sampling delay contribution to PLL phase margin

Sampling Delay becomes significant when the sampling frequency approaches the loop bandwidth.

Sampling delay (secs) = 1/F_pfd

The phase shift at open loop zero crossing frequency (~equal to closed loop bw, Fbw):

One period at Fbw = 1/Fbw = Tbw goes through a 360 degree phase shift.

sampling delay/Tbw = phase shift /360 degrees

phase shift = 360*td/Tbw = 360 * Fbw/F_pfd

The above relations hold true for ideal, impulse sampling.

In practice there is a hold circuit following the sampler, so that the delay is 0.5*Tsample. This results in a phase lag of 180*Fbw/F_pfd