A fluid coupling device in which the input coupling member (11) includes a plate-like member (29) defining a first inlet port (63), and a second inlet port (67) disposed radially outward of the first inlet port. The device includes a valve member (43) having a disengaged position (FIG. 4) blocking flow through both inlet ports. As the valve member (43) moves from the disengaged position toward a first operating position (FIG. 5) the first inlet port (63) is uncovered, while the second inlet port (67) remains covered. Continued movement of the valve member results in progressive uncovering of the second inlet port (67). Finally, there is a third inlet port (73), radially outward from the second inlet port (67), and further movement of the valve member (43) eventually uncovers the third inlet port. As the valve member moves, after uncovering the first inlet port, it passes though a dead band region (D1), then after uncovering the second inlet port, it passes through a dead band region (D2), in both cases helping to insure that the desired amount of fluid has been communicated into the operating chamber (35).