Noninvasive measurement of
high-frequency or pulsed electrical currents
Statement of the problem
Others have developed a variety of ferrous and non-ferrous toroidal current probes to measure time-dependent electrical currents. We have made significant further progress to address four significant needs:
1. The need for increased aperture size at a particular frequency.
2. The need for self-contained current probes with digital readout which have a constant sensitivity over a wide frequency range.
3. The need for a calibration fixture that does not affect the apparent response.
4. The need to determine the spatial distribution of the current within the probe.
1. The need for increased aperture size at a particular frequency.
2. The need for self-contained current probes with digital readout which have a constant sensitivity over a wide frequency range.
3. The need for a calibration fixture that does not affect the apparent response.
4. The need to determine the spatial distribution of the current within the probe.
Key principles we follow in developing current probes
We have learned several key principles in developing current probes used by the Army, Navy, and Air Force to evaluate potential hazards to personnel testing the Electromagnetic Pulse (EMP) sensitivity of their electronics, as well as by NASA, OSHA, NIOSH, and industrial calibration laboratories.
1. The Rogowski technique is used because ferrous materials reduce the propagation velocity along the length of the toroid which limits the size of the probe aperture for use at a given frequency. Ferrous current probes also have greater weight, are more expensive, introduce the uncertainty of a relative permeability, and increase the perturbation of the current which is measured.
2. The calibration fixture must be closed to limit interference from and to other apparatus. However, a closed calibration fixture has resonances causing errors in the apparent response of the probe so the volume must be minimized.
3. “One size fits all” is not correct. For example, an application may require a specific compromise between high sensitivity without a preamplifier and low perturbation of the current that is measured.
1. The Rogowski technique is used because ferrous materials reduce the propagation velocity along the length of the toroid which limits the size of the probe aperture for use at a given frequency. Ferrous current probes also have greater weight, are more expensive, introduce the uncertainty of a relative permeability, and increase the perturbation of the current which is measured.
2. The calibration fixture must be closed to limit interference from and to other apparatus. However, a closed calibration fixture has resonances causing errors in the apparent response of the probe so the volume must be minimized.
3. “One size fits all” is not correct. For example, an application may require a specific compromise between high sensitivity without a preamplifier and low perturbation of the current that is measured.
Specific examples of innovation:
1. Large aperture high-frequency current probe: Figure 1 shows a current probe we developed and used to measure the currents induced in humans and inanimate objects by generators simulating the Electromagnetic Pulse (EMP) that is caused by a nuclear detonation. Typically the peak electric field was 100 kV/m with a rise time of 5 ns and fall time of 200 ns. Peak currents as high as 500 A were measured in the limbs of the personnel but, because of the short duration of the pulse, the average absorbed energy was so low that there was no sensation.
Fig. 1. Large wide-band current probe
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This current probe has a toroidal coil with 200 turns of resistive line wound on a Plexiglas core in a cylindrical shield having an outer radius of 15.2 cm and an inner radius of 10.8 cm. The probe acts as a lossy helical coaxial transmission line having one type-N coaxial connector at each end. The effects of the C’, L’ and R’, the capacitance, inductance, and resistance per unit length for this line are used with numerical integration of the output voltage to determine the current as a function of time during each pulse.
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Figure 2 shows the current probe in its calibration fixture. Our measurements with commercial probe calibration fixtures, which are closed metal boxes, show anomalies at high frequencies which are attributed to the response of the current probes but are actually caused by resonances of the fixture. Thus, in order to minimize the volume of the fixture to increase the frequencies of these resonances, we close the aperture to form a coaxial calibration fixture. Our calibration fixture is completely closed by the two metal plates in contact with the top and base of the probe.
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Fig. 2. Current probe with calibration fixture
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An axial conductor is attached to type-N connectors on the metal plates, and the radius of this conductor is chosen so that the aperture of the probe and the axial conductor form a short section of 50 Ω coaxial transmission line. In calibration, a signal generator is attached to one type-N connector and a 50 Ω radiofrequency power meter is attached to the other connector and adjusted to provide a specified current. The legs supporting the lower metal plate and the screw-on connections make the test fixture convenient to use so that calibration can be performed using a single hand.
Tests made using this calibration fixture show that this current probe is usable at frequencies up to 300 MHz, at which the circumference of the aperture is 0.68 times the wavelength in air. This verifies that this probe is suitable for measurements with the EMP simulator which has a rise time of 5 ns. A current probe having a smaller aperture could be used with shorter pulses but would not have been suitable for measurements with human subjects.
Tests made using this calibration fixture show that this current probe is usable at frequencies up to 300 MHz, at which the circumference of the aperture is 0.68 times the wavelength in air. This verifies that this probe is suitable for measurements with the EMP simulator which has a rise time of 5 ns. A current probe having a smaller aperture could be used with shorter pulses but would not have been suitable for measurements with human subjects.
2. Self-contained wide-band current probe: Figures 3 and 4 show a current probe that uses active antenna techniques with a digital readout which we developed in collaboration with NASA Goddard Space Flight Center. This instrument has a full-scale sensitivity that is adjustable from 1 to 1000 mA, and varies by less than ±1.5 dB over a frequency range of 300 kHz to 120 MHz. The instrument has a mass of 300 grams and overall dimensions of 23 x 20 x 5 cm.
Fig. 3. Self-contained current probe.
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Fig. 4. Current probe and calibration fixture.
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Some novel aspects about this instrument are as follows: (1) The coil is connected to a high-frequency op amp so it is shorted by the virtual ground to dampen resonances of the coil without requiring resistive loading. (2) Shorting the coil by the op amp flattens the response of the instrument so the current is nearly independent of the frequency. This is may be understood because the voltage is proportional to the frequency but the impedance of the coil is proportional to the frequency. (3) Stabilized regenerative amplification, with partial cancellation of the effects of the resistance and inductance of the coil, provides greater usable bandwidth with greater sensitivity than would be obtained using conventional integrators in an attempt to flatten the response.
These portable battery-operated current probes measure the current from 300 kHz through 120 MHz, covering the full AM and FM broadcast bands. This portable instrument is specifically intended in applications to measure the exposure of humans to strong electromagnetic fields. One example is that presently personnel must climb tall radio antenna towers for maintenance including repair and replacement of the aircraft warning lights when the transmitter is operating. These personnel feel the heat caused by the radiofrequency energy but at present there are no instruments to quantify this effect.
3. System of coils to measure the spatial distribution of a current: Ampere’s law may be used to show that a uniformly-wound non-ferrous toroidal coil may be used to determine the total time-dependent current passing through the aperture and is not sensitive to current outside of the aperture. Such a device is called a Rogowski coil, and care must be used to limit the deviations from perfect uniformity which would cause the output voltage to depend on the spatial distribution of the current. We have shown by analysis, numerical solutions, and measurements, that if several toroidal coils have a specific type of nonuniformity it is possible to use them to determine the spatial distribution of a time-dependent current flowing through their common aperture.
We derived analytical expressions for the voltage induced in a toroidal coil by a current filament at various locations within the aperture when the number of turns per unit length is proportional to an integer N multiplied by the azimuthal angle θ in radians. For example, Fig. 5 shows a coil designed with N = 1. These expressions show that for each value of the integer N, the induced voltage has a unique dependence on the radial and azimuthal coordinates of the current filament. Thus, matrix equations have been used to approximate the magnitude and location of a finite number of current filaments that are located within the aperture.
Rapid prototyping was used to prepare the forms for three toroidal coils for which N = 0 (uniformly wound), 1, and 2. Figure 5 is a design drawing for the N = 1 coil, in which the two halves of the winding have opposite sense.
These portable battery-operated current probes measure the current from 300 kHz through 120 MHz, covering the full AM and FM broadcast bands. This portable instrument is specifically intended in applications to measure the exposure of humans to strong electromagnetic fields. One example is that presently personnel must climb tall radio antenna towers for maintenance including repair and replacement of the aircraft warning lights when the transmitter is operating. These personnel feel the heat caused by the radiofrequency energy but at present there are no instruments to quantify this effect.
3. System of coils to measure the spatial distribution of a current: Ampere’s law may be used to show that a uniformly-wound non-ferrous toroidal coil may be used to determine the total time-dependent current passing through the aperture and is not sensitive to current outside of the aperture. Such a device is called a Rogowski coil, and care must be used to limit the deviations from perfect uniformity which would cause the output voltage to depend on the spatial distribution of the current. We have shown by analysis, numerical solutions, and measurements, that if several toroidal coils have a specific type of nonuniformity it is possible to use them to determine the spatial distribution of a time-dependent current flowing through their common aperture.
We derived analytical expressions for the voltage induced in a toroidal coil by a current filament at various locations within the aperture when the number of turns per unit length is proportional to an integer N multiplied by the azimuthal angle θ in radians. For example, Fig. 5 shows a coil designed with N = 1. These expressions show that for each value of the integer N, the induced voltage has a unique dependence on the radial and azimuthal coordinates of the current filament. Thus, matrix equations have been used to approximate the magnitude and location of a finite number of current filaments that are located within the aperture.
Rapid prototyping was used to prepare the forms for three toroidal coils for which N = 0 (uniformly wound), 1, and 2. Figure 5 is a design drawing for the N = 1 coil, in which the two halves of the winding have opposite sense.
Fig. 5. Design drawing of helical coil with J = 1.
Figures 6 and 7 are design drawings showing the precision support which holds each coil within its shield, and the completed device having the coil within its shield.
Fig. 6. Support holding the coil.
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Fig. 7. Completed shielded coil.
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Figure 8 shows the custom test fixture that is used to measure the time dependent voltage from each coil as a function of the radial and azimuthal coordinates of a current filament.
Fig. 8. Custom test fixture.