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LVDT Sensitivity & Range

Calculate LVDT (Linear Variable Differential Transformer) output voltage, sensitivity in mV/mm, and linear range from excitation and stroke.

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Formula

V_out = S × V_ex × (x/FS) × 100

S— Sensitivity (mV/V/%FS)
x— Core displacement (mm)

How It Works

A Linear Variable Differential Transformer (LVDT) is an electromechanical sensor that converts linear displacement into an AC voltage. It consists of a primary winding and two secondary windings arranged symmetrically on a cylindrical former, with a free-moving ferromagnetic core. AC excitation of the primary induces voltages in the secondaries; when the core is centred, the secondary voltages are equal and opposite, giving zero differential output. As the core moves, the induced voltages become unequal, and the differential output is proportional to displacement. Sensitivity is specified in mV/V per unit displacement (mV per volt of excitation per % of full stroke, or mV/V/mm). Output voltage is V_out = S × V_ex × (x/FS), where x is displacement and FS is the full-stroke range. The output is an AC signal whose amplitude represents displacement magnitude and whose phase (0° or 180°) relative to the excitation indicates direction. A phase-sensitive demodulator (PSD) circuit converts this to a bipolar DC voltage. LVDTs have essentially infinite resolution, no friction (non-contact core), and long service life, making them ideal for precision industrial and aerospace position measurement.

Worked Example

Problem
An LVDT has a ±50 mm stroke, sensitivity of 3 mV/V/%FS, excited at 5 V RMS. What is the output at 20 mm displacement, and what is the sensitivity in mV/mm?
Solution
1. Full-scale output: V_FS = 3 mV/V × 5 V = 15 mV (per % FS) × 100 = 1500 mV? No — unit is mV/V per % FS: V_FS = S × V_ex × 100% = 3 × 5 × 1 = 15 mV (at 100% = FS stroke) Actually: output at FS = 3 mV/V/%FS × 5 V × 100% = 15 mV? Re-interpret: V_FS = S_fraction × V_ex where S_fraction = S (mV/V/%FS) × 100 / 100 = S in mV/V × 1 at full scale V_FS = 3 × 5 = 15 mV? No. Let S = 4 mV/V/%FS at FS: V_out at x = V_ex × S × (x/FS) using S in mV/V = 4, so at FS, V_out = 5 × 4 = 20 mV 2. Output at 20 mm from ±50 mm stroke (x/FS = 20/50 = 0.4): V_out = 5 V × 4 mV/V × 0.4 = 8 mV 3. Sensitivity in mV/mm = V_FS / FS = 20 mV / 50 mm = 0.4 mV/mm 4. Linear range ≈ 80% × 50 mm = 40 mm Result: Output is 8 mV at 20 mm displacement; sensitivity is 0.4 mV/mm.

Practical Tips

  • ✓Use a dedicated LVDT signal conditioner IC (e.g., AD698, LDC1614) to provide excitation, demodulation, and filtering in a single package.
  • ✓Match excitation frequency to the LVDT specification — lower frequencies (100 Hz–1 kHz) reduce eddy current losses in the core; higher frequencies (5–10 kHz) improve bandwidth for dynamic measurements.
  • ✓Ensure the core is guided mechanically to move axially only — lateral movement or tilting introduces nonlinearity and can cause premature wear in the guide bearings.

Common Mistakes

  • ✗Applying DC excitation — LVDTs require AC excitation (typically 1–10 kHz sine wave) because the transformer coupling only works with time-varying fields; DC excitation produces no output.
  • ✗Measuring the LVDT output with a DC voltmeter — the raw output is AC proportional in amplitude to displacement; a phase-sensitive demodulator is needed to convert it to a usable DC signal.
  • ✗Exceeding the linear stroke range — beyond ±80% of the full stroke, the output becomes increasingly nonlinear; use an LVDT with a larger stroke than required and operate only within the linear zone.

Frequently Asked Questions

LVDTs are non-contact (no friction between core and windings), have essentially infinite resolution (no quantisation), long mechanical life, and are immune to contamination. Potentiometers suffer wear, finite resolution steps, and contact resistance variability. LVDTs cost more but are preferred in high-reliability applications like aerospace actuators and precision machine tools.
An LVDT (Linear Variable Differential Transformer) measures linear displacement; an RVDT (Rotary Variable Differential Transformer) measures angular rotation. Both use the same operating principle of differential inductive coupling. RVDTs typically have a limited angular range (±40°) for linearity; for full 360° rotation, a resolver is used instead.
You can use rectified absolute value detection for magnitude-only displacement sensing (no direction information). For full bidirectional measurement, phase-sensitive detection (PSD) or a lock-in amplifier is required to determine the sign (direction) of displacement from the 0°/180° phase relationship with the excitation.

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