The Linear Variable Differential Transformer (LVDT)
is a transducer which is designed to convert linear position into a proportional AC voltage. The LVDT is a robust sensor with only a single moving part. The LVDT has essentially infinite output resolution because of its analog nature.

Transformers are used to change an AC electric signal at one voltage level to an AC electric signal at another voltage level. In an ideal transformer the ratio between input voltage and output voltage is simply equal to the equation.

Vs = Vp*Ns/Np = Vp/a
where
Vs is Secondary voltage
Vp is primary voltage
Ns is the number of turns in the secondary winding
Np is the number of turns in the primary winding
a is the voltage/turns ratio and is equal to Np/Ns

This equation is used as a fairly good approximation for the voltage ratio of a real transformer but is not exactly correct for a real transformer. In a real transformer turns ratio is not exactly equal to voltage ratio (though usually it is prety close). The important thing to remember is that transformers transfer energy inductively via the mutual magnetic flux present in the core material. Ideal transformers assume that ALL of the flux generated by the primary and secondary windings are contained within the core material which is not the case. Part of the flux generated by both windings, the leakage flux, flows through the air surrounding the transformer. This flux does not take part in our energy transformation and results in out voltage ratio being slightly larger than our turns ratio.

In general this is often overlooked as the difference is very small but the LVDT takes advantage of this idea. To see how let us examine the construction of an LVDT.

--------------------------------------------
-ssssssssssss|pppppppppppppppp|SSSSSSSSSSSS-
--------------------------------------------
mmmmmmmmmmmmmmmmmmmmmm
mmmmmmmmmmmmmmmmmmmmmm==================> X
mmmmmmmmmmmmmmmmmmmmmm
--------------------------------------------
-ssssssssssss|pppppppppppppppp|SSSSSSSSSSSS-
--------------------------------------------

Figure 1: Construction of an LVDT showing primary winding, secondary windings (2), and moving core. The core is shown in the neutral position. Output voltage would be 0.

Figure 1 shows the construction of an LVDT. the "s"'s represent secondary winding number 1, the "p"'s represent the primary winding, and the "S"'s represent the secondary winding number2. The single dashed lines ("-") represent the cylindrical core that all three windings are wound on (this core is non ferromagnetic). The secondary windings are wound in opposite directions on the cores and their starting leads are connected together. The "m"'s represent the core material. "X" is the coordinate axis we are measuring along.

In the position shown in Figure 1 the output of the LVDT would be 0VAC because the mutual flux between both secondary windings are equal, and therefore the voltages across the two secondaries are the same, but of opposite polarity. Because of the way that these two windings are connected the voltages cancel each other out and the net output is zero. If the core material were moved to the right the mutual flux between the primary winding and secondary winding number two would increase, resulting in a corresponding increase in the voltage across secondary 2. The opposite will happen to secondary 1. If the core were moved to the left the opposite would happen.

As mentioned before there is only one moving part in the LVDT, the core material. This is usually designed so that it does not actually touch the LVDT casing. The result of this is that LVDTs can be added to a device without adding an additional mechanical load other than the weight of the LVDT which can be small.

http://www.lvdtcollins.com/lvdt/lvdt.htm

http://civil.colorado.edu/courseware/struct_labs/tlvdt.html

Niku, Saeed. __Introduction to Robotics__. Upper Saddle River, NJ: Prentice Hall. 2001

Chapman, Stephen J. __Electric Machenery Fundamentals__. Boston: WCB/McGraw-Hill, 1999