Resonator-bolometer theory, microwave read out, and kinetic inductance bolometers

Kinetic inductance bolometers and calorimeters, each consisting of a kinetic inductance device suspended on a membrane and embedded in a resonant circuit, are being developed for applications such as planetary science, climate science, and X-ray spectroscopy. Arrays of these resonator-bolometers, each with a unique resonance frequency, are coupled to a single feedline, allowing many bolometers or calorimeters to be multiplexed using microwave read out. We derive coupled linear differential equations describing resonator-bolometers and means for calculating responses to signal and noise sources. By employing the bolometer matrix formalism, the model compactly describes the effects of demodulation, detuning, electrothermal feedback, resonator to feedline coupling, and bolometer sensitivity to changes in temperature and bias current. Based on this theory, estimates for the bolometer response to phonon noise, Johnson noise, and microwave bias quasiparticle generation noise are derived. The model is represented in terms of accessible parameters, most of which are measurable using a network analyzer. It is applicable to other types of devices such as dielectric bolometers or alternating current biased transition edge sensors and is readily extendible to more complex bolometers or to unsuspended kinetic inductance devices.