fractional-N PLL loop filter order

fractional-N PLL higher order modulators are better,but this pushes more noise out, thus requireing a higher order filter. this noise that is pushed far out can mix with thing s adn come back as spurs closer to the carrier, so higher order filters  really are necessary , The equation:

Loop Fiter Order = Sigma Delta Order +1

is a consequence of applying the constraint that the noise must degrage at a rate of 20dB/decade outside the loop bandwidth. For the 1st order modulator, the noise inreases at a rate of 20dB/decade. therefore the filter must attenuate at 40 dB/decade A second order filter has a pole at 0 and another at T1, therefore it has 40dB/decade roll-off. For the 3rd order modulator, the noise increases at a rate of 60dB/decade. Therefore the filter must attenuate at 60 dB/decade . the 3rd order filter has a pole at0 and the poles T1 and T3 , and therefore has 60 dB/decade roll-off.

from: Advantages and Pitfalls of using Fractional N PLLs 

Dean Banerjee Senior Wireless Applications Engineer. Feb 27,2003. NI