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We use an analytic approach to study the susceptibility of the Planck LowFrequency Instrument radiometers to various systematic effects. We examine theeffects of fluctuations in amplifier gain, in amplifier noise temperature andin the reference load temperature. We also study the effect of imperfect gainmodulation, non-ideal matching of radiometer parameters, imperfect isolation inthe two legs of the radiometer and back-end 1/f noise. We find that with propergain modulation 1/f gain fluctuations are suppressed, leaving fluctuations inamplifier noise temperature as the main source of 1/f noise. We estimate thatwith a gain modulation factor within +- 1% of its ideal value the overall 1/fknee frequency will be relatively small (< 0.1 Hz).Comment: 14 pages, 4 figures. Accepted for publication in A&

$\vec{1/f}$ noise and other systematic effects in the Planck-LFI radiometers