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Pair Rogowski coils, rejustors to measure current

Posted: 17 Mar 2007 ?? ?Print Version ?Bookmark and Share

Keywords:Rogowski coils? current measurement? rejustor? adjustable resistors? amplifier?

By Gennadiy Frolov, Oleg Grudin and Tim Warland
Microbridge Technologies Inc.

Rogowski coils 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 unit. 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.

A family of nonvolatile, adjustable resistors from Microbridge Technologies, rejustors provide a passive compensation solution for Rogowski coils, letting coil manufacturers produce devices with uniform performance. This increases interchangeability while reducing manufacturing complexity.

Rejustor compensation is useful in applications in which 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 percent tolerance. Rejustors improve the accuracy to better than 0.5 percent.

Rejustors are precision-adjustable resistors with resistance that can be set to 0.1 percent precision or better. After adjustment, they maintain their set resistance indefinitely, with no external memory or standby power requirements. The resistance is set using electrical signals from a rejustor calibration tool. This means the complete assembly can be manufactured and encapsulated before calibration, which improves the 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 in which 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 5kW. Therefore, a buffer isn?t required to add a rejustor.

? Rejustors are tiny devices with negligible real-estate impact relative to the size of the coil.

? Both devices are insensitive to temperature change. The TCR for a standard rejustor is less than 100ppm/K.

Design factors
Because of process variations, the sensitivity of the Rogowski coil is typically manufactured with an electrical tolerance of 5 percent, while the target accuracy after calibration may be an order of magnitude better, around 0.5 percent.

For example, consider a Rogowski coil designed to measure a 60Hz, 1,000A current passing through a conductor. Initial sensitivity of the sensor is measured at 30?V/A 5 percent; expected target sensitivity is 24.75?V/A 0.5 percent.

The use of the MBD-472-CL rejustor with Rj1 = 1kW and Rj2 = 5kW (see Figure 1a), provides sufficient adjustment range to compensate for 5 percent coil variation and still meet the output-voltage specification for the system (24.75?V/A 0.5 percent) without affecting amplifier sensitivity or temperature behavior.

The 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.

Sample application
The simplified diagram (Figure 1b), shows a Rogowski coil with an onboard rejustor attenuator, Rj1/Rj2.

For a final Rogowski coil accuracy of 0.5 percent, the measurements during calibration have to provide accuracy of about 0.1 percent. The use of 2A, 60Hz excitation current will create nearly a 50?V output signal, measured with resolution of 50nV.

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 900Hz instead of 60Hz will increase output signal by a factor of 15. In this case, the required resolution of 750nV will be above noise level.

Figure 1: A Rejustor-calibrated Rogowski coil connected to an amplifier and integrator (a) and a Rogowski coil with an onboard rejustor attenuator, Rj1/Rj2 (b).

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 bandpass) filter, is placed close to the coil and allows use of an inexpensive voltmeter or DAQ 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 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 1a), 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 2-3s.

Calibration process
Figure 2
shows the Rogowski coil calibration process.

(Click to view 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 the output DC signal will be changed X times in comparison with the DC signal before adjustment. The last step is to verify if the new sensitivity is within 0.5 percent of target. If necessary, repeat the adjustment.

Note that all DC measurements are ratiometric; 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
The Rogowski coil is an electrical device for noninvasive monitoring and measuring of AC or high-speed current pulses through a conductor. The coil is wrapped around a conductor to be measured, with changes in current inducing an electrical field in the coil. The coil detects a voltage signal (electromotive force or 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 to provide an output signal that is proportional to current in the primary conductor.

From Faraday?s law of induction, the EMF (which represents the output signal of the 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 an N-turn rectangular Rogowski coil is shown by EMF = (?NL/2) ln(c/b) di(t)/dt

where L, b and c are the height, inner diameter 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 on a PCB, performance is dependent on the thickness of the board layers.

About the authors
Gennadiy Frolov
is co-founder and senior member of technical staff of Microbridge Technologies Inc. Oleg Grudin is co-founder and VP of engineering, while Tim Warland is applications engineer, both at Microbridge.

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