1/f noise and other systematic effects in the Planck-LFI radiometers

We use an analytic approach to study the susceptibility of the PLANCK Low Frequency Instrument radiometers to various systematic effects. We examine the effects of fluctuations in amplifier gain, in amplifier noise temperature and in the reference load temperature. We also study the effect of imperfect gain modulation, non-ideal matching of radiometer parameters, imperfect isolation in the two legs of the radiometer and back-end 1/f noise. We find that with proper gain modulation 1/f gain fluctuations are suppressed, leaving fluctuations in amplifier noise temperature as the main source of 1/f noise. We estimate that with a gain modulation factor within $\pm 1\%$ of its ideal value the overall 1/f knee frequency will be relatively small ( <0.1 Hz).