calculation of sigma-delta fractional-N PLL

[niklas.zhu]

assume fractional-N PLL using sigma-delta architecture of MASH 1-1-1 and it is for GSM application (channel bandwidth 200kHz )

since MASH 1-1-1 output from -4 to 3, the integer divided number is C, and the output frequency of VCO is Fout (assume Fout is 960MHz)

Is (Fout/(C-4) - Fout/(C+3))/C the VCO output frequency shift?

since the frequency shift should less than 200kHz*x (x<1), assume x=0.01,
so C should be large than 170 and then reference frequency cannot be 26MHz

do I calculate correct?

 

[niklas.zhu]

nobody knows?

 

[niklas.zhu]

anyone knows?

 

[rfsystem]

Please use a little bit Math notation:

If the Mash generate the number interval {-4...3} (3bit signed)

and the divider is modulated with that output by {C-4...C+3} the output frequency is

FOUT=FREF*{C-4...C+3}={FREF*(C-4)...FREF*(C+3)}

The advanatge is that the total of 8 numbers could approach an gaussian distribution. So spurs could be very low.