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Capacitive Proximity Sensor

Calculate capacitance between sensor plate and target, and sensitivity (pF/mm) for capacitive proximity sensor design.

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Formula

C = ε₀εᵣA/d

ε₀— 8.854 × 10⁻¹² F/m (F/m)
εᵣ— Relative permittivity

How It Works

A capacitive proximity sensor detects the presence of objects by measuring the change in capacitance when a target approaches or contacts the sensor plate. The capacitance between two parallel plates is C = ε₀εᵣA/d, where ε₀ = 8.854 × 10⁻¹² F/m is the permittivity of free space, εᵣ is the relative permittivity of the dielectric between the plates, A is the plate area, and d is the separation distance. The sensitivity (change in capacitance per change in distance) is dC/dd = −ε₀εᵣA/d², which increases as the gap decreases — the sensor becomes more sensitive at shorter distances. Capacitive sensors can detect metallic and non-metallic targets; the permittivity εᵣ of the intervening medium (air = 1, glass = 4–10, water = 80) strongly influences the capacitance. The small capacitances (1–100 pF) are typically measured using oscillator frequency shift, charge amplifier, or Wheatstone bridge AC excitation circuits. Detection range is typically 1–15 mm for standard industrial sensors.

Worked Example

Problem
A capacitive proximity sensor has a 2 cm² plate area and needs to detect a target at 3 mm gap in air (εᵣ = 1). Calculate the capacitance and sensitivity.
Solution
1. Area: A = 2 cm² = 2 × 10⁻⁴ m² 2. Gap: d = 3 mm = 3 × 10⁻³ m 3. Capacitance: C = (8.854×10⁻¹² × 1 × 2×10⁻⁴) / (3×10⁻³) = 5.90 × 10⁻¹³ F = 0.59 pF 4. Sensitivity: dC/dd = ε₀εᵣA/d² = (8.854×10⁻¹² × 1 × 2×10⁻⁴) / (3×10⁻³)² = 0.197 pF/mm Result: The sensor capacitance is 0.59 pF with sensitivity 0.197 pF/mm at 3 mm gap.

Practical Tips

  • ✓Use a guarded (shielded) electrode design to constrain the electric field to the active face and reject interference from the sides and rear of the sensor.
  • ✓For liquid level detection, choose a sensor rated for the liquid's permittivity and ensure the mounting allows the electric field to penetrate the container wall.
  • ✓Reduce sensitivity to temperature by using a differential measurement (two plates with opposite gap changes) rather than a single absolute capacitance measurement.

Common Mistakes

  • ✗Ignoring environmental contamination — water (εᵣ = 80) or oil on the sensor face dramatically increases capacitance and can cause false triggering; use flush-mount sensors with guarding for wet environments.
  • ✗Exceeding the linear detection range — capacitance varies as 1/d, so sensitivity is non-linear; over the first few millimetres near the plate the sensor is highly sensitive and easily saturated.
  • ✗Mounting next to metal (embedding effect) — conductive mounting hardware within the sensor's field lines acts as a target; always follow the manufacturer's recommended metal-free zone.

Frequently Asked Questions

Capacitive sensors detect both conductive and non-conductive materials if they have sufficiently different permittivity from the background. Metals are easily detected (they short-circuit the field). Plastics, glass, wood, liquids, and granular materials are also detectable if their permittivity (εᵣ > 1) shifts the capacitance above the detection threshold.
Inductive sensors detect only conductive (metallic) targets by measuring eddy current losses in an oscillator coil. Capacitive sensors detect any material with permittivity different from air, including non-metallic targets. Capacitive sensors have shorter range and are more sensitive to environmental contamination than inductive sensors.
Many industrial capacitive sensors have a teach-in potentiometer or button that sets the trigger threshold at a specific gap distance. The sensor is positioned at the desired detection distance with the target present, and teach-in stores the capacitance at that point as the switch-on threshold.

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