How to get the Bang-Bang PD PLL difference equations?

[ruwan2]

Hi,

For the first order loop, its difference equations are easily got. But for the second order loop BB PLL, it looks like unclear to get the difference equations. More specifically, I am not clear about the VCO output phase term at the BB PD input, see equ. (4) below please.




First of all, I suspect the 'n' on top of sigma should be a 'n-1'? Then, the ratio of P to I, i.e. Stability Factor(SF), multiplied 2 as the coefficient of the past from 0 to 'n', while the present result for 'n' is (1+1/SF). Yes, for present update, the maximum is sita_bb phase, but why for the past it has different multipliers(2/SF)?


Thanks,

 

[D.A.(Tony)Stewart]

I can't follow equation 4 either.

How about this paper, which describes a better equation and better 3 phase over-sampling detector.