What Is a Differential Transformer (LVDT)? Theory, Wiring, and Signal Math

A differential transformer (most commonly deployed as a Linear Variable Differential Transformer, or LVDT) is an inductive sensor that translates physical linear displacement into a proportional AC voltage output by shifting a magnetic core through three wire coils. In a real circuit or mechanical installation, it changes the game by replacing friction-prone resistive wipers (like string pots or slide potentiometers) with a completely frictionless, wear-free magnetic coupling, providing absolute position feedback with infinite resolution and zero mechanical loading on the moving part.

The Working Principle: Null Position and Phase Reversal

Inside the stainless steel housing of a typical industrial LVDT, you will find one primary coil centered between two identical secondary coils, all wound on a hollow non-magnetic bobbin. A separate ferromagnetic core (usually a nickel-iron alloy) slides freely through the center bore, pushed by the mechanism you are measuring.

Here is how the magnetic flux translates into an electrical signal:

1. Excitation: An external oscillator drives the primary coil with an AC sine wave, typically between 1 kHz and 10 kHz at 3V to 10V RMS.
2. Magnetic Coupling: The alternating current in the primary generates a magnetic field. The movable core acts as a flux conduit, coupling this field into the two secondary coils.
3. The Null Position: When the core is perfectly centered, it couples equal magnetic flux into both secondaries. Because the secondaries are wired in series-opposition, their induced voltages cancel out. The differential output is exactly 0V (the "null").
4. Displacement and Phase Shift: Move the core 2mm to the left, and coil S1 receives more flux than S2. The output voltage rises. Move it 2mm to the right, and S2 dominates. Crucially, the AC output waveform undergoes a 180-degree phase shift relative to the primary excitation when crossing the null point. This phase shift tells your signal conditioner which direction the core moved.

Worked Numeric Example: Calculating the Output Signal

Let us run the math on a standard industrial sensor, such as the TE Connectivity GHSD series. You need to know the exact millivolt output to configure your PLC analog input card or oscilloscope triggering.

The Calculation:
Output Voltage = Sensitivity × Excitation Voltage × Displacement
Output Voltage = 2.5 mV/V/mm × 5.0 V × 4.2 mm
Output Voltage = 52.5 mV RMS

Because LVDTs are ratiometric, if your excitation supply sags by 2% (dropping to 4.9V), your raw output drops to 51.45 mV. This is why modern signal conditioners like the Analog Devices AD698 do not just measure the secondary voltage; they divide the secondary voltage by the primary voltage in real-time, completely canceling out excitation drift.

Where You Meet This In Practice

You will rarely find an LVDT in consumer electronics; they are too large and require AC signal conditioning. Instead, they dominate environments where reliability is non-negotiable and physical contact would destroy a sensor.

• Aerospace Flight Controls: Inside the hydraulic actuators moving ailerons and rudders. The LVDT core is tied to the actuator ram, surviving extreme vibration and temperature swings without a wiper track to wear out.
• CNC Machinery and Probing: Tool-breakage detection and Z-axis probing. The infinite resolution allows the machine to detect sub-micron deviations in workpiece height.
• Civil Engineering: Monitoring expansion joints on suspension bridges or dam gate positions. Macro Sensors and similar manufacturers build DC-LVDTs with internal ASICs specifically for these harsh, outdoor, long-stroke applications.
• Automated Manufacturing: Thickness gauging on steel rolling mills, where the sensor measures the gap between massive rollers.

Real-World Scenario Walkthrough: The Hydraulic Press Drop-Out

Theory is clean; the jobsite is noisy. Here is a real-world failure mode I troubleshooted on a 100-ton automated hydraulic stamping press.

The Setup:
An LVDT with a 150mm stroke was mounted to the main ram to provide closed-loop position feedback to an Allen-Bradley PLC. The system used a 10 kHz excitation frequency to get a fast response time for the high-speed stamping cycle.

The Numbers:
The press cycled perfectly from 0mm down to 100mm. However, precisely at the 120mm mark (near the bottom of the stroke where the hydraulic pressure peaked), the PLC analog input read erratic, jumping between 115mm and 145mm, triggering a safety halt.

The Outcome:
The machine halted, costing $4,000 per hour in downtime. The maintenance team initially assumed the LVDT core was binding or the internal windings were shorting at the end of the stroke.

What Went Wrong (The Fix):
I hooked an oscilloscope to the secondary leads and saw massive high-frequency noise riding on the 10 kHz sine wave. The culprit was not the LVDT itself, but the proportional hydraulic solenoid valves. At 120mm of stroke, the press engaged a high-force holding circuit, which utilized a 2 kHz PWM (Pulse Width Modulation) driver for the solenoids. The unshielded LVDT signal wires were routed in the same cable tray as the 40A solenoid power lines. The PWM switching noise coupled into the LVDT wires, corrupting the synchronous demodulation inside the signal conditioner.
The Fix: We swapped the signal wiring to Belden 9438 twisted-pair shielded cable, grounded the shield at the PLC panel only (to avoid ground loops), and dropped the LVDT excitation frequency to 3 kHz to separate the frequency bands. The erratic readings vanished.

What People Commonly Confuse It With

When spec'ing parts or reading schematics, do not mix up the differential transformer with these lookalikes:

• Standard Power Transformers: A power transformer steps AC voltage up or down using fixed primary and secondary windings. It has no moving core and does not measure position. An LVDT uses transformer principles strictly for measurement, not power transfer.
• String Potentiometers (String Pots): A string pot measures linear distance by unspooling a spring-loaded wire attached to a resistive potentiometer. While cheaper and easier to wire (it outputs a simple DC voltage divider), the internal wiper will eventually wear out, and the spring mechanism introduces mechanical hysteresis. LVDTs have no wipers and no mechanical loading.
• RVDTs (Rotary Variable Differential Transformer): An RVDT operates on the exact same inductive principle but uses a butterfly-shaped rotating core to measure angular displacement (typically ±40 degrees), not linear stroke. You will find these on flight control yokes and valve actuators, not linear rams.

Frequently Asked Questions