Parametric transducers for resonant bar gravitational wave antennae

A new lumped element model of a two-mode resonant bar antenna coupled to a parametric transducer is presented and verified experimentally. The capacitance-modulated cavity transducer is represented in scattering parameter form, and is augmented to include the observable amplitude- and phase-modulated components of the pump oscillator, which simplifies calculations of amplitude-modulated to phase-modulated and phase-modulated to amplitude-modulated conversions. This representation enables the definition of the amplitude-modulated and phase-modulated components of transducer electro-mechanical coupling. Theory is verified from experimental data from the detector at the University of Western Australia, which uses a superconducting re-entrant cavity transducer. Comparisons for a proposed high-Q sapphire transducer are presented and compared with the present re-entrant cavity transducer. This model allows us to optimize the transfer function of the UWA detector, minimizing the effect of seismic noise at a set electro-mechanical coupling.