  Bolometers are most often biased by alternating current (AC) in order to get
rid of low-frequency noises that plague direct current (DC) amplification
systems. When stray capacitance is present, the respon- sivity of the bolometer
differs significantly from the expectations of the classical theories. We
develop an analytical model that facilitates the optimization of the AC readout
electronics design and tuning. This model is applied to cases similar to the
bolometers in the Planck space mission. We study how the re- sponsivity and the
noise equivalent power (NEP) of an AC biased bolometer depend on these
essential parameters: bias current, heat sink temperature and background power,
modulation frequency of the bias, and stray capacitance. We show that the
optimal AC bias current in the bolometer is significantly different from that
of the DC case as soon as a stray capacitance is present due to the difference
in the electrothermal feedback. We also compare the performance of square and
sine bias currents and show a slight theoretical advantage for the latter. This
work resulted from the need to be able to predict the real behavior of AC
biased bolometers in an extended range of working parameters. It proved to be
applicable to optimize the tuning of the Planck High-Frequency Instrument
bolometers.
