The electrically variable transmission family of the present invention 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, and six selectable torque-transfer devices, which may include a dog clutch. The selectable torque transfer devices are engaged singly or combinations of two to yield an EVT with a continuously variable range of speeds (including reverse) and up to four 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.