Self-integrating Rogowski Coil Research Articles

Lightning Peak Current Sensor Based on Electret Technology

Lightning peak current is one of the most important parameter concerning the studies of the lightning phenomena. Nowadays, with a continuous dissemination of elevated structures, such as telecommunication towers, the study of the lightning peak current could be intensified with the installation of measurement devices in large scale. Thus, it is useful to develop a device that is robust, compact, low cost, and allows data collection. This paper describes a high-current sensor operating in a range up to 100- and 7.7-kA resolution. The system consists of a self-integrating Rogowski coil connected to the electret sensor by a coaxial cable. The electret sensor is installed in a sturdy and inexpensive casing at the tower base. Measurements indicate a linear and precise correlation between the voltage generated by the coil, installed on the top of the tower, and the impulse current from lightning.

Two Compact Coaxial Cable Connectors With Self-Integrating Sensors to Measure Nanosecond Pulse Signals

It is put forward that an attenuator can be integrated into an n-type or an Subminiature version A-type cable connectors to realize the compactness of the signal measurement system for certain types of pulsed power systems. Two types of compact cable connectors are designed and fabricated for the nanosecond high-voltage (HV) and the nanosecond large current (LC) signal measurements, respectively. As to the nanosecond HV signals, it is suggested that the HV arm resistor of a series resistor voltage division circuit (SRVDC) can be integrated into a coaxial cable connector. This integrated connector can link a self-integrating capacitive voltage divider (CVD) to an oscilloscope directly with a voltage attenuation factor of $\beta _{1}(1+R_{1}/Z$ ), where $\beta _{1}$ is the voltage ratio of the CVD, $R_{1}$ is the HV arm resistor of the SRVDC, and $Z$ is the characteristic impedance of the cable. As to the nanosecond LC signals, it is suggested that n resistors with a resistance of $nR_{s}$ can bridge angularly between the two conductors of the integrated HV cable connector to play the role of current viewing resistor. This integrated connector can also link a self-integrating Rogowski coil to an oscilloscope directly with a current sensitivity of $N(1+R_{1}/Z)/R_{s}$ , where $N$ is the turn number of the Rogowski coil. These two compact cable connectors have the advantages of small volume, lightweight, and adjustable attenuation factor. In the end, the application of these two types of compact cable connectors to test the nanosecond signals of a Tesla-type generator is presented.

Development of a new type of large-size self-integrating Rogowski coils applied in TPG-series generators

Different meter-class, thousand-turn, self-integrating Rogowski coils for the TPG-series generators are designed. The features of this type of coils are the extremely large turn number (several thousands) and the 50-Ω characteristic impedance of the cable used as the current viewing resistor. After calibrations for these large-size coils, it is found that the experimental sensitivities are larger than the theoretical ones and that the deviations range from 4% to 20%, which cannot be accepted. The deviations are analysed in perspective of coil size and cable length. It is concluded that the sensitivity deviations are mainly due to the increased coil size and partly due to the long cables. A modified theoretical sensitivity expression of the large-size, self-integrating Rogowski coils is presented based on the transmission-line model, which embodies the factors of coil size and cable length. A method to test the key parameter in the model, the characteristic impedance of the coil, Z, is also presented. With this expression and the method, the theoretical sensitivities for the TPG-series generators are re-calculated, which agree well with the experimental ones, only with a deviation around 2%. It is suggested that the modified theoretical sensitivity expression can be used to calculate the sensitivity of the self-integrating Rogowski Coils with a large size.

Experimental Demonstration of a High-Efficiency Relativistic Magnetron With Diffraction Output With Spherical Cathode Endcap

A previous computational study of a relativistic magnetron with diffractive output at the University of New Mexico using the particle-in-cell code MAGIC achieved an efficiency of 70%. The research described in this paper aimed to achieve an experimental verification of 70% efficient operation of this design. Changes to the topology were necessary, such as the introduction of a Helmholtz-like magnetic coil pair and the use of a polished stainless steel endcap on the downstream end of the transparent cathode. These structures maintain a high degree of magnetic field uniformity in the anode–cathode gap interaction space and intercept leakage electrons that might otherwise impact the dielectric output window. The use of these structures stands in contrast to the modified magnetic fields used in the work of others to protect the window. An ethanol calorimeter and S-band waveguide detector were placed in the near-field to obtain radio frequency pulse shape and frequency and to infer peak power through a measurement of total energy radiated. A coaxial D-dot probe and self-integrating Rogowski coil were used to measure pulser voltage and total current, respectively, and showed that the tube operated at an efficiency of 63.5% until the endcap started emitting electrons, after which the efficiency was 40.4% in $\pi $ -mode. Images of radiated field pattern on a neon-bulb grid and of air breakdown outside of the 21-cm diameter output window were captured to confirm conversion of the $\pi $ -mode of operation to a TE31 circular radiated output mode.

Hybrid PCB Rogowski Coil for Measurement of Nanosecond-Risetime Pulsed Current

Self-integrating Rogowski coil has been widely used for measurements of pulsed currents from nanosecond timescale to microsecond timescale in pulsed power systems. Appropriate designs of coil’s structure are vital to high-frequency response. This paper proposed a new structure of Rogowski coil so as to provide a better response to fast pulsed current. Four Rogowski coils with different structures were tested in three different platforms. Experimental results showed that the hybrid Printed Circuit Board Rogowski coil had the best performance in this paper, which could respond to square waves with fronts of $\sim 2$ ns and had a sensitivity of 0.585 V/kA. The designed maximal peak current was 100 kA.

A novel design of Rogowski coil for measurement of nanosecond-risetime high-level pulsed current.

In pulsed power systems, pulsed currents with risetimes from nanosecond to microsecond can be effectively measured by self-integrating Rogowski coils. Appropriate design of the structure and the integrating resistor is crucial to the high-frequency response of a coil. In this paper, several novel designs of Rogowski coil's integrating resistors were proposed and tested. Experimental results showed that the optimized coil could response square waves with fronts of ∼1.5 ns and had a sensitivity of ∼0.75 V/kA. The maximal peak current was designed as 100 kA.

Multi-layer self-integrating Rogowski coils for high pulsed current measurement

This paper presents design and calibration of a self-integrating Rogowski coil to measure high impulse currents. This coil is wound in single-, double-, and triple-layers by a coaxial cable without its polyvinyl chloride (PVC) jacket “sheath.” Overdamped unidirectional and oscillatory impulse currents are generated up to 7 kA and measured by different methods, namely, a commercial impulse current transformer (ICT), a commercial Rogowski coil (CRC) and the newly designed self-integrating Rogowski coil. The output voltage linearity of the designed self-integrating Rogowski coil with different layers is checked using different stages of the impulse-current generator, linear and nonlinear loads, and coil termination resistances. It is found that at a termination resistance of 1.1 Ω, satisfactory impulse current waveforms are measured by taking the commercial impulse current transformer as a reference signal. Results reveal that the magnitudes of measurement errors for the current peak, and front and tail times are <1.4%, <1.9%, and <4.5%, respectively. Overdamped impulse currents are generated by different generator capacitances, where impulse currents measured by double- and triple-layer coils have shown good agreement to those measured by the commercial devices. The trend of the results is also explained in terms of reflection, coil transit time and sensitivity bandwidth.

New Side-Looking Rogowski Coil Sensor for Measuring Large-Magnitude Fast Impulse Currents

This paper presents a new design of a side-looking “flat spiral” self-integrating Rogowski coil that is wound by twin coaxial cable with individual sheath. The coil is tested with different impulse current waveforms up to 7 kA peak value to improve its performance. The coil design is optimized to achieve bandwidth and sensitivity up to 7.854 MHz and 3.623 V/kA, respectively. The coil is calibrated versus two commercial impulse-current measurement devices at different coil-to-wire separations, coil inclination angles, and impulse current waveforms. Distortion of the coil output voltage waveform is examined by using the lumped-element model to optimize the connections of the four cable winding sheaths and the coil termination resistance. Finally, the coil frequency response is investigated to optimize the coil design parameters and achieve the desired bandwidth (large low-frequency time constant), high rate of rise, no overshoot, very small droop, high rate of fall, and no backswing.

High magnetic pulse by solenoids for intense ion beam transport

A high voltage pulser up to 50 kV, with a main pulse of 2 μs time duration, was realized using a fast high voltage capacitor of 150 nF (50 kV) connected to the ground by a homemade spark-gap. The circuit, contained in a metallic box to avoid irradiation, had short electric connections in order to reduce the inductances. The diagnostic was performed by two systems: a self-integrating Rogowski coil and an integrator connected to a current transformer, both suitable for pulses longer than 1 μs. To focus ion beams with energy reaching 40 keV, we made two solenoids having an inductance of 3.6 and 16 μH which were fed by the current generated by the pulser up to 12 kA, 1 μs at 50 kV of charging voltage of capacitor. The measurements determined a magnetic field at the solenoid center of 0.61 T for the more inductive solenoid and 1.14 T for the other one.

Novel designs of wideband Rogowski coils for high pulsed current measurement

This study presents design, calibration and testing of six novel flat-spiral self-integrating Rogowski coils wound in two layers. These coils are two varnished-wire wound coils with air and ferrite cores (RC1 and RC2, respectively), two flat-twin wire wound coils with air and ferrite cores (RC3 and RC4, respectively) and two coaxial-cable wound coils with and without the insulating jacket and with ferrite core and RC5 and RC6, respectively. All coil parameters are calculated and good agreement is found between these values and the corresponding measured ones. Coil sensitivity decreases as coil-to-wire separation increases and so does mutual inductance between the coil and the current-carrying wire. Linearity of all coil sensitivities are checked for different separations and waveforms, and good agreement is found. Designed coils with ferrite core give better response than those with air core because the low cutoff frequency decreases. On the contrary, the droop effect is slightly observed for coils wound on wooden core, where RC4 and RC6 give the best response. Finally, the frequency response analysis for all coils shows that the percentage relative errors of the measured and the calculated coil sensitivities are within ±0.1%.

Performance Improvement of Slow-Wave Rogowski Coils for High Impulse Current Measurement

This paper presents the operating principles, design, and performance improvement and limitations of three slow-wave air-core Rogowski coils that enable plateau bandwidths up to 11 MHz and sensitivities of less than 0.25 V/kA to be achieved. The frequency response for these coils is examined to optimize the coil termination resistance in order to achieve the suitable transit time, minimize the droop effect, and achieve desired bandwidth. In the present design, the coil inductance is increased to compensate for the resulting reduction in the sensitivity due to the coil termination resistance. Oscillatory and overdamped unidirectional current waveforms up to 10 kA peak value are generated by using different linear and nonlinear loads, and impulse current generator configurations. These high impulse currents are measured by different methods, namely, a commercial impulse current transformer (ICT), a commercial Rogowski coil (CRC), and the three newly designed self-integrating Rogowski coils. Distortion of the measured current pulses is studied by using the lumped-element model of Rogowski coil and its termination resistance, and the signal cable and its matching resistance. The optimal coil termination resistance is obtained under these impulses, and the linearity of all newly designed self-integrating Rogowski coils' output voltages are also investigated. Calibration results and a comparison between ICT, CRC, and the developed three coils for measurements of different high impulse currents demonstrate that the developed coils can accurately reproduce the actual waveform with a constant sensitivity over the desired bandwidth.

Coaxial-Cable Wound Rogowski Coils for Measuring Large-Magnitude Short-Duration Current Pulses

In this paper, the design, calibration, and performance improvement of four self-integrating Rogowski coils are presented. These coils are wound in single and double layers by a coaxial cable without its polyvinyl chloride (PVC) jacket and with air and ferrite cores. Nonuniformities due to the variation of turn density and/or core deformation are compensated by using a one-turn return loop placed inside the helical winding in the opposite direction to the pitch advancement. Oscillatory and overdamped unidirectional current waveforms up to a 7-kA peak value are generated by using different linear and nonlinear loads and impulse-current generator configurations. These large-magnitude short-duration current pulses are measured by different methods, namely, a commercial impulse-current transformer, a commercial Rogowski coil, and the four newly designed self-integrating Rogowski coils. The distortion of the measured current pulses is studied by using the lumped-element model of Rogowski coil and its termination resistance and the signal cable and its matching resistance. The optimal coil termination resistance is obtained under these impulses, and the linearity of all newly designed self-integrating Rogowski coils' output voltages is also investigated. Results reveal that the magnitudes of measurement errors for the current peak and front and tail times are very low when using ferrite cores with a low termination resistance. The trend of the results is also explained in terms of coil termination resistance, transit time, and sensitivity bandwidth.

A Self-Integrating Rogowski Coil for Lightning Current Sensor

Lightning current is very important parameter for evaluating the overvoltage of the power system and characterizing the electromagnetic compatibility of the electronic equipments. Therefore, it is indispensable to measure lighting current by a suitable sensor. This paper presents a self-integrating rogowski coil for lightning current sensor, and introduces the operating principle and analyses characteristics of it. In addition, to improve the precision of the sensor this paper proposes design procedure of the phase compensation method and the circuit structure to implement the phase compensation method. The simulation results verify that the phase compensation method can enhance the precision of the self-integrating rogowski coil.

Effect of Medium on Deposited Energy in Microsecond Electrical Explosion of Wires

The properties of the medium have an obvious effect on the process of the electrical explosion of the wire. In this paper, the electrical explosions of copper and aluminum wires were investigated in air and water with pulsed voltage in a time scale of a few microseconds. Based on the measurements of the current and voltage waveforms in wire explosion with a self-integrating Rogowski coil and a voltage divider, respectively, the deposited energy in the stages of melting, liquid state, and vaporization was calculated by mathematical method. The effect of air and water on deposited energy in the three stages previously mentioned was analyzed by experiments and calculation. The results show that the pressure of the medium around the wire generated by compression from wire material expansion is an important factor of the effect of the medium on the energy deposition and the time of duration in the different stages. Additionally, the species of the medium also has an important effect on the formation of plasma discharge channel. The deposited energy in the electrical explosion of copper and aluminum wire in water is more than that in air, particularly after the beginning of vaporization.

Analysis of damping resistor’s effects on pulse response of self-integrating Rogowski coil with magnetic core

A self-integrating Rogowski coil with magnetic core is investigated for accurate measurement of high-impulse current in this paper. Usually, the distributed parameters of Rogowski coil generate deleterious high-frequency resonant signal parasitizing in the useful signal of the coil circuit. Damping resistors can be used to eliminate the parasitic resonant component of the signal. In this paper, damping effects of the damping resistors on the output signal of Rogowski coil are studied in detail. According to circuit theory, approximate circuit equations of Rogowski coil with lumped parameters in simplification are put forward. Response signal of coil is analyzed and a reasonable method for choosing damping resistance is also presented. When the 50Ω damping resistance is used, the amplitude of parasitic resonant signal has been damped by 5.7 times in contrast to the situation without any damping resistance. Result of Pspice circuit simulation corresponds to the theoretical calculation result. A standard 10ns square pulse has been used to calibrate the coil signal before and after the damping resistors soldering on the coil, respectively. Experimental results show that the response time of the coil with magnetic core is 1.1ns and the parasitic resonance in the coil signal is almost eliminated. The coil can accurately detect high-pulse current at kA range.

测量1 MA/100 ns脉冲大电流的微分环

The Qiangguang-Ⅰ (QG-Ⅰ) accelerator can produce high current pulses with rise time of about 100 ns and amplitude of about 2 MA. The load current is usually monitored by self-integrating Rogowski coils. In order to verify the obtained results of the coils, a differential loop with fast response time, relatively simple design, and appropriate performance against electromagnetic noise, has been developed. Calibration experiments show that the differential loop has a response time of about 1.2 ns, a response frequency range from 10 kHz to 100 MHz, and a sensitivity of 6.1310-11(Vs)/A. The fast response may help to monitor transient variation of the load current related to some rapid physical processes. The differential loop has been tested within short-circuit diode of QG-I accelerator and compared with self-integrating Rogowski coils. The current waveforms obtained through numerical integration of the loop signal exhibit good agreements with those from the coils, with an amplitude deviation less than 10%. Comparison of the results confirms the availability of the loop, and also verifies the reliability of the load current measurements on the accelerator.

Effect of Circuit Parameters and Wire Properties on Exploding a Copper Wire in Water

The physical processes that occur during the initial stages of nanosecond explosion of thin wires play an important role in the development of plasma for nanoparticle preparation. The transition of the wire material from the condensed state to conducting plasma has not yet been fully understood. In this paper, underwater electrical explosions of copper wires were investigated with pulsed voltage in the timescale of a few microseconds. A self-integrating Rogowski coil and a voltage divider were used for the measurements of the current and the voltage on the wire load, respectively. The current rise rate was adjusted by changing the circuit parameters, including the discharge voltage and circuit inductance, and the copper wire properties consisting of the length and the diameter. The effect of the current rise rate on the phase transitions involving melting from solid to liquid and vaporization from superheated liquid to the vapor-drop mixture was obtained by the analysis of the current and voltage waveforms of copper wire explosion. The energy of melting and vaporization was calculated based on experimental waveforms of current and voltage. In addition, the effect of applied voltage, circuit inductance, and the length and diameter of copper wire was acquired on the electrical explosion characteristics of copper wires.

Self-Integrating Rogowski Coil for High-Impulse Current Measurement

This paper presents the operating principle, the performance under impulse condition, and the design of a self-integrating Rogowski coil for measuring high-impulse currents. Oscillatory and overdamped unidirectional impulse currents are generated up to 10 kA and measured by different methods, namely, two commercial impulse current transformers, a resistive shunt, and the newly designed self-integrating Rogowski coil. For the resistive method, the voltage drop across the shunt affects the total voltage measured across the test object and causes distortion in the case of simultaneous measurement by an impulse current transformer having a small aperture. The Rogowski coil theory under impulse current conditions is presented. The concept of transmission lines is used, and the line parameters are optimized to achieve a self-integrating mode and avoid spurious effects of reflections and stray capacitances. The output voltage linearity of the designed self-integrating Rogowski coil is checked using different linear and nonlinear loads and coil termination resistances. It is found that at a termination resistance of 1 ?, satisfactory impulse current waveforms are measured by taking the commercial impulse current transformer as a reference signal. Results reveal that the measurement errors for the current peak and front and tail times are ±2%, ?6%, and ? 12%, respectively. Overdamped impulse currents are generated by different generator capacitances, where comparisons between the measured and calculated current waveform parameters have shown good agreement.

自己積分型ロゴスキーコイルの共振特性

自己積分型ロゴスキーコイルの共振特性

New structure for a slow-wave Rogowski coil

The author proposes the construction of a slow-wave Rogowski coil wound by using a novel type of three-layered wire that is formed by placing a flexible dielectric strip between two conducting strips. This structure results in a distributed capacitance along the wire. The construction of a slow-wave Rogowski coil can then be easily achieved by directly winding this kind of wire on a toroid with either rectangular or circular cross sections. The construction is then as simple as that for a conventional self-integrating Rogowski coil. Design and experimental results are presented. >