Cement backer board can provide a solid flat surface to install tiles on if you have a wood subfloor.
Subfloor material for ceramic tile.
When installing a ceramic tile floor on a concrete subfloor you don t have to worry about flexing as long as the concrete slab is at least 1 1 8 inch thick which most slabs are.
It sounds like your joists are well within the acceptable limits of l 300 so your main concern is the deflection of the subfloor between joists.
Tile floors are heavy and tile is a hard material.
A plywood subfloor must be structurally sound and able to support the installation.
For ceramic tile the tile council recommends using joists that are 16 inches on center a 3 4 inch thick plywood subfloor and a 1 2 inch thick cement backer board or concrete slab.
Because of issues of moisture movement and adhesion ceramic tile will work well with certain types of subfloor underlayment systems and can go dramatically wrong with other subfloor materials.
It will break or dislodge if the surface bends under the load.
Materials such as vinyl and carpeting are flexible enough to tolerate engineered floor truss systems with larger joist spacings such as 24 inches on center.
Concrete expands and contracts and that type of movement can also crack the tiles and the grout.
However you re not out of the woods.
Laying tile on plywood.
2 prepare a wood subfloor for tile a successful tile installation project requires a level surface.
With ceramic tile you also need to limit the deflection between joists which is a function of the subfloor thickness and how it is installed.