An Analytical Model for the Linear Variable Differential Transformer

The linear variable differential transformer (LVDT) is widely used for displacement measurement in both industry and research due to its high accuracy and working ability in harsh environments. However, the lack of a precise and detailed analytical model limits the application and development of the LVDT. The traditional LVDT model, the magnetic circuit model, and finite-element method (FEM) models all have limitations when it comes to customizing LVDT designs for specific applications. This article builds an analytical model for the LVDT by solving Maxwell’s equations, which can investigate a broader range of parameters to design LVDTs. The truncated region eigenfunction expansion (TREE) method, based on the magnetic vector potential, is used to solve the finite-length magnetic core problem. The model is validated by experiments, showing that the maximum discrepancy is smaller than 1.5%. FEM is used to validate the model in a broader range of parameters, and the maximum discrepancy between the model results and FEM is below 0.9% at different working frequencies and magnetic core permeabilities. This article presents an example of using the model to investigate LVDT parameters’ influences on the output’s sensitivity and linearity error, quantifying the impact of the magnetic core’s geometric parameters. This model can optimize LVDT design and facilitate the advancement of LVDT-related sensors.