  A fundamental requirement in the new generation of high resolution Cosmic
Microwave Background imaging experiments is a strict control of systematic
errors that must be kept at micro-K level in the final maps. Some of these
errors are of celestial origin, while others will be generated by periodic
fluctuations of the satellite environment. These environment instabilities will
cause fluctuations in the measured signal output thus generating correlated
effects in the reconstructed maps. In this paper we present an analytical study
of the impact of periodic signal fluctuations on the measured sky maps produced
by the Planck survey. In particular we show how it is possible to estimate
analytically the damping factor of the peak-to-peak amplitude of the
fluctuation at the instrument output after the projection in the final maps.
