Microfluidic devices have many attractive qualities such as low cost, small size, and in-field use. Micromixers are very important components of these devices because affect their efficiency. In a passive mixer, the structural characteristics of the mixer are crucial and must be analyzed. This paper presents a numerical study of the mixing in passive Y-shaped micromixers with a spherical mixing chamber for a volume constrained system. The effect of asymmetric bifurcated ducts, the angle in between the inflow ducts, eccentricity and, obstacles inserted in the mixing sphere, on the mixing efficiency and flow impedance is evaluated. Vortical structures characteristics and the possible occurrence of engulfment are also identified. The results show that flow impedance (pressure drop for unit volumetric flow rate) can be decreased greatly for the same mixing efficiency as the volume of the spherical mixing chamber is 20% of the total volume. Insertion of the obstacles into the sphere mixing chamber decreases the mixing efficiency while they increase the flow impedance. The results also show that spherical mixing chamber enhances mixing efficiency while decreasing flow impedance if the volume reserved for it is greater than a limit value which depends on the diameter and length scale ratios in between the mother and daughter ducts as well as the total volume. Overall, the paper documents the variation of mixing efficiency and flow impedance based on the geometrical parameters of three-dimensional asymmetric passive micromixer with sphere mixing chamber.