Measure small impedances with Rogowski current probes
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.
next; Measuring impedance
Measuring impedance
The VNA can be used with the Rogowski probe to measure impedance, such as the input and output impedance of a power supply or passive device. The probe should be calibrated using the setup shown in Figure 3 before making any measurements.
Figure 3. Calibration setup for measuring impedance. A THRU calibration with this setup calibrates the magnitude and phase measurement and corrects the scale to read in Ohms.
The 1Ω resistor in Figure 3 transforms the current in the wires to an equivalent voltage at CH2 of the VNA. Clamp the probe around the calibrator wire and connect it to VNA CH1. Performing a THRU calibration in this measurement will scale the current probe magnitude and phase measurement to 1 V/A. It also compensates for any deviations in the response versus frequency. Figure 4 is a photo of this calibration setup. The calibrator uses five parallel 5.1Ω resistors in order to minimise inductance. The five resistors in parallel with the port impedance result in a resistance of precisely 1Ω.
Figure 4. Picture of the current probe calibration setup. Note this calibrator uses five parallel 5.1Ω resistors to minimise inductance. It results in exactly 1Ω when connected to a 50Ω port.
After calibration, the 1-Ω resistor is replaced with the device to be measured (DUT) and the VNA is set to measure gain as CH1/CH2. This is the voltage across the DUT divided by the current in the DUT which is the DUT impedance.
The measurement in Figure 5 shows the response prior to the THRU calibration, reflecting the 100 mV/A sensitivity and a 3 dB bandwidth of approximately 30 MHz. After performing the THRU calibration, the measurement is automatically rescaled and the frequency response magnitude and phase are compensated to the full measurement bandwidth or 40 MHz. The measurement correctly reports the resistance as 1Ω after calibration. The dynamic range and accuracy of the measurement method is confirmed by replacing the 1Ω resistor with 1 mΩ and 10 mΩ.
Figure 5. The red trace is the response prior to the THRU calibration, reflecting the 100 mV/A sensitivity, while the blue trace is the response after to the THRU calibration. The THRU calibration automatically corrects the scaling. The black trace is the result of a 10 mΩ resistor and the green trace is the result of a 1 mΩ resistor (which actually measured 1.3 mΩ in a DC measurement).
The signal is slightly noisy below approximately 1 kHz and the noise can be seen to be independent of the value of the impedance being measured. The noise magnitude is only related to the amplitude of the signal source from the VNA and not from the magnitude of the DUT impedance. The measurements of the 1 mΩ and 10 mΩ resistors are very slightly inductive at 400 pH and 300 pH, respectively. The slight inductance is most likely due to the solder mounting of the resistor to the PCB. As expected, the Rogowski current probe works very well for measuring passive impedance above 1 kHz and up to 30 MHz or more.
next; The time domain
The Time Domain
Nearly all oscilloscopes include bandwidth-limiting filters, but as we have previously shown, most of the noise is at frequencies below 1 kHz. Therefore, bandwidth limiting won’t significantly reduce noise.
There are three methods of minimising the noise from the Rogowski probe in the time domain. Any combination of the three can be used, allowing excellent control of the noise.
The highest noise will occur at higher timebase settings because the noise is mostly low frequency. The noise is naturally limited by the time span of the measurement as you reduce the time setting.
A series capacitor can be used to set the high-pass corner frequency if the oscilloscope input termination is set to 50Ω. The total series resistance is 100Ω because the Rogowski probe output is also 50Ω. A cutoff frequency of 1.5 kHz results from using a 1 µF ceramic capacitor.
The 50Ω Rogowski output is connected to a passive two-way splitter for demonstration purposes. Two oscilloscope channels are both set to 50Ω and gain corrected in order to account for the 6dB splitter insertion loss. One splitter output is connected to the oscilloscope through a 1µF series capacitor, while the other splitter output is connected directly to the other 50Ω oscilloscope input (Figure 6).
Figure 6. The Rogowski probe output is connected to a passive 2 way (6 dB) splitter. One splitter output connects directly to CH1, while the second splitter output is connected to CH2 through a 1 µF series capacitor. The capacitor is installed in a PI network board with SMA connectors.
The noise is measured simultaneously using two oscilloscope channels at various time base settings. The measurement results are shown graphically in Figure 7.
Figure 7. The noise measurement at different time bases with the series capacitor (red trace) and without the capacitor (blue trace).
Figure 7 illustrates the natural reduction in noise due to faster time base settings without the high-pass filter. The significant improvement from the high pass filter is also seen, though the noise improvement is at the expense of degrading the low-frequency cutoff.
Trace averaging
Averaging multiple traces can reduce noise because noise is random. To use averaging, you must have perfectly uniform cycle-to-cycle measurements of the signal or you will degrade the accuracy of the measurement. The measurements in Figure 8 show the sampled noise measurement, the envelope of the noise, and the noise averaged over ten traces. It is interesting to see that the envelope is greater than the peak-to-peak signal measurement. The noise is reduced approximately 8 dB by averaging the traces.
Figure 8. The top trace (yellow) shows the sampled noise while the middle trace (blue) shows the noise envelope of the same measurement. The lower trace (green) shows the same measurement with ten-trace averaging.
These noise reduction techniques can be combined for even greater noise reduction. Using the same splitter setup, a 5 µsec wide, 40 mAP-P current pulse is measured with and without averaging. The measurements, using colour persistence to show the repeatability of the signal, are shown in Figure 9.
Figure 9. The top window shows the 40 mAP-P current pulse without the series capacitor. The lower window shows the measurement with the series capacitor. In both cases, the pink colour is without averaging and the orange colour is with trace averaging.
The measurements show the combined benefits of both averaging and high-pass filtering. The measurements without averaging are shown in pink. The measurements with averaging are shown in orange. The upper window is without the high-pass filter, while the lower window is with the high pass filter.
A Picotest J2112A current injector is modulated by a Picotest G5100A AWG to produce a 900-mA, 1-µsec current pulse with approximately 25 nsec rise and fall times in the next measurement. The current is monitored by the precision current monitor port of the J2112A and also the P6022 and CWT15 probes. The measurement results are shown in Figure 10.
Figure 10. PEM CWT015 Rogowski (yellow, top) Tektronix P6022 (green, middle) and J2112A current monitor (orange,bottom) all measure the 25 nsec rise time well and the Rogowski coil is closest to the current injector monitor port. The 1 µF series capacitor is used for the Rogowski probe and all traces use trace averaging.
The Rogowski current probe has been shown to work well in both the time domain and the frequency domain. Using the noise management techniques presented in this article, the Rogowski probe can even be used for small signal impedance measurements using a VNA.
About the Author
Steve Sandler is the founder and former CEO of Analytical Engineering, Inc., the predecessor of AEi Systems. He has over 30 years experience in the design and analysis of power conversion equipment for military and space applications. Mr. Sandler is also the CEO of Picotest.com, a company that distributes test equipment including the Signal Injector product line designed for testing linear and switching power supplies, a Test & Measurement World "Best in Test" Finalist.
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