Rogowski coils (see Sidebar and References 1 and 2 at end) perform passive current measurement and are used in test and measurement devices and power-monitoring activities. Calibration is required to account for manufacturing variations in the coil, and to provide uniform device-to-device sensitivity.
The accuracy of mass-produced coils is compromised by manufacturing tolerances. The challenge for vendors is to find a method to calibrate each coil to produce uniform output voltage and signal sensitivity. Designers traditionally configure their systems with an amplifier and integrator calibrated to match the properties of the coil.
Using this configuration, the entire assembly (coil, integrator and amplifier) must be treated as a single, field-replaceable assembly. For example, current probes are sold as a coil with integrated electronics. With this configuration, users can't replace the coil without also replacing the active electronics, or vice versa.
Rejustors, which are a family of non-volatile, adjustable resistors from Microbridge Technologies (Montreal, Canada) provide a passive compensation solution for Rogowski coils, enabling coil manufacturers to produce devices with uniform performance; thus increasing interchangeability while reducing manufacturing complexity.
Rejustor compensation is useful in applications where an all-passive system is required, for example, on a power line where no dc-power is available, or to allow current-probe manufacturers to sell replacement coils without the integrated amplifier. The coil used in this design is manufactured with 5% tolerance. Rejustors improve the accuracy to better than 0.5%.
Rejustors are precision adjustable resistors with resistance can be set to 0.1% precision or better. After adjustment, they maintain their set resistance indefinitely, with no external memory or stand-by power requirements. The resistance is set using electrical signals from a Rejustor Calibration Tool. This means the complete assembly can be manufactured and encapsulated prior to calibration, which improves manufacturability and accuracy of the system.
There are several good reasons to consider a Rejustor with the Rogowski coil:
- Both Rejustors and Rogowski coils are passive devices. This is important for field applications where a current sensor is supposed to consume no power.
- Both are high-bandwidth devices. This is key for applications where monitoring current waveforms is required.
- Both are low-cost devices.
- Rogowski coils are low-impedance devices (typically tens of ohms) while Rejustors are manufactured with much higher resistance, starting at around 5 kΩ. Therefore, adding Rejustors to the coil doesn't require a buffer.
- Rejustors are tiny devices having negligible real-estate impact relative to the size of the coil.
- Both devices are insensitve to temperature change. The temperature coefficient of resistance (TCR) for a standard Rejustor is less than 100 ppm/K.
Design considerations
Due to process variations, the sensitivity of the Rogowski coil is typically manufactured with an electrical tolerance of 5% while the target accuracy after calibration may be an order-of-magnitude better, around 0.5%.
For example, consider a Rogowski coil designed to measure 60 Hz, 1000 A current passing through a conductor. Initial sensitivity of the sensor is measured at 30 μV/A ±5%; expected target sensitivity is 24.75 μV/A ±0.5%.
The use of the MBD-472-CL Rejustor with Rj1 =1 kΩ and Rj2 = 5 kΩ, Figure 1, provides sufficient adjustment range to compensate for ±5% coil variation, and still meet the output-voltage specification for the system (24.75 μV/A ±0.5%) without impacting amplifier sensitivity or temperature behavior.
Figure 1: Simplified diagram of Rejustor-calibrated Rogowski coil connected to amplifier and integrator
(Click to enlarge image)
This diagram shows Rs connected in series with the AC sensor source, representing the coil and the resistance of the wire (copper, for example) that was used to build the coil. An integrator (analog or digital) is added to make the output signal Vout proportional to the current (instead of proportional to the time-derivative of the current), thus making the output frequency-independent.
Calibration challenge
The simplified diagram, Figure 2, shows a Rogowski coil with an on-board Rejustor-attenuator Rj1/Rj2 onboard.
Figure 2: Calibration setup using reference signal
(Click to enlarge image)
For a final Rogowski coil accuracy of 0.5%, the measurements during calibration have to provide accuracy of about 0.1%. The use of 2 A, 60 Hz excitation current will create nearly a 50 μV output signal, measured with resolution of 50 nV. Even though the Rejustor has the lowest noise of any adjustable resistor technology, the combination of thermal noise in the resistor and amplifier noise in the measurement equipment challenges the ability to make this measurement.
By increasing the frequency of the input signal, the output voltage increases proportionally. Using 900 Hz instead of 60 Hz will increase output signal by a factor of 15. In this case, the required resolution of 750 nV will be above noise level.
Calibration uses a high-quality reference Rogowski coil with accurately-known sensitivity. The reference coil reduces calibration requirements (tolerance) for the whole chain of equipment. A simple, low-noise, ac amplifier, preferably with differential output and a low-pass (or band-pass) filter, is placed close to the coil, and allows use of an inexpensive voltmeter or data acquisition board. It also protects small signals from EMI. If an ac amplifier is used, it is important to make sure that the gain bandwidth product (GBW) doesn't distort the signal.
Rejustor adjustment is performed with Rejustor Calibration Tools from the vendor. An adaptive, successive"approximation process consists of a series of voltage pulses (30 to 60) applied to pins "trim1" and "trim2" (Figure 1) including output-signal measurement after each pulse. The entire process to set the resistance of the Rejustors to match the requirements of the coil is complete in two to three seconds.
Calibration Process
The flowchart of Figure 3 illustrates the Rogowski-coil calibration process.
Figure 3: Calibration process flow chart
(Click to enlarge image)
The first step is performing the ac measurements. The goal is to determine the Target Ratio "X", which is the ratio between sensitivity of the coil under test and the target sensitivity.
The second step is the adjustment itself. Applying a dc signal, the user adjusts one of two Rejustors until output dc signal will be changed X times in comparison with dc signal before adjustment. The last step is to verify if the new sensitivity is within 0.5% of target. If necessary, repeat adjustment.
Note that all dc-measurements are ratiometric, and therefore there are no strict requirements for Vref and buffer/amplifier gain. In fact, the only requirement is that these devices must not drift during a single adjustment session (which usually takes a few seconds).
Sidebar: Rogowski coil theory of operation
The Rogowski coil is an electrical device for non-invasive monitoring and measuring of alternating-current (ac) or high-speed current pulses through a conductor. The coil is wrapped around a conductor to be measured, where changing currents induce an electrical field in the coil. The coil detects voltage signal (EMF) proportional to the change in the current passing through this wire.
The Rogowski coil can be made open-ended and flexible, allowing it to be wrapped around a live conductor without disturbing it. Unlike conventional iron-core transformers, the transformer in a Rogowski coil uses an air core, which provides low impedance along with no danger of saturating the core.
The voltage induced in the coil is proportional to the rate of change (derivative) of current in the conductor. The output is connected to an integrator and amplifier in order to provide an output signal that is proportional to current in the primary conductor. Figure SB-1 provides a simplified block diagram of a system using a Rogowski coil to measure changes in current and convert it to a representative voltage output.
Figure SB-1: Simplified diagram of Rogowski coil connected to an amplifier and integrator.
(Click to enlarge image)
The cross section of a Rogowski coil is shown in Figure SB-2.
Figure SB-2: Inside a Rogowski coil
(Click to enlarge image)
From Faraday's law of induction, thet EMF (which represents the output signal of Rogowski current sensor) induced in this coil is proportional to the derivative of the current, the number of turns in the coil, and their area. The exact equation for output signal of N-turn rectangular Rogowski coil is shown by Equation 1:
(Reference 3) where L, b and c are height, inner and outer diameter of the coil, respectively. Producing precision Rogowski coils depends on the ability to control the physical dimensions of the device. When the coil is manufactured in a printed circuit board (PCB), performance is dependant on the thickness of the PCB layers.
References
1. "Rogowski coils," David Ward, Rocoil Limited, http://homepage.ntlworld.com/rocoil/Pr9.pdf
2. "Rogowski coil," (Wikipedia), http://en.wikipedia.org/wiki/Rogowski_coil
3. "Current sensing for energy metering", William Koon, Analog Device, Inc.
About the authors
Oleg Grudin is a co-founder of Microbridge Technologies, Montreal, Canada, and the Vice President of Engineering. Oleg has Over 20 years experience in advanced technological R&D in Russia and Ukraine. Over 15 years R&D and Entrepreneurial experience in micro-thermal devices. Oleg earned a Ph.D. at the Moscow Institute of Physics and Technology and is a member of the IEEE.
Gennadiy (Gena) Frolov is a co-founder of Microbridge and a senior member of technical staff. He earned a Masters degree in electronics from Kiev Polytechnic State University (Ukraine). He has 20 years of hands-on experience in electronics and sensor applications, and is a co-author of numerous technical publications including Rejustor-related patents.
Tim Warland is an application engineer responsible for customer support and product marketing at Microbridge. He holds a bachelor's degree in electrical engineering from Carleton University and an MBA from the University of Ottawa.
