We derive theoretical expressions for output errors that occur in two types of superconducting level sensors. One is a conventional level sensor composed of a thin superconducting wire located vertically inside a cryostat. The other is a parallel level sensor with both superconducting and non-superconducting wires, which has been proposed to improve the output error in level sensors for liquid hydrogen using an MgB2 wire. The theoretical expressions are validated by comparing them with output errors estimated using numerical simulations based on a one-dimensional heat balance equation. It is assumed that the superconducting wire has an MgB2 monofilament surrounded by a metal sheath of stainless steel or cupronickel, whereas the non-superconducting wire is an as-drawn wire before superconducting heat treatment or a non-composite solid wire identical to the metal sheath in the superconducting wire. The level sensors are calibrated for the condition where the liquid hydrogen is spontaneously evaporated inside the cryostat or the cryostat is slowly refilled with liquid hydrogen. The output error is also estimated for three different cases of rapidly refilling with liquid hydrogen and discharging liquid hydrogen from the cryostat by internal pressurization using each gaseous hydrogen and helium.
