Using current probes to estimate E-fields
Figure 1 - A couple of DIY current probes made from split ferrite chokes.
My article on current probes published in Interference Technology has been their most-read article over the last two years. For more detail, I’d refer you to that article. For this posting, I’d just like to take you through the math involved in estimating E-field levels at a given distance - typically 3m or 10m. This technique was largely drawn from Dr. Clayton Paul’s excellent “Introduction to Electromagnetic Compatibility” (Wiley Interscience, 2006) and refined by Henry Ott in his classic “Electromagnetic Compatibility Engineering (Wiley, 2009).
Figure 2 – A matched set of clamp-on Fischer Custom Communications model F-33-1 current probes. While not imperative to purchase, a matched set is very useful for advanced troubleshooting of I/O cable emissions. They can sense RF currents of a few microamps.
By measuring the common-mode current on your I/O or power cables, it’s possible to estimate the E-field contribution from the cable in question. We’ll use the Fischer F-33-1 current probe for this example, but other calibrated probes are equally useful. The F-33-1 probe is useful from 1 MHz to 250 MHz - the flat region in Figure 3 below.
While near field probes, such as H-field or E-field) can help track down the sources of harmonics, current probes can be used to measure the common-mode current on the cable that creates the radiating E-field. The E-field may then be calculated from the amount of current measured on an I/O or other product cable. Thus, a good commercial current probe is often one of the most useful troubleshooting tools, because it is possible to predict (within reason) whether your product can pass or fail during the radiated emissions compliance test, at least based on cable emissions.
Clamping a Fischer F-33-1 current probe around a 1m-long cable yields several harmonics, the largest of which, measures 37 dBµV at 120 MHz on the spectrum analyzer.
To calculate the actual current, you would utilize the transfer impedance chart in Figure 3. We see that the transfer impedance at 120 MHz is about +12 dBO (this can vary from 12 to 16 dBO, depending on the probe calibration). To calculate the current in dBµA, we use:
Using logarithm identities and converting to Amps, the calculated current through the wire is:
Figure 3 – Manufacturers of current probes include a plot of transfer impedance versus frequency. Transfer impedance (Zt) is simply the measured current divided by the terminal voltage at the coaxial port of the probe, expressed in dB. By taking the measured voltage at a particular frequency the current in amps may be calculated (plot for F-33-1 probe pictured). Courtesy, Fischer Custom Communications.
Given this current of 17.783 µA, we can use the equation below to calculate the E-field in V/m for the cable in question:
Ec is the calculated E-field in V/m due to common-mode current flowing on the cable,
Ic is the current through the wire or cable (A),
f is the harmonic frequency being measured (Hz),
L is the length of the cable in meters and
d is the measured distance during the compliance testing (usually 3 or 10m).
If we assume a test distance of 3m, converting 8.94*10-4 V/m to dBµV/m, we get 59.03 dBµV/m. Comparing with the FCC Class B limit, we see that at 120 MHz and at a 3m test distance, the E-field limit is 43.5 dBµV/m, so the result is potentially 15.5 dB above the limit from that one cable.
Figure 4 – Using a current probe to measure the common-mode currents on a DC power cable.
Note: If the common-mode current in the wire or cable exceeds about 3 µA (this equals about 9.5 dBµA, or for the Fischer F-33-1 current probe, the reading is about 21.5 dBµV as measured at the probe), you will equal the FCC Class B limit at 120 MHz and assuming a 3m test distance. This illustrates why it’s important for these very small currents to be managed and controlled.
CAUTION: While this technique may provide an estimate, it will not give you a precise prediction of E-field level at 3m or 10m - only a “ballpark” number. For accurate measurements, your product will have to be measured using a calibrated semi-anechoic chamber or open area test site (OATS).
Measuring resonance in cables
Questions on cables for EMC mitigation
Identifying emission sources and propagating structures
An EMC troubleshooting kit - part 1a (emissions)
An EMC troubleshooting kit - part 1b (emissions)