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We present the characterisation of the most recent parametric transducersdesigned to enhance the Mario Schenberg Gravitational Wave Detectorsensitivity. The transducer is composed of a microwave re-entrant cavity thatattaches to the gravitational wave antenna via a rigid spring. It functions asa three-mode mass-spring system; motion of the spherical antenna couples to a50 $\mu m$ thick membrane, which converts its mechanical motion into afrequency shift of the cavity resonance. Through the optical spring effect, themicrowave transducer frequency-displacement sensitivity was measured to be 726$MHz/\mu$m at 4 K. The spherical antenna detection sensitivity is determinedanalytically using the transducer amplification gain and equivalentdisplacement noise in the test setup, which are 5.5 $\times$ 10$^{11} V/m$ and$1.8 \times 10^{-19} m\sqrt{Hz}^{-1}$, respectively.

Sensitivity Characterisation of a Parametric Transducer for Gravitational Wave Detection Through Optical Spring Effect