A Rogowski coil is an electrical transducer used for measuring AC currents such as high-speed transients, pulsed currents of a power device, or power line sinusoidal currents at 50 or 60 Hz. The Rogowski coil has a flexible clip-around sensor coil that can easily be wrapped around the current-carrying conductor for measurement and can measure up to a couple thousand amperes of very large currents without an increase in transducer size.
 

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How does a Rogowski coil work?

The theory of operation behind the Rogowski coil is based on Faraday’s Law which states that the total electromotive force induced in a closed circuit is proportional to the time rate of change of the total magnetic flux linking the circuit.

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The Rogowski coil is similar to an AC current transformer in that a voltage is induced into a secondary coil that is proportional to the current flow through an isolated conductor. The key difference is that the Rogowski coil has an air core as opposed to the current transformer, which relies on a high-permeability steel core to magnetically couple with a secondary winding. The air core design has a lower insertion impedance, which enables a faster signal response and a very linear signal voltage.

An air-cored coil is placed around the current-carrying conductor in a toroidal fashion and the magnetic field produced by the AC current induces a voltage in the coil. The Rogowski coil produces a voltage that is proportional to the rate of change (derivative) of the current enclosed by the coil-loop. The coil voltage is then integrated in order for the probe to provide an output voltage that is proportional to the input current signal.



Advantages

Rogowski coil current probes offer many advantages over different types of current transducers or sensing techniques.

• Large current measurement without core saturation --

  Rogowski coils have the capability to measure large currents (a very wide range from a few mA to more than a few hundred kA) without saturating the core because the probe employs non-magnetic “air” core. The upper range of the measurable current is limited by either the maximum input voltage of a measuring instrument or by the voltage breakdown limits of the coil or the integrator circuit elements. Unlike other current transducers, which get bulkier and heavier as the measurable current range grows, the Rogowski coil remains the same small size coil independent of the amplitude of current being measured. This makes the Rogowski coil the most effective measurement tool for making several hundreds or even thousands of amperes of large AC current measurements.

 

• Very flexible to use --

  The lightweight clip-around sensor coil is flexible and easy to wrap around a current-carrying conductor. It can easily be inserted into hard-to-reach components in the circuit. Most

  Rogowski coils are thin enough to fit between the legs of a T0-220 or TO-247 power semiconductor package without needing an additional loop of wire to connect the current probe. This also gives an advantage in achieving high signal integrity measurement.

• Wide bandwidth up to >30 MHz --

  This enables the Rogowski coil to measure the very rapidly changing current signal – e.g., several thousand A/usec.

  High bandwidth characteristic allows for analyzing high-order harmonics in systems operating at high switching frequencies, or accurately monitoring switching waveforms with rapid rise- or fall-times.

• Non-

  intrusive or lossless measurement -- The Rogowski coil draws extremely little current from the DUT because of low insertion impedance. The impedance injected into the DUT due to the probe is only a few pico-Henries, which enables a faster signal response and very linear signal voltage.

• Low cost

  Compared to a hall effect sensor/transformer current probe, the Rogowski coil typically comes in at lower price point.

 

Limitations

• AC only -- Rogowski cannot handle DC current. It is AC only.
• Sensitivity - Rogowski coil has a lower sensitivity compared to a current transformer due to the absence of a high permeability magnetic core.

 

Applications

Rogowski coil current probes have a large number of applications in broad power industries and power measurement applications. The following are some examples of Rogowski coil applications:

• Flexible current measurement of power devices such as MOSFET or IGBT device as small as TO-220 or TO-247 package or around the terminals of large power modules

• To measure power losses in power semiconductors

• To monitor currents in small inductors, capacitors, snubber circuits, etc.

• To measure small AC current on a conductor with high DC current or in the presence of a high DC magnetic field.

• To measure high frequency sinusoidal, pulsed, or transient currents from power line frequency to RF applications

• To measure current in motor drives and, in particular, power quality measurements in VSD, UPS or SMPS circuits

• To evaluate switching performance of power semiconductor switches (double pulse tester).

• Power distribution line monitoring or utilities pole probe monitoring

• Smart grid applications

• Plasma current measurement

Conclusion

There are a number of different ways of measuring electric current where each method has advantages and limitations.

The Rogowski coil is similar to an AC current transformer in that a voltage is induced into a secondary coil that is proportional to the current flow through an isolated conductor. However, Rogowski coils have the capability to measure large currents (very wide range from a few mA to more than a few kA) without saturation because of its non-magnetic “air” core. The air core design also has a lower insertion impedance to enable a faster signal response and a very linear signal voltage and is very cost effective compared to its hall effect sensor/current transformer counterpart. This makes the Rogowski coil the most effective measurement tool to make several hundreds or thousands of amperes of large AC current measurement.

Device for measuring alternating current

A Rogowski coil is a toroid of wire used to measure an alternating current

I(t)

through a cable encircled by the toroid. The picture shows a Rogowski coil encircling a current-carrying cable. The output of the coil,

v(t)

, is connected to a lossy integrator circuit to obtain a voltage

Vout(t)

that is proportional to

I(t)

.

A Rogowski coil, named after Walter Rogowski, is an electrical device for measuring alternating current (AC) or high-speed current pulses. It sometimes consists of a helical coil of wire with the lead from one end returning through the centre of the coil to the other end so that both terminals are at the same end of the coil. This approach is sometimes referred to as a counter-wound Rogowski.

Other approaches use a full toroid geometry that has the advantage of a central excitation not exciting standing waves in the coil. The whole assembly is then wrapped around the straight conductor whose current is to be measured. There is no metal (iron) core. The winding density, the diameter of the coil and the rigidity of the winding are critical for preserving immunity to external fields and low sensitivity to the positioning of the measured conductor.[1][2][3]

Since the voltage that is induced in the coil is proportional to the rate of change (derivative) of current in the straight conductor, the output of the Rogowski coil is usually connected to an electrical (or electronic) integrator circuit to provide an output signal that is proportional to the current. Single-chip signal processors with built-in analog to digital converters are often used for this purpose.[2] It can also be made "self integrating" (e.g., no external circuit) by placing a low inductance resistor in parallel with the output.[1] This approach also makes the sensing circuit more noise immune.

Advantages

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This type of coil has advantages over other types of current transformers.

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• It is not a closed loop, because the second terminal is passed back through the center of the toroid core (commonly a plastic or rubber tube) and connected along the first terminal. This allows the coil to be open-ended and flexible, allowing it to be wrapped around a live conductor without disturbing it. However, positioning of the measured conductor is important in that case: It has been shown that, with flexible sensors, the effect of the position on the accuracy ranges from 1 to 3%. Another technique uses two rigid winding halves with a precise locking mechanism.[3]
• Due to its low inductance, it can respond to fast-changing currents, down to several nanoseconds.[4]
• Because it has no iron core to saturate, it is highly linear even when subjected to large currents, such as those used in electric power transmission, welding, or pulsed power applications.[4] This linearity also enables a high-current Rogowski coil to be calibrated using much smaller reference currents.[2]
• No danger of opening the secondary winding.[4]
• Lower construction costs.[4]
• Temperature compensation is simple.[2]
• For larger currents conventional current transformers require an increase of the number of secondary turns, in order to keep the output current constant. Therefore, a Rogowski coil for large current is smaller than an equivalent rating current transformer.[5]

Disadvantages

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This type of coil also has some disadvantages over other types of current transformers.

• The output of the coil must be passed through an integrator circuit to obtain the current waveform. The integrator circuit requires power, typically 3 to 24Vdc, and many commercial sensors obtain this from batteries.[6]
• Traditional split-core current transformers do not require integrator circuits. The integrator is lossy, so the Rogowski coil does not have a response down to DC; neither does a conventional current transformer (see Néel effect coils for DC). However, they can measure very slow changing currents with frequency components down to 1 Hz and less.[3]
• Constant DC current cannot be measured. The Rogowski coil samples the field, generating a voltage as the field changes.[7]

Applications

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Rogowski coils are used for current monitoring in precision welding systems, arc melting furnaces, or electromagnetic launchers. They are also used in short-circuit testing of electric generators and as sensors in protection systems of electrical plants. Another field of usage is the measurement of harmonic current content, due to their high linearity.[6] Also for lightning research.

Formulae

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Example waveform of RC output for switched-mode load. As explained above, the output waveform CH4 (green) represents the derivative of the current waveform CH2 (blue); CH1 (yellow) is 230 V AC mains waveform

The voltage produced by a Rogowski coil is

v ( t ) = − A N μ 0 l d I ( t ) d t , {\displaystyle v(t)={\frac {-AN\mu _{0}}{l}}{\frac {dI(t)}{dt}},}

where

• A = π r 2 {\displaystyle A=\pi r^{2}}

• N {\displaystyle N}

• l = 2 π R {\displaystyle l=2\pi R}

• d I ( t ) d t {\displaystyle {\frac {dI(t)}{dt}}}

• μ 0 = 4 π × 10 − 7 {\displaystyle \mu _{0}=4\pi \times 10^{-7}}

  V·s/(A·m) is the magnetic constant,

• R {\displaystyle R}

• r {\displaystyle r}

This formula assumes the turns are evenly spaced and that these turns are small relative to the radius of the coil itself.

The output of the Rogowski coil is proportional to the derivative of the wire current. The output is often integrated so the output is proportional to the wire's current:

V out = ∫ v d t = − A N μ 0 l I ( t ) + C integration . {\displaystyle V_{\text{out}}=\int v\,dt={\frac {-AN\mu _{0}}{l}}I(t)+C_{\text{integration}}.}

In practice, an instrument will use a lossy integrator with a time constant much less than the lowest frequency of interest. The lossy integrator will reduce the effects of offset voltages and set the constant of integration to zero.

At high frequencies, the Rogowski coil's inductance will decrease its output.

The inductance of a toroid is[8]

L = μ 0 N 2 ( R − R 2 − r 2 ) . {\displaystyle L=\mu _{0}N^{2}\left(R-{\sqrt {R^{2}-r^{2}}}\right).}

Similar devices

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A device similar to the Rogowski coil was described by Arthur Prince Chattock of Bristol University in 1887.[9] Chattock used it to measure magnetic fields rather than currents. The definitive description was given by Walter Rogowski and W. Steinhaus in 1912.[10]

More recently, low-cost current sensors based on the principle of a Rogowski coil have been developed.[11] These sensors share the principles of a Rogowski coil, measuring the rate of change of current using a transformer with no magnetic core. The difference from the traditional Rogowski coil is that the sensor can be manufactured using a planar coil rather than a toroidal coil. In order to reject the influence of conductors outside the sensor's measurement region, these planar Rogowski current sensors use a concentric coil geometry instead of a toroidal geometry to limit the response to external fields. The main advantage of the planar Rogowski current sensor is that the coil winding precision that is a requirement for accuracy can be achieved using low-cost printed circuit board manufacturing.

See also

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References

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