Linear Variable Differential Transformer (LVDT) Sizing and Circuit Theory

A Linear Variable Differential Transformer (LVDT) is a frictionless, inductive position sensor that converts precise linear motion into a proportional AC voltage output. Unlike resistive sensors that degrade over time, an LVDT relies on magnetic coupling between a movable ferromagnetic core and stationary wire coils, offering infinite resolution and zero mechanical wear. If you are designing a feedback loop for a high-vibration environment or need sub-micron repeatability, understanding LVDT theory is the difference between a noisy, drifting system and one that runs for a decade without recalibration.

The Core Principle: How an LVDT Actually Works

An LVDT consists of three coils wound around a hollow, non-magnetic bobbin. The center coil is the primary, and the two outer coils are the secondaries. A separate, rod-shaped ferromagnetic core slides freely through the hollow center without touching the walls.

When you apply an AC excitation voltage (typically 1V to 10V RMS at 1 kHz to 10 kHz) to the primary coil, it generates an alternating magnetic field. This field induces voltages in the two secondary coils via mutual inductance. The secondaries are wired in series-opposition, meaning their output voltages subtract from one another.

• Null Position (Center): The core is exactly centered. Both secondaries are coupled equally. The induced voltages are identical, so the differential output is exactly 0V.
• Positive Displacement: The core moves toward Secondary 1. Coupling increases in S1 and decreases in S2. The output voltage rises, in-phase with the primary excitation.
• Negative Displacement: The core moves toward Secondary 2. The output voltage rises, but is shifted 180° out-of-phase with the primary excitation.

This phase shift is how the downstream signal conditioner determines the direction of the movement, while the amplitude determines the distance. For a deep dive into the signal conditioning ICs that handle this demodulation, the Analog Devices guide on LVDT signal conditioners is the definitive bench reference.

Worked Numeric Example: Calculating LVDT Output Voltage

Let’s calculate the raw AC output of a standard industrial LVDT before it hits the demodulator. We will use specs typical of a mid-range sensor like the TE Connectivity GH-Series.

The formula for the raw differential output voltage ($V_{out}$) is:

V_out = Sensitivity × V_ex × d

Plugging in our real-world numbers:

V_out = 2.4 mV/V/mm × 3.0 V × 4.5 mm
V_out = 32.4 mV RMS

Because the displacement is positive (+4.5 mm), this 32.4 mV RMS signal is in-phase (0° shift) with the 3.0V excitation. If the core moves to -4.5 mm, the output remains 32.4 mV RMS, but the phase flips to 180°. Your signal conditioner (like an Analog Devices AD598 or AD698 chip) will rectify and filter this into a clean +4.5V or -4.5V DC signal for your microcontroller.

Where You Meet LVDTs in Practice

You will rarely find an LVDT in consumer electronics; they are strictly industrial, aerospace, and heavy-machinery components. You meet them in practice when a system demands absolute reliability over millions of cycles.

• Hydraulic Cylinder Stroke Feedback: In heavy presses, the LVDT core is threaded directly into the end of the hydraulic piston rod. Because there is no physical contact, the violent shocks of the press don't destroy the sensor.
• Rolling Mill Automatic Gauge Control (AGC): In steel mills, LVDTs measure the microscopic gap between massive rolling cylinders to ensure sheet metal thickness is held to sub-millimeter tolerances.
• Aerospace Flight Control Actuators: Aircraft aileron and rudder actuators use redundant LVDTs to feed position data back to the fly-by-wire flight computers, operating flawlessly across extreme temperature swings.

Decision Matrix: LVDT vs. Alternative Position Sensors

Choosing the right linear position sensor requires matching the physical environment to the sensor's operating principle. Use this decision path to terminate your selection process with a concrete part type.

Common Confusions and Wiring Pitfalls

When engineers first work with LVDTs, they frequently make three specific mistakes that lead to noisy or drifting data.

Confusion 1: LVDT vs. Standard Power Transformers

Despite having "Transformer" in the name, an LVDT does not transfer power to a load. It is strictly a signal transducer. Do not attempt to use an LVDT to step down AC voltages; the secondary coils are wound with ultra-fine wire meant only to carry millivolt signals into high-impedance instrumentation amplifiers.

Confusion 2: LVDT vs. RVDT

An RVDT (Rotary Variable Differential Transformer) operates on the exact same inductive principle but uses a cam-shaped core that rotates to measure angular displacement (typically ±40°). They are not interchangeable; forcing linear motion into an RVDT will mechanically destroy the bearings.

Pitfall: Ignoring Ratiometric Drift

The most common bench failure is watching the DC output drift over time even when the core is stationary. This happens if you use a non-ratiometric signal conditioner. If your AC excitation voltage drops by 2% due to thermal drift in the oscillator, your raw LVDT output drops by 2%, causing a false position reading. Always use a ratiometric signal conditioner (like the AD698), which measures the primary excitation voltage in real-time and divides the secondary output by it, mathematically canceling out any excitation drift. For more on sensor signal chain design, consult the Omega Engineering LVDT learning center.

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