  We investigate quantum phase transitions among the spin-gap phases and the
magnetically ordered phases in a two-dimensional frustrated antiferromagnetic
spin system, which interpolates several important models such as the
orthogonal-dimer model as well as the model on the 1/5-depleted square lattice.
By computing the ground state energy, the staggered susceptibility and the spin
gap by means of the series expansion method, we determine the ground-state
phase diagram and discuss the role of geometrical frustration. In particular,
it is found that a RVB-type spin-gap phase proposed recently for the
orthogonal-dimer system is adiabatically connected to the plaquette phase known
for the 1/5-depleted square-lattice model.
