How a Linear Variable Differential Transformer (LVDT) Measures Displacement

A linear variable differential transformer (LVDT) is a frictionless, inductive sensor that converts precise linear displacement into a proportional AC electrical voltage. Unlike a standard potentiometer that relies on a physical wiper scraping across a resistive track, an LVDT uses magnetic coupling between a primary coil and two secondary coils to measure position. This fundamental difference changes how you design the front-end of your measurement circuit: you cannot simply feed an LVDT 5V DC and read an analog pin. Instead, you must provide an AC carrier excitation and synchronously demodulate the output to extract both the magnitude (distance) and phase (direction) of the core's movement.

The Core Principle: How an LVDT Actually Works

Inside the sensor housing, you will find three coils of wire wound around a hollow, non-magnetic bobbin. The center coil is the primary, and the two outer coils are the secondaries, wound in series opposition. A separate, ferromagnetic core (usually a nickel-iron alloy rod) slides freely through the center of the bobbin without touching the coils.

When you drive the primary coil with an AC sine wave (typically 1 kHz to 10 kHz), it generates an alternating magnetic field. This field induces a voltage in the two secondary coils. The magic happens based on the core's position:

• Null Position (Center): The core couples equal magnetic flux to both secondaries. Because they are wired in opposition, their voltages cancel out, resulting in a net output of zero (or practically, a few millivolts of residual null voltage).
• Displaced Position: As the core moves off-center, it couples more flux to one secondary and less to the other. The voltages no longer cancel. The resulting differential voltage increases linearly with displacement.
• Direction Detection: The phase of the output AC voltage tells you which way the core moved. If it moves left, the output is in-phase with the excitation. If it moves right, the output shifts 180 degrees out-of-phase.

The Math on the Bench: A Worked Numeric Example

Let's look at the actual numbers you will see on your oscilloscope when testing a standard industrial LVDT, such as a TE Connectivity GH-Series or Macro Sensors GCD-SE. These sensors are rated by their sensitivity, usually expressed in millivolts per Volt of excitation per millimeter of stroke (mV/V/mm).

Given Specifications:

• Sensor Sensitivity: 2.4 mV/V/mm
• Excitation Voltage ($V_{ex}$): 3.0 V RMS at 2.5 kHz
• Core Displacement ($d$): +4.5 mm from the null (center) position

The Formula:
$V_{out} = Sensitivity \times V_{ex} \times d$

The Calculation:
$V_{out} = 2.4 \times 3.0 \times 4.5 = 32.4$ mV RMS

If the core had moved -4.5 mm in the opposite direction, the magnitude would still be 32.4 mV RMS, but the waveform on your scope would be flipped 180 degrees relative to the primary excitation signal. This phase relationship is what allows the demodulator circuit to output a bipolar DC voltage (e.g., +5V DC for full forward stroke, -5V DC for full reverse stroke).

Where You Meet LVDTs in Practice

You will rarely find an LVDT in consumer electronics or basic hobby projects due to the signal conditioning overhead. However, they are the undisputed king of harsh, high-reliability industrial and aerospace environments. You will meet them in:

• Hydraulic Cylinder Stroke Measurement: Inside the rod of heavy machinery where shock and vibration would shatter optical encoders.
• Turbine Valve Positioning: In power generation, where high ambient temperatures rule out standard resistive sensors.
• Material Testing Machines: Tensile testers requiring infinite resolution to measure microscopic material deformation before failure.

Here is how the LVDT stacks up against alternatives when you are specifying a position feedback loop for a new machine build:

Field Scenario: When the Phase Angle Lies

Theory is clean; the jobsite is not. Here is a real-world scenario demonstrating what happens when you ignore the AC nature of the LVDT signal.

The Setup: We were automating a 50-ton stamping press, using a 100mm stroke LVDT to measure die closure. The sensor was mounted on the press frame, connected via 15 meters of standard 18 AWG unshielded multi-core control cable to a PLC analog input card featuring an integrated Analog Devices AD698 LVDT signal conditioner. Excitation was set to 5 kHz.

The Numbers: At full open (null position), the expected residual voltage was < 5 mV. However, our scope showed a measured null of 45 mV. Worse, as the die closed to the 10mm mark, the PLC readout became highly non-linear and jittery, fluctuating ±2mm.

The Outcome: The PLC interpreted the erratic position data as a die crash, faulting out the press and halting production every few cycles.

What Went Wrong: Cable capacitance. Fifteen meters of standard control cable introduced roughly 1.5 nF of parallel capacitance between the secondary return wires. At a 5 kHz carrier frequency, this capacitance created a low-pass filter effect with the coil's internal impedance, shifting the phase angle of the secondary return signal by nearly 12 degrees. The synchronous demodulator inside the AD698 relies on a strict phase relationship to determine direction. When the phase shifted, the demodulator miscalculated the vector, interpreting the phase error as a massive, erratic displacement.

The Fix: We replaced the standard cable with a low-capacitance shielded twisted pair (Belden 8770) and dropped the excitation frequency on the signal conditioner to 2.5 kHz. Lowering the frequency reduced the capacitive reactance, restoring the phase margin. The null voltage dropped to 3 mV, and the press ran flawlessly.

Common Confusions and Misapplications

When specifying sensors, buyers and junior engineers frequently confuse LVDTs with other position-sensing technologies. Here is what an LVDT is not:

1. Inductive Proximity Sensors: A standard inductive prox is just a switch. It outputs a discrete ON/OFF signal when metal enters its field. An LVDT provides continuous, proportional analog data across its entire stroke.
2. String Potentiometers (Draw-wire sensors): String pots measure linear distance by pulling a wire attached to a spring-loaded spool connected to a resistive potentiometer. They suffer from spring hysteresis, wiper wear, and wire sag. LVDTs have no springs, no wipers, and no physical connection to the moving target.
3. RVDTs (Rotary Variable Differential Transformer): An RVDT operates on the exact same electromagnetic principle as an LVDT, but it measures rotary angle (typically ±40 degrees) using a butterfly-shaped rotating core instead of a linear sliding rod.

LVDT Specification and Selection FAQ

For deeper technical reference on coil topologies and core materials, consult the Macro Sensors LVDT tutorials, which remain the industry-standard primer on inductive transducer physics.