AC LVDT Theory: How Linear Variable Differential Transformers Work

An AC LVDT (Linear Variable Differential Transformer) is an electromechanical transducer that converts linear mechanical displacement into a proportional alternating current (AC) electrical signal using a movable ferromagnetic core and three transformer coils. In a real control circuit or installation, it changes physical position into an isolated, frictionless AC voltage output, replacing wear-prone DC potentiometers with infinite-resolution feedback where signal amplitude dictates distance and phase angle dictates direction.

People commonly confuse AC LVDTs with linear potentiometers (which rely on a sliding wiper and DC voltage), Hall-effect linear sensors (which suffer from limited range and temperature drift), and RVDTs (Rotary Variable Differential Transformers, which measure angular rather than linear displacement). Unlike those alternatives, the AC LVDT has no electrical contact between the moving core and the coil assembly, granting it a theoretically infinite mechanical life.

What an AC LVDT Is and How It Actually Works

At its core, an AC LVDT is a specialized mutual-inductance transformer. The stationary stator contains three coils wound on a hollow, non-magnetic form: one primary coil in the center, and two identical secondary coils flanking it. The secondary coils are wired in series-opposition (also known as differential series). A separate, cylindrical ferromagnetic core slides freely through the hollow center, mechanically linked to the object you are measuring.

When you apply an AC excitation voltage (typically 1V to 6V RMS at 1kHz to 10kHz) to the primary coil, it generates an alternating magnetic field. This field couples to the secondary coils via the movable core.

Electrically, when the core is at the exact center (the null position), the magnetic flux linking both secondary coils is identical. Because they are wired in series-opposition, their equal voltages cancel out, resulting in a theoretical 0V output (in reality, a tiny residual 'null voltage' remains due to winding imperfections). As the core moves off-center, the mutual inductance increases in one secondary and decreases in the other. The differential output voltage rises linearly. Crucially, if the core crosses the null point to the opposite side, the output voltage phase shifts by exactly 180 degrees relative to the excitation signal, telling the controller which direction the core has moved.

AC LVDT Specifications and Selection Data

Selecting an LVDT requires matching the sensor's electromagnetic characteristics to your signal conditioner and mechanical stroke requirements. Below is a data-dense specification matrix comparing typical industrial-grade AC LVDTs across short-stroke and long-stroke variants, based on current 2026 manufacturing standards from major suppliers like TE Connectivity and Sensata.

Note: Sensitivity is highly dependent on the core material (typically a nickel-iron alloy) and the coil winding density. Always verify the exact mV/V/mm rating on the manufacturer's calibration sheet, as swapping cores between different LVDT bodies will destroy linearity.

Worked Example: Calculating Displacement from Output Voltage

Let's walk through a real-world calculation to see how an AC LVDT translates physical movement into an electrical signal that a PLC or signal conditioner must interpret. For deeper theoretical background on transformer coupling in these sensors, refer to the All About Circuits LVDT chapter.

Given Parameters:

• Sensor Sensitivity: 2.4 mV/V/mm (or 0.0024 V/V/mm)
• AC Excitation Voltage ($V_{exc}$): 3.0 V RMS at 3 kHz
• Measured Core Displacement ($d$): 12.5 mm from the null position

The Formula:
The raw AC output voltage ($V_{out}$) is the product of the excitation voltage, the sensor's sensitivity, and the physical displacement.

$V_{out} = V_{exc} \times Sensitivity \times d$

The Calculation:

1. $V_{out} = 3.0 \text{ V} \times 0.0024 \text{ (V/V/mm)} \times 12.5 \text{ mm}$
2. $V_{out} = 0.0072 \times 12.5$
3. $V_{out} = 0.09 \text{ V RMS}$ (or 90 mV RMS)

What the Controller Sees:
The signal conditioner reads a 90 mV RMS signal. Because the conditioner performs phase-sensitive demodulation, it compares the phase of this 90 mV signal to the original 3 kHz excitation signal. If the phases match (0° shift), the conditioner outputs a positive DC voltage (e.g., +5V DC), indicating the core moved 12.5 mm to the right. If the phase is inverted (180° shift), it outputs a negative DC voltage (e.g., -5V DC), indicating a 12.5 mm leftward movement.

Where You Meet AC LVDTs in Practice (And What They Replace)

You will rarely find an AC LVDT in consumer electronics or basic hobbyist projects; they are strictly industrial, aerospace, and heavy-machinery components. You will meet them bolted to the side of hydraulic press cylinders, embedded inside CNC machine tool ball-screws for closed-loop axis positioning, and mounted inside rolling mills to measure steel strip thickness down to the micron.

According to Macro Sensors' technical documentation, the primary reason engineers specify LVDTs in these harsh environments is their immunity to mechanical wear and electrical noise. Here is how they stack up against the alternatives they typically replace:

What it changes in the installation: When you swap a linear potentiometer for an AC LVDT on a hydraulic valve actuator, you eliminate the 'dead spots' and erratic voltage spikes caused by wiper bounce during high-vibration events. However, you must add an LVDT signal conditioner module to your DIN rail to handle the AC demodulation, adding roughly $100 to $250 per axis to your BOM (Bill of Materials).

Frequently Asked Questions