When the Simplest Circuit Outperforms the Complex Ones: A Fresh Look at Differential Capacitance Sensors

Think the best capacitive sensing interface has to be a DSP-powered, multi-stage amplifier with a $50 price tag? Think again. Jordan Dimitrov, an electrical engineer with 40 years of experience, just threw that assumption out the window with a relaxation oscillator built from one SR latch and two RC networks.

The secret lies in how the circuit swaps roles between the two capacitors — while one is slowly charging through its resistor, the other is being rapidly discharged through a parallel switch. When the charging capacitor hits the gate’s trip voltage, the latch flips and they switch. This back-and-forth generates a square wave at VQ1, which a microcontroller reads by measuring the two time intervals t1 and t2.

The math is elegant: VAVR = VDD × t1 / (t1 + t2). Subtract a calibration constant so equal capacitors read as zero, and you get a differential output — positive when C1 > C2, negative when C1 < C2. No expensive instrumentation amplifier needed.

Testing with a bank of ten 50-pF capacitors, Dimitrov found the duty cycle fits a perfect straight line (R² = 1), but nonlinearity error sits at ±0.3%. Here’s where it gets clever: a second-order polynomial (y = 1×10⁻⁵x² + 0.182x + 4.21) cuts that error down to ±0.1% — and that’s trivially easy to implement in firmware.

The takeaway isn’t just about saving components. It’s that the simplest circuit in your parts bin might outperform the one you’ve been specifying. Sometimes the best engineering move is to strip away the complexity and trust the fundamentals.