Your first encounter with this as a crafting requirement will likely be a bit of a weird one if you have not constructed the more advanced buildings in the game. Where the hell is this supposed to come from?
Where to find Circuit Boards
Circuit boards are a component you craft. You will not find them in the wild through mining and harvesting resources. You can craft this item at a factory using other advanced materials. It is best to save this one until you have plenty of plastic, oil and lots of gems as you will be needing to make the most out of royal cloth and steel.