Various embodiments of electrically-variable transmissions are provided that have a first and a second motor-generator, a first and a second planetary gear set, and two torque-transmitting mechanisms, including a rotating-type clutch and a stationary-type clutch. An input member is connected for common rotation with a ring gear of the first planetary gear set. Carriers of both of the planetary gear sets are connected for common rotation with one another, and with an output member. The first motor/generator is connected for common rotation with the sun gear of the first planetary gear set. The second motor/generator is connected for common rotation with the sun gear of the second planetary gear set. The rotating-type torque-transmitting mechanism is a dog clutch with a synchronizer. The stationary-type torque-transmitting mechanism may be either a dog clutch with a synchronizer or a selectable one-way braking clutch (SOWBC).