  The low-level RF system (LLRF) generates the drive sent to the high-power
equipment. In synchrotrons, it uses signals from beam pick-ups (radial and
longitudinal) to minimize the beam losses and provide a beam with reproducible
parameters (intensity, bunch length, average momentum and momentum spread) for
either the next accelerator or the physicists. This presentation is the first
of three: it considers synchrotrons in the lowintensity regime where the
voltage in the RF cavity is not influenced by the beam. As the author is in
charge of the LHC LLRF and currently commissioning it, much material is
particularly relevant to hadron machines. A section is concerned with radiation
damping in lepton machines.
