An electronic device, such as a watch, has a housing to which a carrier is attached. The carrier has a first surface interior to the electronic device, and a second surface exterior to the electronic device. A set of electrodes is deposited on the exterior surface of the carrier. An additional electrode is operable to be contacted by a finger of a user of the electronic device while the first electrode is positioned against skin of the user. The additional electrode may be positioned on a user-rotatable crown of the electronic device, on a button of the electronic device, or on another surface of the housing of the electronic device. A processor of the electronic device is operable to determine a biological parameter of the user based on voltages at the electrodes. The biological parameter may be an electrocardiogram.