A variable differential transformer (most commonly deployed as a Linear Variable Differential Transformer, or LVDT) is an inductive transducer that converts linear mechanical displacement into a proportional AC electrical signal by moving a magnetic core through one primary and two secondary coil windings. In a real motion control circuit, it replaces friction-prone resistive potentiometers, giving your PLC or PID loop infinite resolution and zero mechanical wear in the feedback path. Makers and junior techs frequently confuse it with a standard audio transformer or a string potentiometer, but an LVDT relies on shifting mutual inductance, not a physical wiper scraping across a resistive track.

The Core Mechanism: How a Variable Differential Transformer Works

Inside the stainless steel housing of an LVDT, you will find three coils wrapped around a hollow, non-magnetic form. The center coil is the primary winding, and the two outer coils are the secondary windings. A separate, movable ferromagnetic core slides freely through the center bore without touching the walls.

When you drive the primary coil with an AC excitation voltage (typically 1V to 10V RMS at 1kHz to 10kHz), it generates an alternating magnetic field. This field couples with the secondary windings based on the physical position of the core. The two secondary coils are wired in series-opposition—meaning their outputs are subtracted from one another.

The Null Position: When the core is perfectly centered, the magnetic flux coupling to both secondary coils is identical. Because they are wired in opposition, the induced voltages cancel out, yielding a net output of exactly 0V. Move the core left, and Secondary A dominates. Move it right, and Secondary B dominates, accompanied by a 180-degree phase shift in the AC waveform. This phase shift is how your controller knows the direction of the movement.

The Math: Sensitivity, Excitation, and a Worked Numeric Example

Unlike a digital encoder that outputs discrete pulses, an LVDT is purely analog. The output voltage amplitude is strictly proportional to displacement, but it is also directly dependent on your excitation voltage. If your excitation sags, your position reading will drift, which is why we use ratiometric signal conditioners.

The governing formula for output voltage is:

Vout = S × Vex × d

  • S = Sensor sensitivity (provided by the manufacturer in mV/V/mm)
  • Vex = Primary excitation voltage (V RMS)
  • d = Displacement from the null position (mm)

Worked Numeric Example

Let's look at a real-world scenario using a TE Connectivity GHSA-100 hermetic LVDT, which has a ±50mm stroke range.

  • Datasheet Sensitivity (S): 0.8 mV/V/mm
  • Applied Excitation (Vex): 5V RMS at 3kHz
  • Measured Core Displacement (d): +25mm from the null position
Calculation: Vout = 0.8 mV/V/mm × 5V × 25mm = 100 mV RMS.

Your PLC's analog input module will read this 100 mV AC signal, check the phase angle relative to the 3kHz excitation reference, and calculate that the cylinder has extended exactly 25mm. If the core had moved -25mm, the amplitude would still be 100 mV RMS, but the phase would be inverted by 180 degrees.

Where You Meet This in Practice (And Where It Fails)

You will rarely find an LVDT in consumer electronics; they are the workhorses of heavy industry, aerospace, and precision manufacturing. You will meet them in:

  • CNC Machine Tool Axes: Providing closed-loop position feedback on the actual slide movement, bypassing ball-screw backlash errors.
  • Hydraulic Cylinder Stroke Sensing: Integrated directly into the rod end of heavy press cylinders to monitor tonnage and stroke depth.
  • Steam Turbine Governor Valves: Monitoring the exact opening percentage of high-pressure steam valves where temperatures exceed 150°C.

Common Failure Modes on the Jobsite

While the sensor itself is practically immortal because there is no physical contact between the core and the coil, installations fail due to external factors:

  1. Core Binding: If the push-rod is subjected to side-loading, the core rubs against the inner bore. This introduces friction and eventually wears through the coil form, destroying the sensor. Always use flexible couplings or non-magnetic push-rods with spherical bearings.
  2. Moisture Ingress: Standard LVDTs are vented. If deployed in a washdown environment without an IP69K-rated hermetic seal (like the TE GHSA series), condensation forms inside the coil, altering the dielectric constant and causing non-linear output drift.
  3. VFD Noise Coupling: The millivolt-level AC output is highly susceptible to electromagnetic interference (EMI). Running an unshielded LVDT cable parallel to a Variable Frequency Drive (VFD) power cable will induce massive noise spikes, causing the PLC to read phantom position jumps.

Decision Tree: Choosing the Right Position Sensor

An LVDT is not the only way to measure linear displacement. Use this decision matrix to select the correct technology and a concrete part number for your next build or retrofit.

Application Scenario Recommended Technology Concrete Pick / Part Number
Stroke < 100mm, high vibration, high temp (up to 200°C), requires infinite resolution. AC LVDT (Standard) TE Connectivity GHSA-100 (Hermetic, 316 stainless steel)
Stroke > 500mm, dirty/harsh environment, standard industrial PLC integration (4-20mA). Magnetostrictive Sensor Temposonics R-Series V (IO-Link / Analog output)
Budget < $150, low vibration, clean indoor environment, simple 0-10V analog needed. DC-LVDT (Built-in conditioner) Omega LD400-50 (±50mm stroke, 10-30VDC input)
Ultra-long stroke (>2 meters), dusty environment, low precision required. String Potentiometer WPS-2000-MK46 (Micro-Epsilon draw-wire sensor)
Bench Tip: If you are retrofitting an old machine that already has an analog input card but no excitation source, skip the raw AC LVDT and buy a DC-LVDT. It contains an internal ASIC that generates its own AC excitation and demodulates the output to a standard 0-10VDC or 4-20mA signal, saving you from buying a separate $300 signal conditioning module.

Wiring, Signal Conditioning, and Shielding Rules

Wiring a raw AC variable differential transformer requires more care than a standard 4-20mA pressure transmitter. According to Omega Engineering's LVDT application guidelines, you are dealing with a ratiometric AC system that demands strict signal integrity.

The Signal Conditioner:
You cannot wire a raw AC LVDT directly to an Arduino or a standard PLC analog input. You need a dedicated LVDT signal conditioner (like the OMEGA DRF-LVDT DIN-rail module). This module performs three critical jobs:

  1. Generates a stable, low-distortion sine wave for the primary coil excitation.
  2. Amplifies the millivolt-level secondary outputs.
  3. Performs synchronous demodulation (phase-sensitive detection) to convert the AC amplitude and phase into a bipolar DC voltage (e.g., -10V to +10V representing -50mm to +50mm).

The Shielding Mandate:
Because the secondary outputs are high-impedance, low-voltage AC signals, the cable shield is non-negotiable. Use a twisted-pair shielded cable. Ground the shield at exactly one end—specifically, at the signal conditioner's chassis ground. If you ground the shield at both the sensor housing and the DIN rail, you create a ground loop. In an industrial plant with varying ground potentials, a ground loop will push 60Hz hum directly into your position reading, rendering the LVDT's infinite resolution useless.

Frequently Asked Questions

Can I use a standard audio transformer as an LVDT?

No. While both rely on mutual inductance, an audio transformer is designed to transfer maximum power across a specific frequency band with a fixed core (usually laminated steel or ferrite). An LVDT is designed with an intentionally variable magnetic air gap and a moving ferromagnetic core to create a highly linear change in flux linkage. An audio transformer will not yield a linear voltage-to-displacement curve.

What is the difference between an LVDT and an RVDT?

An LVDT (Linear Variable Differential Transformer) measures straight-line displacement using a cylindrical core sliding through a bore. An RVDT (Rotary Variable Differential Transformer) measures angular displacement (typically ±40 degrees) using a butterfly-shaped rotor that rotates within the stator windings. The underlying series-opposition circuit theory is identical, but the mechanical packaging and core geometry differ entirely.

Does temperature affect LVDT accuracy?

Yes, but primarily through the copper windings, not the core. As temperature rises, the resistance of the primary copper winding increases. If your excitation source is a constant-voltage driver, the primary current will drop, weakening the magnetic field and lowering the output sensitivity. This is why precision installations use a constant-current excitation driver or a ratiometric conditioner that mathematically compensates for primary impedance changes. For high-temp environments (up to 230°C), Macro Sensors recommends specifying units wound with high-temperature polyimide magnet wire rather than standard enamel.