PLL transfer function

[kartikabr]

Hi,
I have come across the transfer function of a charge pump PLL in many papers, tutorials etc., defined on the assumption of the average charge pump current being proportional to the input phase. I am unable to justify this assumption to myself. After all the output phase is always slewing because of the non linear nature of the loop.

Could someone explain this to me or maybe give some references where the validity of this assumption is discussed assumption .

H( s ) = IKvcoZ(s)/s^2
Z( s ) = Impedance Transfer Function of network thru which the charge pump current passes

Regards,
kartik

 

[mmohsen]

when we take this assumtion we assume that we are working in the linear region of the loop .

would you clarify what you mean by slewing of the o/p phase??

Regards

 

[eng_Semi]

This assumotion comes from the continous time approximation, which is satisfied if the loop BW is much smaller than the reference frequency.

 

[kartikabr]

Hi,
Firstly ,
Thanks Mohsen and eng_Semi.



I am actually trying to model a PLL using an early - late phase detector, ideal VCO and a Z(s) = R + 1/sC .

Now I've got a big problem because from calculations i find that the output of the phase detector is directly proportonal to the frequency difference ( if it is small ) and has no particular relationship to phase.


I basically want to know whether the transfer function ( mentioned in the first post ) can be applied for any Z(s) or is it limited to low pass Z(s) .

Mohsen :
I should have said frequency slewing .. i'm sorry . just wanted to convey non-linearity

Regards
Kartik

 

[kartikabr]

Hi,

Just had a thought. Perhaps the linear approximations is valid for PLLs which use bang bang phase detctors also because in practical circuits issues like flip flop metastability make the phase detectors linear for small values of phase error!!

Can someone confirm this.

Regards
Kartik

 

[layes2]

what are you ask?
3rd order ?
just use 2nd order