A Linear Variable Differential Transformer (LVDT) is a displacement transducer, used to measure displacement, based on the effect of the mutual inductances. It is also used in some hydraulic applications, steam control and pressure measurement.
Figure 1 shows the structure of an LVDT, which consists of the primary winding, excited by an AC source, displacable magnetic core, and two secondary windings, connected to the output voltage. The displacement distance determines the mutual coupling of the primary and secondary windings. The middle position of the core corresponds to the zero output voltage.
Let’s consider the primary coil with the parameters:
So voltages induced in the secondary winding are:
Here M1 and M2 are mutual inductances between the primary and secondary windings. Where M1 and M2 are depend on the position of the magnetic core. So:
An LVDT is designed in a way that vout is linearly dependent on the position r of the magnetic core. If the core is displaced closer to M1, v1 increases and v2 is decreases. If the core is displaced closer to the M2 winding, v2 increases and v1 decreases. If the core is displaced closer to the winding, increases and decreases. As the excitation signal is the AC signal, the vout will be an AC signal as well.
It’s amplitude and phase are dependent on the magnetic core r position. The output vout signal is the Amplitude-Modulated (AM) Signal. One of the applications of the LVDT is a position balancing detector. The LVDT’s sensor has evolved since the time it was first designed and implemented as a very useful technology for reliable measurements into applications for different industries, like industrial, military, aerospace, sea, and so on.
The modern LVDT sensor is upgraded with a microcontroller and innovative construction materials, and the supporting electronics are often already included in the LVDT package.
 Engineering Principles and Applications of Electrical Engineering, 3rd edition, Rizzoni.
 Modern LVDT’s in new applications in the Air, Ground and Sea, John Matlack, 2010
 TE Connectivity, White Paper, Linear Variable Differential Transformer.