### 8.4.2 Rogowski coils
A type of current transducer that is rising in popularity is an air-core current transformer called a Rogowski coil. This is a toroidal coil wound on a rigid or flexible nonmetallic core. A sinusoidal current
will induce in the coil a voltage
w here M is the mutual inductance between the transducer and the circuit that carries the distorted current to be measured. A high input impedance analyzer ( 10 M) can measure the magnitudes MhI_{h}. The system is calibrated at 60 Hz with a known current I_{K} that yields a reading V_{K}. The magnitude of a certain harmonic current is determined from the expression
T his method is convenient for large harmonic currents. For smaller currents, a larger value of M is required. This translates in a larger number of turns and the inter-turn capacitances may deteriorate the linearity of the frequency response.
Commercial units use precision integrators that reconstruct the signal [3]. The geometry of the coil, shielding method, length and characteristics of the coaxial cables connecting the coil with the integrator and the integrator with the analyzer, and especially the design of the integrator will affect the accuracy of the measurement. A simulated frequency response is shown in Fig. 8-4. Accurate amplitude measurements can be obtained for a wide frequency range. The phase angle, however, may be measured with a significant error. A most annoying problems is the effect caused by the location of Rogowski coil with respect to the conductor whose current is to be measured. Based on the data published in [3] and graphed in Fig. 8-5, results that it is imperative to run the instrument calibration and the actual measurements with Rogowski coil fixed in one rigid location with respect to the conductor. This should not present a problem for laboratory measurements, but may disqualify this method for precision field measurements.
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