Capacitor as Pressure Sensor: Exploiting Deformation Physics
A capacitor’s job is to store charge. But its capacitance is directly determined by its physical geometry — and that geometry changes under pressure. This makes a carefully constructed capacitor an elegant, zero-power, broadband pressure transducer.
The Governing Physics
Capacitance of a parallel-plate capacitor:
C = ε₀ × εᵣ × A / d
Where:
- A — plate overlap area (m²)
- d — plate separation (m)
- εᵣ — dielectric permittivity
When pressure compresses the dielectric (reducing d) or bends a membrane (changing A), capacitance increases measurably. A 1µm change in a 10µm air gap produces a 10% capacitance shift — easily resolved.
Two Structural Approaches
1. Diaphragm-Type (MEMS Style)
A thin conductive membrane suspended over a fixed plate. Applied pressure deflects the membrane, decreasing the air gap:
ΔC ≈ C₀ × (Δd / d)
MEMS devices use this principle at µm-scale. At the benchtop, a thin PCB layer over a milled cavity works surprisingly well for 10–100kPa ranges.
2. Dielectric Compression
Soft dielectrics (silicone, foam) between plates compress under load. Since d decreases and εᵣ of compressed foam increases simultaneously, you get a strongly non-linear but reproducible transfer function.
Readout Circuit
Capacitance change is tiny (femtofarads to picofarads). The standard readout approach uses a relaxation oscillator whose frequency depends on C:
f = 1 / (2 × R × C × ln(2))
An LTC1799 or a 555 in astable mode works. The frequency shift maps directly to pressure. For better linearity, a charge amplifier topology or a sigma-delta CDC (e.g., AD7746) gives direct capacitance-to-digital conversion with 4aF resolution.
Noise and Stability Concerns
- Guard rings: Use PCB ground rings around sense traces to eliminate parasitic coupling from adjacent traces
- Shield the dielectric: Any moisture ingress changes εᵣ dramatically — conformal coat or hermetic packaging is essential
- Temperature drift: ε of most dielectrics has a 100–500 ppm/°C coefficient. Compensate with a reference capacitor not exposed to pressure
Practical Build Notes
I used a stack of two FR4 copper pours separated by a 100µm Kapton film on a prototype EGSE board. At 20kPa, the measured capacitance shift was ~8pF over a nominal 47pF — clean, repeatable, and resolvable with an AD7746 in differential mode. The key insight: sensitivity scales inversely with gap thickness, so thinner films win.
The capacitor-as-sensor model is used in everything from MEMS accelerometers to touchscreens. Understanding the underlying deformation mechanics makes you a better designer at every scale.