (< 30 deg).
Therefore, it is correct that the input and output quantities are PHASE informations in the Laplace domain.