Matching of transducers to resonant gravitational wave antennas.

A theory is developed for the matching of a transducer to a resonant gravitational wave antenna for the cases of a transducer directly coupled to the bar and coupled to the bar through another resonant mass. The antenna sensitivity, representing the minimum detectable spectral energy density of gravitational radiation, is expressed in terms of the ratio between the effective temperature and the antenna mass, the former of which depends on bar temperature, transducer noise temperature, the matching between bar, transducer and preamplifier, and the data analysis algorithm. An expression for the optimum matching conditions is derived which holds for both configurations, and it is found that when the matching conditions are met, the effective temperature becomes equal to twice the amplifier noise temperature if the Wiener-Kolmogoroff algorithm is used in the data analysis.