There is provided a transmission device having an electrically variable output that employs three electrically powered motor-generators, or machines. The electrically-variable transmission device comprises first, second and third electrical machines coaxial to and coupled to a plurality of planetary gear sets. Each planetary gear set coupled to a main shaft operative to transmit torque therebetween and operative to transmit torque to an output. There is an input mechanically coupled to one of the planetary gear sets. This transmission device can transmit mechanical power with a continuously variable ratio of the input shaft speed to the output shaft speed using two of the electric motors at a time, forming an input-split or either an output-split or a compound-split. A selectively actuable brake device is operative to multiply torque output from the second electrical machine.