  We report the results of a detailed numerical analysis of a real resonant
spherical gravitational wave antenna operating with six resonant two-mode
capacitive transducers read out by superconducting quantum interference devices
(SQUID) amplifiers. We derive a set of equations to describe the
electro-mechanical dynamics of the detector. The model takes into account the
effect of all the noise sources present in each transducer chain: the thermal
noise associated with the mechanical resonators, the thermal noise from the
superconducting impedance matching transformer, the back-action noise and the
additive current noise of the SQUID amplifier. Asymmetries in the detector
signal-to-noise ratio and bandwidth, coming from considering the transducers
not as point-like objects but as sensor with physically defined geometry and
dimension, are also investigated. We calculate the sensitivity for an
ultracryogenic, 30 ton, 2 meter in diameter, spherical detector with optimal
and non-optimal impedance matching of the electrical read-out scheme to the
mechanical modes. The results of the analysis is useful not only to optimize
existing smaller mass spherical detector like MiniGrail, in Leiden, but also as
a technological guideline for future massive detectors. Furthermore we
calculate the antenna patterns when the sphere operates with one, three and six
resonators. The sky coverage for two detectors based in The Netherlands and
Brasil and operating in coincidence is also estimated. Finally, we describe and
numerically verify a calibration and filtering procedure useful for diagnostic
and detection purposes in analogy with existing resonant bar detectors.
