FMS Publications

RMS Induced Current - A Broadband Magnetic Field Exposure Assessment

OBJECTIVE:

Simple numeric comparison of magnetic field exposure from different sources has not been practical when the waveform and frequency of the magnetic fields differ significantly between the sources. An approach, using total RMS induced current, is proposed which unifies magnetic field magnitude, frequency and waveform exposure metrics into a single easily computed metric. Furthermore, the metric, RMS induced current, may be used to compare other potential magnetic field effects, including induced power, heat, voltage differentials, etc.

APPROACH:

The magnetic field is made of a fundamental, typically 50 or 60 Hz for fields produced by power lines and most appliances, along with an infinite series of harmonics, each having a frequency equal to an integer times the fundamental frequency. If a toroidal conductor is placed perpendicular to the magnetic field, the field will produce a current (in the toroid) proportional to the derivative of magnetic field. The RMS magnitude of this current can be calculated as follows:

METHOD:

A broadband instrument is used to digitize and record the magnetic field waveform(s) as shown in Figures 1 and 2. If necessary, multiple instruments may be used to cover the desired frequency spectrum. For example, one instrument may record the waveform using a low pass cutoff filter of 2 kHz and a second instrument may record the waveform using a band pass filter of 2 kHz to 125 kHz. A Fast Fourier Transform is used to calculate the frequency components in the magnetic field waveform (Figures 3 and 4). Each of the Fourier (frequency) components of the magnetic field (in mG) is then multiplied by it's frequency (in Hz) to produce the induced current Fourier (frequency) components (Figures 5 and 6). Each of the induced current components is squared and summed and the square root of the sum is calculated to give the RMS induced current. Calculation of the current requires one to know the "conductor's" geometry, conductivity and orientation to the magnetic field. However, in many cases, one is more interested in a comparison of induced current from different sources. In this case, the proportionality equations given above can be used to compare magnetic fields.

RESULTS:

The RMS induced current metric has been used by the authors to compare magnetic fields produced by various sources. Figures 1 through 6 apply the method to a heavy-duty drill press using a 1.5 horsepower universal motor. All measurements were taken at a distance of one foot from the motor. The low frequency (0 to 2 kHz) measurement utilized a Bartington Flux Gate sensor with a 2 kHz low pass filter. The high frequency measurement utilized a Horizon 44A sensor. Absent specific data on orientation, conductivity and geometry of the conductive body placed in the field, the authors use the term "RMS Current Induction" in place of current and express the results in mG-Hz. The RMS Current Induction is defined as:

In the example presented, RMS Current Induction by the frequency components of the magnetic field in the 0 to 2 kHz band is 380 mG-Hz. The RMS Current Induction in the 2 kHz to 125 kHz band is 107 mG-Hz. The total RMS Current Induction is found from:

DISCUSSION:

The RMS Induced Current metric, proposed by the authors, provides investigators with a powerful and simple method to compare magnetic fields; even if those magnetic fields differ significantly in frequency and waveform. Furthermore, the metric represents known effects, including induced current, induced voltage, power, and heat. The metric RMS Current Induction (mG-Hz), is independent and requires no specific knowledge of the conductive body placed within the field. Instrumentation capable of digitizing and recording magnetic field waveforms over a broad frequency spectrum is readily available for this application. And finally, the approach recognizes and accounts for the substantially greater ability of higher frequency fields to induce voltages and currents into conductive bodies.