A steam generator system for a cooking appliance includes an in-line heating element coupled to a heating tube, wherein water from a water reservoir is gravitationally fed into the heating tube for heating by the in-line heating element to produce a hot water and steam mixture. A first supply line is coupled to the heating tube to carry the mixture to a separator without the need for moving or complex pump parts. The separator separates steam and hot water from the mixture of the two. A second supply line is coupled to the separator at a first end and opens into the cooking cavity of the cooking appliance at a second end. The second supply line is configured to supply steam separated at the separator to the cooking cavity via a steam outlet disposed in the cooking cavity.