A steam generator includes an inlet configured to receive a liquid (such as water); a heating element for converting the liquid into a vapor (such as steam), the vapor bearing particles such as mineral deposits formed by the converting of the liquid; an outlet in fluid communication with the inlet, the outlet configured to discharge filtered vapor and having a size on the order of larger ones of the particles; and a filter structure adjacent to the outlet to filter the larger particles out of the vapor to produce the filtered vapor for discharge from the outlet. By action of the filter structure, larger particles are prevented from reaching the outlet, reducing clogging and extending the usable lifetime of a small appliance containing the steam generator. The filter structure may include spaced-apart members such as posts or pillars extending perpendicularly in a planar fluid flow passage.