A Rogowski coil produces a voltage that is proportional to the rate of change (derivative) of current enclosed by the coil-loop. The coil voltage must be integrated for the probe to provide an output voltage that is proportional to the current signal. This also means that the Rogowski can't perform at DC, but can operate to a frequency lower than most AC clamp-on current probes.
Table 1 highlights the key performance attributes of three different clamp on current probes. The comparison results are based on the PEM CWT015, Tektronix P6022 and Teledyne Lecroy CP031 current probes. The three probe heads are shown in Figure 1.
Table 1. A comparison of current probes.
Figure 1 CP031 (top), P6022 (middle), and Rogowski (bottom).
Both the AC current probe and the Rogowski current probe can be used with test equipment from any manufacturer. This includes oscilloscopes, VNAs (vector network analysers), and spectrum analysers. Hall-effect probes, on the other hand, are generally keyed to a particular equipment manufacturer. Comparing the AC and Rogowski probes, the Rogowski current probe excels in all performance characteristics except noise and the ability to measure DC. You can, though, manage the noise and make the Rogowski probe one of your most-used probes.
Consider the noise
The low frequency noise from the Rogowski current probe is a result of the high gain integrating amplifier needed by the probe. The CWT015 noise is predominantly below 1.5kHz as shown in the noise density measurement in Figure 2. (Note; the noise is mostly below 1 kHz because of the opamp 1/f noise which is greatly amplified at low frequencies due to the integrator configuration: all Rogowski probes require a high gain integrator to create an output that varies linearly with current. Most linear regulators also exhibit 1/f noise at low frequencies (typically below 1kHz))
Figure 2. The noise density is 200 µV/√Hz at 100 Hz, 20 µV/√Hz at 1 kHz, and 2.4 µV/√Hz at 10 kHz. When used with a spectrum analyser or VNA the resolution bandwidth can be set to 30 Hz or even lower. At 1 kHz with a 10 Hz resolution bandwidth the noise is approximately 100 µV and at 10 kHz and above only 10 µV.
The frequency domain
When using the Rogowski current probe with a VNA or spectrum analyser, the resolution bandwidth can be set to 30 Hz or even lower. This narrow bandwidth minimises the measurement noise. The sensitivity of the CWT-015 probe is 100 mV/A. At 1 kHz, the noise density indicates 20 µV/√Hz noise. Converting through the sensitivity this equates to a noise current density of 200 µA/√Hz.
The peak-to-peak noise can be calculated from the noise density and the resolution bandwidth as:
Using this relationship, a 30 Hz resolution bandwidth results in a peak-to-peak noise of 2 mAP-P at 1 kHz and 260 µAP-P at 10kHz. If the current being measured is maintained above 20 mAP-P at 1 kHz or 2 mAP-P at 10 kHz, then the signal-to-noise ratio will result in measurements with acceptable fidelity.
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