2026-09-11
A Rogowski coil is an air-cored toroidal winding that clips around a current-carrying conductor and outputs a voltage proportional to di/dt. Unlike a current transformer, it has no iron core — so it cannot saturate, and it can measure enormous currents (kiloamps to megaamps) with a lightweight flexible coil that literally wraps around a busbar like a rubber band.
The physics is Ampère's law plus Faraday's law. A conductor carrying current i(t) creates a magnetic field. If you wrap a coil of N turns per meter around a closed path enclosing that conductor, the induced voltage is:
v(t) = −μ₀ · N · A · (di/dt)
where A is the cross-sectional area of the coil's former. Note the derivative: the raw output is not current — it's the rate of change of current. To recover i(t), you follow the coil with an integrator, typically an op-amp integrator with a large feedback resistor to bleed off DC offset. That integrator is where most of the design pain lives.
Concrete example: You want to measure 100 A peak at 50 Hz through a welding cable. A commercial Rogowski coil rated at 50 mV/(kA/μs) sees di/dt = 2π · 50 · 100 = 31,400 A/s, or 0.0314 A/μs. Raw output: 50 mV × 0.0314 = 1.57 mV peak — tiny. After a 1/RC = 1/(100 kΩ · 1 μF) = 10 rad/s integrator with gain, you can scale that to a clean 1 V per 100 A.
Rule of thumb: the integrator's low-frequency cutoff (fL = 1/(2πRC)) must sit at least a decade below your lowest signal frequency, or phase error becomes ugly. For 50 Hz mains, put fL at 1–5 Hz. But go too low and DC offset from op-amp bias current will rail the integrator — always include a large parallel resistor across the feedback cap (10× to 100× the impedance at fL) to define DC gain.
Advantages worth remembering:
Watchouts: the coil is sensitive to conductor position (center it in the loop), external fields can couple in (use a return wire routed back through the toroid to cancel), and DC currents are invisible — Rogowski coils fundamentally cannot measure DC. For DC, use a Hall sensor or shunt instead.