The electrically variable transmission family provides low-content, low-cost electrically variable transmission mechanisms including first, second and third differential gear sets, a battery, two electric machines serving interchangeably as motors or generators, up to six selectable torque-transfer devices, and possibly a dog clutch. The selectable torque transfer devices are engaged to yield an EVT with a continuously variable range of speeds (including reverse) and mechanically fixed forward speed ratios. The torque transfer devices and the first and second motor/generators are operable to provide five operating modes in the electrically variable transmission, including battery reverse mode, EVT reverse mode, reverse and forward launch modes, continuously variable transmission range mode, and fixed ratio mode.