  The Dick effect can be a limitation of the achievable frequency stability of
a passive atomic frequency standard when the ancillary frequency source is only
periodically sampled. Here we analyze the Dick effect for a pulsed vapor cell
clock using coherent population trapping (CPT). Due to its specific
interrogation process without atomic preparation nor detection outside of the
Ramsey pulses, it exhibits an original shape of the sensitivity function to
phase noise of the oscillator. Numerical calculations using a three-level atom
model are successfully compared with measurements; an approximate formula of
the sensitivity function is given as an easy-to-use tool. A comparison of our
CPT clock sensitivity to phase noise with a clock of the same duty cycle using
a two-level system reveals a higher sensitivity in the CPT case. The influence
of a free-evolution time variation and of a detection duration lengthening on
this sensitivity is studied. Finally this study permitted to choose an adapted
quartz oscillator and allowed an improvement of the clock fractional frequency
stability at the level of 3.2x10-13 at 1s
