LVDT Position Sensor

What an LVDT is, and why it is built like a transformer

A linear variable differential transformer — LVDT — is a position sensor that reports linear displacement as an electrical signal, without anything in the moving path touching anything in the measuring path. That single property, contactless sensing, is the whole reason it has survived since the 1930s in places where every competing technology eventually fails: hydraulic servo valves, jet-engine actuators, nuclear control-rod drives, and precision gauging heads.

The clue is in the name. An LVDT is literally a transformer. It has one primary winding in the centre and two secondary windings, one on each side, all wound coaxially around a hollow non-magnetic bore tube. A short rod of high-permeability nickel-iron — the core — slides freely inside that bore. The core is the only moving part, and it is mechanically coupled to whatever you want to measure: a valve spool, an actuator piston, a test-specimen surface. The coils never touch the core; they sense it purely through magnetic coupling.

Energise the primary with an alternating current and it sets up an alternating magnetic flux. The core concentrates and channels that flux into the secondaries. Here is the geometric trick that makes the device differential: the two secondaries are wound in series-opposition — connected so their induced voltages subtract rather than add. When the core sits dead centre, it couples flux equally into both secondaries, the two voltages are equal in amplitude and opposite in phase, and they cancel to a near-zero output. This is the null. Slide the core a fraction of a millimetre toward one secondary and that coil now sees more flux while the far coil sees less; the cancellation breaks, and a differential voltage appears whose size grows almost perfectly in proportion to how far the core has moved.

The governing equation, with real numbers

Each secondary develops an EMF set by Faraday's law applied to a transformer: the induced voltage is proportional to the mutual inductance between primary and that secondary, times the rate of change of primary current. Calling the two mutual inductances M₁ and M₂ and the primary current iₚ = Iₚ·sin(ωt):

V_s1 = M1 · (di_p/dt) = M1 · ω · I_p · cos(ωt)
V_s2 = M2 · (di_p/dt) = M2 · ω · I_p · cos(ωt)

Series-opposition output:
V_out = V_s1 − V_s2 = (M1 − M2) · ω · I_p · cos(ωt)

The entire behaviour of the LVDT lives in the term (M₁ − M₂). When the core is centred, M₁ = M₂, the difference is zero, and V_out collapses to the null. As the core moves a distance x off centre, M₁ rises and M₂ falls by very nearly the same amount, so (M₁ − M₂) becomes proportional to x over the linear range:

V_out(rms) ≈ S · x · V_exc

where  S   = sensitivity, in (mV out) / (V excitation) / mm
       x   = core displacement from null (mm)
       V_exc = primary excitation voltage (RMS)

A representative ±5 mm LVDT might quote a sensitivity of S = 50 mV/V/mm. Drive it at V_exc = 3 V RMS and move the core to its x = +5 mm end of travel:

V_out = 50 mV/V/mm × 3 V × 5 mm = 750 mV RMS

At null (x = 0):       V_out ≈ 0  (plus residual ~1 mV)
At full negative (x=−5): V_out ≈ 750 mV RMS, but 180° phase-shifted

Notice the crucial detail: at +5 mm and −5 mm the amplitude is identical. Amplitude alone cannot tell you which side of null you are on. The direction is carried in the phase: on one side of null the output is in phase with the excitation, on the other it is 180° out of phase. Recovering both amplitude and sign is the job of a phase-sensitive (synchronous) demodulator, which multiplies the output by a reference derived from the excitation and low-pass filters the result. That demodulation step turns the AC envelope into a clean bipolar DC voltage — say −10 V to +10 V mapped across −5 mm to +5 mm — that any controller or ADC can read directly.

Excitation, frequency, and bandwidth

Because an LVDT is a transformer, it cannot work on DC: a constant primary current makes a constant flux, which induces nothing in the secondaries. It is fundamentally an AC instrument. The excitation frequency, commonly 1 to 10 kHz with 2.5 kHz a popular default, is a balance. Higher frequency raises the induced voltage (the ω term in the equations above) and allows faster mechanical tracking, but it also increases eddy-current losses in the core and laminations and makes stray capacitance matter more. Lower frequency reduces those parasitics but cuts sensitivity and bandwidth.

The hard rule on bandwidth is the carrier sampling limit: the excitation frequency must be at least about ten times the highest mechanical frequency you intend to measure, because the demodulator can only reconstruct the displacement envelope by sampling the carrier. A 2.5 kHz carrier comfortably resolves motion up to a couple of hundred hertz; measuring a 1 kHz vibration demands a 10 kHz or higher carrier. So-called DC-LVDTs hide all of this: they pack a miniature oscillator, the AC-LVDT element, and a demodulator into one housing, accept a DC supply, and emit a DC output — but internally they still run on AC, and they inherit the same carrier-versus-bandwidth trade-off.

The null point and residual voltage

In an ideal LVDT the output at null would be exactly zero. In a real one a small residual voltage remains, typically held below 0.5 percent of full-scale output by careful manufacturing. It has two distinct components, and they behave very differently under demodulation:

• In-phase (fundamental) residual. Caused by tiny asymmetries between the two secondary windings — a few turns difference, slightly unequal geometry. It is at the excitation frequency and in phase with the wanted signal, so a phase-sensitive demodulator rejects it almost completely along with everything else off-phase.
• Quadrature residual. 90° out of phase with the excitation, arising from interwinding capacitance and harmonic distortion in the excitation. It survives synchronous demodulation more stubbornly and sets the practical noise floor right around null — exactly where high-precision measurements often need to sit.

This is why a precision LVDT specification always lists a null voltage and why high-end designs add an electrostatic shield between primary and secondaries, use precision-wound symmetric coils, and sometimes trim the null electronically. It is also why the most accurate region of an LVDT is not always dead centre, and why gauging applications frequently bias the working point slightly off null to escape the quadrature floor.

Real-world devices and specifications

LVDTs span an enormous range, from sub-millimetre gauging heads to long-stroke ram-position sensors, but the family resemblance holds throughout:

• Precision gauging / metrology. A ±0.5 mm gauging probe with a spring-loaded contact tip, 5 kHz excitation, and resolution down to tens of nanometres reads part dimensions on a coordinate-measuring machine or a production gauge. Linearity within 0.1 percent over the central ±0.25 mm.
• Hydraulic servo-valve spool position. A ±2 mm short-stroke LVDT embedded in the valve body closes the position loop on the spool. The contactless principle is essential: the spool is bathed in hydraulic fluid at high pressure, and a contacting sensor would clog and wear in hours.
• Aerospace flight-control and engine actuators. Triplex or quadruplex LVDTs (three or four independent sensing elements in one body) give the redundancy a fly-by-wire actuator needs. They survive −55 °C to +150 °C, severe vibration, and the demand for an absolute reading the instant power is applied.
• Nuclear control-rod position. Stacked-coil LVDTs and their cousins report rod insertion depth inside reactor pressure vessels, where radiation hardness and the impossibility of maintenance rule out anything with optics or contacts.
• Materials-testing extensometers. An LVDT clipped across a tensile specimen measures elongation to microns through fracture, where the violent failure event would destroy a delicate optical or strain-gauge extensometer.

Temperature is the dominant real-world error source. The copper windings change resistance with temperature, the core permeability drifts, and the bore tube expands. A well-designed LVDT is intrinsically ratiometric — it measures the ratio of the secondaries, not an absolute voltage — which cancels most common-mode drift. Reading the sum of the two secondaries as well as their difference, and dividing, makes the position estimate largely immune to excitation amplitude and temperature-driven gain changes.

Failure modes and trade-offs

• Core/bore contact or contamination. If the bore fills with debris or the guidance external to the sensor lets the core rub the bore, you reintroduce the very friction and wear the LVDT exists to avoid. The sensor itself rarely fails; its mechanical mounting does.
• Excitation amplitude or frequency drift. A raw AC-LVDT output scales directly with excitation. If the oscillator drifts, the reading drifts. Ratiometric demodulation and a stable, regulated excitation source are the cure.
• Cable capacitance and length. Long lead runs add capacitance that shifts phase and inflates the quadrature residual, degrading near-null accuracy. Beyond a few metres, the signal conditioning is moved close to the sensor or a DC-LVDT is used.
• Off-axis core motion. The model assumes the core moves purely along the axis. Lateral or tilting motion changes the coupling unpredictably and shows up as apparent position error. The mechanical design must constrain the core to pure axial travel.
• Operating beyond the linear range. Push the core past its rated stroke and the secondaries begin to saturate; linearity collapses and the calibration is meaningless even though a voltage still appears.
• Temperature-induced null shift. Differential thermal expansion can move the apparent null. Aerospace and nuclear units use matched materials and sometimes a temperature sensor for compensation.

LVDT versus the alternatives

The LVDT is not the only way to measure linear position. Its niche is best understood by comparison with the technologies it routinely beats — and the ones that beat it on the margins it does not own.

Property	LVDT	Potentiometer	Optical encoder (linear)	Capacitive	Magnetostrictive
Contact / wear	None — contactless	Wiper drags, wears out	None (optical)	None	None
Output	Absolute analog	Absolute analog	Incremental (or absolute)	Analog	Absolute
Resolution	Infinite (analog)	~0.1 % limited by track	Quantised by grating	Sub-micron	~1–5 µm
Linearity	0.1–0.25 % FS	0.5–1 % FS	Excellent (digital)	0.1–0.5 % FS	0.02–0.05 % FS
Typical stroke	0.5–250 mm	1–500 mm	mm to metres	< 10 mm	50 mm–7 m
Harsh-environment	Excellent (radiation, oil, heat)	Poor	Poor (dirt blinds optics)	Sensitive to humidity	Good
Electrical isolation	Full (transformer)	None	None	Partial	Partial
Needs AC excitation	Yes (or built-in osc.)	No	No	Yes (capacitance bridge)	Pulse / waveguide
Best use	Servo valves, actuators, gauging	Cheap, low-spec position	Long travel, digital axes	Tiny precision gaps	Long hydraulic cylinders

The pattern is clear. Against a potentiometer the LVDT wins decisively on life, resolution, and shock tolerance — the potentiometer's wiper is a wear part, the LVDT has none. Against an optical encoder the LVDT wins where dirt, oil, vibration, radiation, or temperature would blind the optics, and where an absolute reading is needed at power-up with no homing move; the encoder wins on long travel, direct digital output, and cost-per-millimetre over a long axis. Against capacitive sensors the LVDT covers far longer strokes and tolerates humidity and contamination. Against magnetostrictive sensors the LVDT is faster and better at very short strokes, while magnetostrictive wins on multi-metre hydraulic cylinders. For the band it owns — short to medium stroke, harsh environment, absolute analog, electrically isolated — nothing has displaced it in ninety years.

Rotary cousins and stacked-coil variants

• RVDT (Rotary Variable Differential Transformer). The same differential-transformer principle applied to angle. A shaped rotor steers flux between two secondaries; output is linear over roughly ±40°. Standard for throttle and flap-position feedback in aircraft.
• Half-bridge / ratiometric LVDT. Two coils read as a ratio rather than a difference, trading some sensitivity for excellent immunity to excitation and temperature drift — favoured in metrology gauges.
• Stacked-coil (multi-section) LVDT. A long series of short coils extends the absolute measuring range to metres for applications like nuclear control-rod position, where a single long winding would be impractical.
• Gauging-head LVDT. A spring-loaded, contact-tipped probe version optimised for repeatable dimensional measurement on production lines and CMMs.

Common pitfalls when applying an LVDT

• Confusing physical core travel with linear range. The core can move farther than the sensor stays linear. Always specify the usable linear stroke, not the mechanical limit.
• Under-clocking the carrier. If the excitation frequency is not roughly ten times the fastest motion of interest, the demodulated signal cannot follow it. Size the carrier to the dynamics first.
• Ignoring the quadrature null floor. Expecting micron accuracy right at null without addressing quadrature residual leads to disappointment; bias off-null or shield and trim.
• Long unshielded cables. Cable capacitance corrupts the phase reference and inflates near-null error; keep conditioning close or use a DC-LVDT.
• Forgetting the core is the only thing you measure. Any lateral play, tilt, or off-axis motion of the core becomes position error. Constrain the core to pure axial travel with proper external guidance.