  An electrothermal model of Kinetic Inductance Detectors (KIDs) is described.
The non-equilibrium state of the resonator's quasiparticle system is
characterized by an effective temperature, which because of readout-power
heating is higher than that of the bath. By balancing the flow of energy into
the quasiparticle system, it is possible to calculate the steady-state
large-signal, small-signal and noise behaviour. Resonance-curve distortion and
hysteretic switching appear naturally within the framework. It is shown that an
electrothermal feedback process exists, which affects all aspects of behaviour.
It is also shown that generation-recombination noise can be interpreted in
terms of the thermal fluctuation noise in the effective thermal conductance
that links the quasiparticle and phonon systems of the resonator. Because the
scheme is based on electrothermal considerations, multiple elements can be
added to simulate the behaviour of complex devices, such as resonators on
membranes, again taking into account readout power heating.
