What is an LVDT? Theory, Math, and Sensor Selection Guide

An LVDT (Linear Variable Differential Transformer) is an inductive sensor that converts straight-line mechanical movement into a proportional alternating current (AC) voltage without any physical electrical contact between the moving core and the coil assembly. If you are designing a feedback loop for a hydraulic press, a CNC mill, or a flight control actuator, specifying an LVDT changes your circuit from a simple DC voltage divider (like a potentiometer) into a robust, phase-sensitive AC bridge that survives millions of cycles without wiper wear.

The Core Principle: How an LVDT Actually Works

Think of an LVDT as a standard iron-core transformer, but instead of a fixed core, the center slug is free to slide back and forth. The sensor consists of three coils wound around a hollow, non-magnetic cylindrical form:

• Primary Coil (P): Located in the center, driven by an AC excitation voltage.
• Secondary Coil 1 (S1) & Secondary Coil 2 (S2): Located symmetrically on either side of the primary, wired in series-opposition.

A separate, rod-shaped ferromagnetic core is attached to the object you are measuring and slides through the hollow center. When the core is dead center (the null position), the magnetic flux coupling to S1 and S2 is identical. Because they are wired in opposition, their voltages cancel out, yielding a net output of 0V.

When you push the core toward S1, the magnetic coupling to S1 increases while coupling to S2 decreases. The output voltage rises, and its AC phase matches the excitation phase. Pull the core toward S2, and the voltage rises again, but the AC phase flips 180 degrees. This phase shift is how the downstream electronics know which direction the core moved.

The Math: A Worked Numeric Example

To size your signal conditioner and ADC (Analog-to-Digital Converter), you need to calculate the expected full-scale and partial-stroke output voltages. LVDT sensitivity is universally specified in mV/V/mm (millivolts of output per volt of excitation per millimeter of displacement).

Let’s run a real-world calculation using a standard industrial sensor, such as the TE Connectivity GH-Series.

• Sensor Sensitivity: 2.4 mV/V/mm
• Excitation Voltage: 5V RMS (at 3 kHz)
• Core Displacement: +6.5 mm from null

Calculation:
V_out = 2.4 mV/V/mm × 5V × 6.5 mm
V_out = 12 mV/mm × 6.5 mm = 78 mV RMS

Because the output is in the millivolt range, you cannot wire this directly to a 0-5V Arduino or PLC analog input. You must pass it through a signal conditioner to amplify the 78 mV AC signal, demodulate the phase, and output a clean ±5V or 4-20mA DC signal.

Where You Meet LVDTs in Practice

You will rarely find an AC LVDT in consumer electronics; they are the workhorses of heavy industry, aerospace, and precision manufacturing where failure is not an option.

• Hydraulic Cylinder Stroke Feedback: The LVDT is often housed inside the hollow piston rod of a hydraulic cylinder. Because the core is non-contacting, it survives the high-pressure, high-vibration environment of a stamping press that would destroy a potentiometer in a week.
• CNC Machine Tool Axes: Used as a secondary, absolute position verifier on high-end milling machines to confirm the linear encoder hasn't drifted due to thermal expansion.
• Aerospace Flight Controls: Redundant LVDTs measure the exact deflection angle of ailerons and rudders by converting linear actuator stroke into rotational feedback via mechanical linkages.
• Automated Manufacturing: Gauging stations that measure the thickness of rolled steel or the diameter of machined shafts on the fly.

Common Confusions: What an LVDT is Not

When sourcing position sensors, engineers and buyers frequently confuse LVDTs with other transducers. Here is how to tell them apart:

• Not a Potentiometer (String Pot): A string pot uses a physical wiper sliding across a resistive carbon or wire-wound track. It wears out over time and is susceptible to contact bounce. An LVDT has infinite resolution and zero wiper wear.
• Not an RVDT: A Rotary Variable Differential Transformer operates on the exact same inductive principle, but uses a rotating butterfly armature instead of a linear sliding core. RVDTs measure angles (typically ±40°); LVDTs measure linear stroke.
• Not a Magnetostrictive Sensor: Magnetostrictive sensors (like MTS Temposonics) measure the time-of-flight of a torsional strain pulse in a waveguide. They are absolute and highly accurate, but significantly more expensive and slower to update than an LVDT.

Decision Tree: Specifying the Right Position Sensor

Use this matrix to terminate your selection process and pick the exact hardware for your application.

Signal Conditioning and Real-World Wiring

The raw output of an AC LVDT is useless to a microcontroller. You must demodulate it. The industry standard for this is a synchronous demodulator, such as the Analog Devices AD698. This IC drives the primary coil, reads the secondary voltages, and computes the ratio (S1 - S2) / (S1 + S2). By using a ratiometric calculation, the AD698 eliminates errors caused by temperature-induced changes in the coil's resistance or fluctuations in the excitation voltage.

Wiring Best Practices:

• Cable Choice: Always use a 5-conductor or 6-conductor shielded twisted-pair cable (typically 24 AWG or 22 AWG). Twist the primary pair and the secondary pairs individually to reject EMI from nearby VFDs and contactors.
• Shield Grounding: Ground the cable shield at the signal conditioner end only. Grounding it at both the sensor and the PLC creates a ground loop that will inject 50/60Hz mains hum directly into your millivolt-level signal.
• DC-LVDT Alternative: If you lack the board space for an AD698 demodulator, buy a "DC-LVDT." These have the oscillator and demodulator built directly into the sensor housing. They accept a 10-30V DC supply and output a 0.5-4.5V DC signal. They are more expensive per unit but save hours of PCB design time.