# Introduction to linear variable differential transformers (LVDTs)

The linear variable differential transformer (LVDT) is an electromechanical transducer that senses the mechanical displacement of a core and produces a proportional AC voltage at the output. High resolution (infinite in theory), high linearity (0.5% or better), high sensitivity and zero mechanical friction are some of the important features of the LVDT devices.

In this article, we’ll look at the structure and working principles of LVDTs. We’ll also examine three important parameters of these sensors: linear range, linearity error, and sensitivity.

## Structure of an LVDT

Figure 1 shows the cutaway view and circuit model of a basic LVDT. It consists of one primary winding coupled to two secondary windings through a movable core. As the magnetically permeable core moves, the magnetic coupling between the primary and each of the secondary windings changes accordingly. This produces position-dependent voltage signals across the two windings that can be used to determine the position of an object.

 Figure 1(a). Cutaway view of an LVDT.
 Figure 1(b). Circuit model of an LVDT.

The two secondary windings are series-opposed meaning that they are connected in series but wound in opposite directions. The core, typically through a non-ferromagnetic rod, attaches to the object whose movement is being measured and the coil assembly is typically fixed to a stationary form.

## How does it work?

Figure 2 shows how a perfectly centered core ideally produces a zero output. The input is excited by an AC voltage of appropriate frequency (VEXC). Since the two secondaries are wound symmetrically on the two sides of the primary coil, a centered core leads to equal magnetic coupling from the primary to the two secondaries. With the secondary windings being series-opposed, equal voltages with opposite polarities will be induced across the two secondaries (VS1 = –VS2). Hence, the voltages of the two windings will cancel out and we’ll have an overall output of zero (VOUT = 0).

 Figure 2. LVDT with a perfectly centered core.

When the core is displaced upward as shown in Figure 3, the coupling between the primary and the first secondary becomes stronger. This leads to a larger AC voltage across the first secondary compared to the second secondary (|VS1| > |VS2|) and a non-zero output (VOUT). Note that the output is in phase with VS1 but its amplitude is relatively smaller.

 Figure 3. LVDT with the core moved upward.

With the example depicted in Figure 3, the output should be ideally in-phase with VEXC when the core experiences an upward displacement.

The typical waveforms for the downward displacement of the core is shown in Figure 4.

 Figure 4. LVDT with the core moved downward.

In this case, the magnetic coupling between the primary and the second secondary increases leading to |VS2| > |VS1|. As you can see, we’ll have a non-zero VOUT that is ideally 180° out-of-phase with respect to the excitation voltage.

## Transfer function

Figure 5 shows the transfer function of a typical LVDT. The x-axis is the core displacement from the center. The Y-axis is the amplitude of the output AC voltage.

At the origin (X = 0), the output is ideally zero. As the core is moved off center in either direction, the amplitude of the output increases linearly with the core displacement. Note that measuring only the amplitude of the output, we cannot determine whether the core is displaced to the left or to the right. We need to know both the amplitude and phase of the output.

## Linear range

As shown in Figure 5, an LVDT exhibits a linear transfer function only over a limited range of the core displacement. This is specified as the linear range of the LVDT.

 Figure 5. Transfer function of a typical LVDT.

Why does the device stop having a linear relationship beyond this range?

We can imagine that, when the core displacement from the null position goes beyond a certain value, the magnetic flux that gets to couple to the core from the primary winding reduces. This, consequently, leads to a reduction in the voltage that appears across the corresponding secondary winding. The maximum distance that the core can travel from its null position while having a linear transfer function is referred to as the full-scale displacement.

Broad ranges of LVDTs are available covering displacement ranges as little as ±100 μm to ±25 cm. LVDTs capable of measuring larger ranges also find use in laboratory, industrial and submersible environments.

## Linearity error

The plot of the LVDT output versus the core displacement is not a perfect straight line even in the linear range. The output can slightly deviate from the straight line constructed to have the best fit to the output data.

One mechanism that can lead to non-linearity in the nominal linear range of the device is saturation of the magnetic material. This can produce the 3rd harmonic component even when the core is at the null position. This harmonic can be suppressed by applying a low-pass filter to the LVDT output.

The maximum deviation of the LVDT output from the expected straight line fit is considered as the linearity error. Linearity error is typically expressed as a +/- percentage of the full-range output. For example, the E-100 LVDT from Measurement Specialties, Inc., has a maximum linearity error of ±0.5% of full-scale range.

## Sensitivity

Sensitivity or transfer ratio allows us to relate the output voltage to the core displacement D. To determine the sensitivity, we energize the primary at the recommended drive level (3 VRMS for E-100 LVDT) and move the core off the null position by the full-scale displacement. Now, we measure the voltages across the two secondary windings to find the overall output voltage (VOUT). Substituting these values in the following equation, we can find the LVDT sensitivity S:

Sensitivity is usually specified in terms of millivolt output per Volt of excitation per thousandths of an inch core displacement (mV/V/mil). For example, the sensitivity of the E-100 is 2.4 mV/V/mil. Having sensitivity, we can determine the required gain of the signal conditioning circuitry.