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Capacitive Proximity Sensor

Calculate capacitance and sensitivity (pF/mm) between sensor plate and target. Design capacitive proximity and touch sensor detection circuits.

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Formula

C=ε0εrA/dC = ε₀εᵣA/d
ε₀— 8.8542 × 10⁻¹² F/m (F/m)
εᵣ— Relative permittivity

How It Works

This calculator computes capacitive proximity sensor parameters including capacitance and sensitivity versus distance, essential for industrial automation engineers, liquid level sensor designers, and touchscreen developers. Capacitive sensors detect objects by measuring capacitance change when a target approaches the sensing electrode. The parallel-plate capacitance is C = e0 er A / d, where e0 = 8.8541878128e-12 F/m (vacuum permittivity per CODATA 2018), er is relative permittivity (air = 1.0, glass = 4-10, water = 80, human body = 50-80), A is electrode area, and d is gap distance. Sensitivity dC/dd = -e0 er A / d^2 increases at shorter distances (inverse-square relationship). Industrial capacitive sensors (Balluff, IFM, Omron) achieve 1-25 mm detection range with +/-10% repeatability per IEC 60947-5-2. Capacitance measurement circuits use oscillator frequency shift (delta_f/f proportional to delta_C), charge transfer (QTouch), or sigma-delta modulation (AD7745, 4 aF resolution). Temperature coefficient is typically 0.3%/C due to electrode expansion and permittivity change.

Worked Example

Problem

Design a capacitive liquid level sensor for a 5 mm thick HDPE tank wall (er = 2.3). Electrode is 50 mm x 100 mm. Calculate capacitance through wall and sensitivity to water (er = 80) presence.

Solution
  1. Electrode area: A = 0.05 * 0.1 = 0.005 m^2
  2. Gap through HDPE wall: d = 5 mm = 0.005 m
  3. Capacitance (air behind wall): C_air = 8.854e-12 2.3 0.005 / 0.005 = 20.4 pF
  4. Wait - must consider fringe fields. Effective area ~1.5x geometric: A_eff = 0.0075 m^2
  5. With water present: er_eff = (er_HDPE er_water)^0.5 = (2.3 80)^0.5 = 13.6 (simplified)
  6. C_water = 8.854e-12 13.6 0.0075 / 0.005 = 181 pF
  7. Delta_C = 181 - 30.6 = 150 pF (air C_air = 30.6 pF with fringe field)
  8. Detection threshold: set at 50 pF above air baseline for reliable detection
  9. Use AD7746 CDC (24-bit, +/-4 pF range, 4 aF resolution) in high-range mode
Result: Capacitance changes from 31 pF (air) to 181 pF (water) through 5 mm HDPE wall. Set threshold at 80 pF for reliable level detection with margin.

Practical Tips

  • ✓Use guarded (driven-shield) electrode design to constrain the electric field to the active face and reject interference from sides and rear; guard electrode driven at same potential as sense electrode per Analog Devices AN-1301
  • ✓For liquid level detection through non-metallic container walls, choose sensor rated for the liquid's permittivity; water (er = 80) provides strong signal, oils (er = 2-4) require higher sensitivity settings per Balluff application notes
  • ✓Reduce temperature sensitivity using differential measurement (two electrodes with opposite gap changes) rather than single absolute capacitance; this rejects thermal expansion common-mode error to <0.05%/C

Common Mistakes

  • ✗Ignoring environmental contamination: water (er = 80) or oil on the sensor face dramatically increases capacitance, causing false triggers; use flush-mount sensors with guard electrode design for wet environments per IFM application guide
  • ✗Exceeding linear detection range: capacitance varies as 1/d, so sensitivity is highly nonlinear; within the first 2 mm near the plate, the sensor is extremely sensitive and easily saturates at small displacement changes
  • ✗Mounting next to metal (embedding effect): conductive mounting hardware within the sensor's fringe field acts as a virtual target; maintain metal-free zone of 2x sensing distance per manufacturer installation guides

Frequently Asked Questions

Capacitive sensors detect both conductive and non-conductive materials if their permittivity differs sufficiently from air (er = 1). Metals are easily detected (they short-circuit the electric field, maximizing delta_C). Plastics (er = 2-4), glass (er = 4-10), wood (er = 2-5), water (er = 80), and granular materials are detectable if their permittivity shifts capacitance above the detection threshold (typically 0.5-2 pF). Detection range scales as sqrt(er): water is detectable at 3x the range of plastic per IEC 60947-5-2 test methods.
Inductive sensors detect only conductive (metallic) targets by measuring eddy current losses in an oscillator coil; range 2-60 mm for ferrous metals, 40% less for non-ferrous (aluminum, copper). Capacitive sensors detect any material with er > 1, including non-metallic targets like plastics, liquids, and paper. Trade-offs: capacitive sensors are more sensitive to contamination (water films, dust) and have shorter range (1-25 mm typical) but can detect through non-metallic container walls. Per IFM and Balluff selection guides, use inductive for metal detection, capacitive for non-metallic or level sensing.
Many industrial capacitive sensors have teach-in capability (potentiometer or pushbutton) that sets the trigger threshold at a specific gap. Procedure: position sensor at desired detection distance with target present, activate teach-in, and the sensor stores that capacitance as the switch-on point. Hysteresis (typically 10-20% of sensing distance) is applied automatically to prevent chatter. This calibrates for actual installation geometry, target material, and environmental conditions per Omron and Sick sensor operating instructions.

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