LVDT Linear Variable Differential Transformer: Theory, Wiring, and Signal Conditioning

An LVDT (Linear Variable Differential Transformer) is an inductive transducer that converts rectilinear mechanical displacement into a proportional AC electrical signal by varying the magnetic coupling between a primary coil and two secondary coils via a movable ferromagnetic core. Unlike resistive sensors, integrating an LVDT into a real circuit fundamentally changes your signal chain: it demands an AC excitation oscillator and a phase-sensitive synchronous demodulator to translate AC amplitude and phase into a usable DC voltage, meaning you cannot simply wire it to a microcontroller’s DC analog-to-digital converter (ADC).

The Working Principle of an LVDT Linear Variable Differential Transformer

At its core, an LVDT is a specialized AC transformer with one primary winding and two secondary windings. The primary coil is driven by an alternating current (the excitation signal), typically a sine wave between 1 kHz and 10 kHz. The two secondary coils are wound identically and placed symmetrically on either side of the primary. They are wired in a series-opposing configuration, meaning their output voltages subtract from one another.

A movable ferromagnetic core (usually a nickel-iron alloy rod) slides through the hollow center of the coil assembly without making physical contact. This frictionless operation is why LVDTs boast near-infinite mechanical life.

• Null Position (Center): When the core is perfectly centered, it couples an equal amount of magnetic flux to both secondary coils. The induced voltages are equal in amplitude but opposite in phase due to the series-opposing wiring. The net differential output is zero (or a very small residual "null voltage").
• Displacement in Direction A: Moving the core toward Secondary 1 increases the mutual inductance of that coil while decreasing it for Secondary 2. The differential output voltage increases, and the phase of the output matches the phase of the primary excitation (0° phase shift).
• Displacement in Direction B: Moving the core toward Secondary 2 reverses the imbalance. The amplitude increases identically, but the output phase flips 180° out of phase with the primary excitation.

This phase shift is critical. The amplitude of the AC signal tells you how far the core has moved, while the phase (0° or 180°) tells you which direction it moved. To read this with a standard DC voltmeter or microcontroller, you must use a signal conditioning IC (like the Analog Devices AD598 or AD698) that performs synchronous demodulation, converting the AC signal into a positive or negative DC voltage.

Worked Numeric Example: Sizing and Signal Output

Let’s calculate the expected output of a standard industrial AC LVDT, such as a TE Connectivity GCA series sensor, to understand how sensitivity and excitation interact.

The Scenario: The core is displaced +5.0 mm from the center null position. What is the raw AC output voltage, and how does the demodulator read it?

1. Calculate Full-Scale Output: Sensitivity is normalized per volt of excitation. At 4.0 V RMS excitation, the sensitivity becomes 2.5 mV/V/mm × 4.0 V = 10.0 mV/mm.
2. Calculate Displacement Output: For a +5.0 mm displacement, the raw AC output is 10.0 mV/mm × 5.0 mm = 50.0 mV RMS.
3. Determine Phase: Because the displacement is in the positive direction, the 50.0 mV RMS signal is in-phase (0°) with the 5.0 kHz excitation signal.
4. Demodulated DC Output: If your signal conditioner is scaled to output ±10 V DC for the full ±10 mm stroke (1 V/mm), a +5.0 mm displacement will yield exactly +5.0 V DC. If the core moves to -5.0 mm, the raw AC output remains 50.0 mV RMS, but the phase flips to 180°. The demodulator detects this phase inversion and outputs -5.0 V DC.

Edge Case - Cable Capacitance: If you extend the sensor cable by 50 feet using standard unshielded twisted pair, the added shunt capacitance will introduce a phase shift in the excitation signal. At 5 kHz, this can cause a phase error at the demodulator, resulting in a non-zero DC offset even when the core is at the null position. Always use the manufacturer's specified low-capacitance shielded cable (like Belden 8723) for runs over 10 feet.

Where You Meet This in Practice

You won't typically find LVDTs in consumer electronics or basic hobbyist robotics; they are the domain of high-reliability, high-precision industrial and aerospace systems. Because the core does not touch the coil assembly, there is zero mechanical friction and no wear-out mechanism.

Common Applications:

• Aerospace Flight Controls: Redundant LVDTs are mounted inside hydraulic actuators on aircraft wings to provide fly-by-wire feedback on control surface positioning. They operate flawlessly despite extreme vibration and temperature swings.
• CNC Machine Tool Gauging: Used in automated part inspection stations to measure machined tolerances down to sub-micron levels. The hermetic sealing allows them to operate while submerged in cutting fluids.
• Hydraulic Cylinder Stroke Measurement: Heavy-duty LVDTs are inserted directly into the bores of hydraulic rams in mobile heavy equipment and industrial presses to monitor ram extension under high shock loads.

LVDT vs. Potentiometers and Magnetostrictive Sensors

When designing a linear positioning system, you will usually choose between an LVDT, a resistive potentiometer (or string pot), and a magnetostrictive sensor. Here is how they stack up for precision applications.

Choose an LVDT when you need absolute reliability, infinite resolution over a short stroke (typically under 12 inches), and operation in harsh, fluid-filled environments. Choose a magnetostrictive sensor if your stroke length exceeds 1 meter, as LVDT coil assemblies become prohibitively long and expensive at those scales.