Zahra Pourmoghian A Rogowski coil is a current measurement transformer used to measure alternating current. Without integration, the output of the coil is a voltage signal proportional to the rate of change of the current being measured. Because it involves an integration of the current over time, this voltage signal is generally distorted and non-sinusoidal.

The phase difference between the primary and secondary of the Rogowski coil is 90 degrees, which implies that the voltage signal on the secondary is 90 degrees out of phase with the current on the primary. Because the current being measured is not always a perfect sine wave, the secondary voltage is not entirely sinusoidal. The current might be warped as a result of harmonics or other power disturbances.

The output of the coil is often integrated using a circuit called as an integrator to provide an accurate representation of the current. This circuit is used to average the coil output over time and provide a voltage signal proportionate to the current. The coil's output will be a smooth, sinusoidal signal that correctly depicts the current being measured after integration.

Hello Zahra Pourmoghian ,

Have you looked at the Wikipedia page for Rogowski coils: https://en.wikipedia.org/wiki/Rogowski_coil ? Rogowski coils are torodially-wound, air core, coils, also called I dot (İ) sensors because their output is proportional to the derivative with respect to time of the primary winding current, hence, to get I(t) you need to integrate İ(t). Note, the "primary winding" is usually a single conductor or busbar.

From the last sentence of your question, it appears that the primary winding's current is sinusoidal. Is that true? If, yes, can you tell us the frequency?

The distortion you are seeing could be caused by a number of things: 1) the primary current might be driving a nonlinear load; 2) the source of the primary current might be a transformer operating near the saturation point of its ferrous core; 3) primary current might be a transient current measured a short time after the transformer is switched on, as this transient current may have a DC component superimposed on it; 4) if you are using an integrator, the distortion may be caused by losses in the integrator; etc.

Regards,

Tom Cuff

Hello @Thomas Cuff

I have built several Rogowski rigid coil models with air cores. I will post a picture of one of them. The primary current is 500 A, sinusoidal with a frequency of 50 Hz.

I sampled the primary current: using a series shunt resistor in the path (yellow waveform). According to the primary waveform, which is without distortion then apparently there is no problem on the primary current side.

But the output waveform of the Rogowski coil is distorted. Please give your opinion.

https://fastupload.io/PGjVA19db7kPMQL/file

Thanks for your time.

Hello Zahra Pourmoghian ,

Sorry, it took so long to get back to you, but I don't remember seeing any notification that you mentioned my name in your post. Would you please open your link, https://fastupload.io/PGjVA19db7kPMQL/file, in the answer window.

Regards,

Tom Cuff

Hello Thomas Cuff

I have built several Rogowski rigid coil models with air cores. I will post a picture of one of them. The primary current is 500 A, sinusoidal with a frequency of 50 Hz.

I sampled the primary current: using a series shunt resistor in the path (yellow waveform). According to the primary waveform, which is without distortion then apparently there is no problem on the primary current side.

But the output waveform of the Rogowski coil is distorted. Please give your opinion

thanks

Dear Zahra Pourmoghian, maybe the distortions are due to the fact that the coil diameter is not small when compared to the toroid radius.

Hello Paulo Edmundo Fonseca Freire , Thomas Cuff

I have made several models of rigid Rogowski coils with various diameters. I leave the result of making another sample.

I will be happy to solve the distortion problem in the coil with your opinion and experience.

Thanks

Hello Zahra Pourmoghian and Paulo Edmundo Fonseca Freire ,

Here is my best explanation for what you are seeing. When you measure the primary current with a current viewing resistor, the voltage signal on your oscilloscope (the white curve) is proportional to the current, I(t). When you measure the primary current with your Rogowski coil, the voltage signal signal on your oscilloscope (the blue curve) is proportional to the derivative of the current, dI(t)/dt. The dI(t)/dt waveform has larger high frequency components than the I(t) waveform. Note, it is not that these high frequency components are missing from the I(t) waveform - if you increase the vertical sensitivity of the channel with the I(t) waveform enough, you will see the non-smooth changes - it is that the differentiation process accentuates these non-smooth changes so that you can more easily see them.

Of course, your next question is going to be why are there non-smooth changes in I(t), the current through the primary of the iron-core transformer? The answer is Barkhausen jumps [1-3], also sometimes called Barkhausen radiation or Barkhausen effect, which was discovered in 1919. The magnetization and demagnetization of iron takes place in discontinuous jumps as domain walls move. These changes were heard by Barkhausen when he monitored the magnetization with an audio amplifier and headphones.

[1] E. U. Condon, Hugh Odishaw (editors); Handbook of Physics, Second Edition; McGraw-Hill, Inc.; 1967; p. 4-140.

[2] Richard Milton Bozorth; Magnetism; in Anonymous; Encyclopedia Britannica, Volume 14, Libid-Mary; William Benton; 1964; p. 645 - Section 7 - Barkhausen Effect.

[3] Frederick Seitz; The Modern Theory of Solids; McGraw-Hill Book Company, Inc.; 1940; p. 21 [Note, the Subject Index section of this book erroneously claims the "Barkhausen effect" is on p. 25, while the Name Index section correctly indicates that "Barkhausen, H." is on p. 21. Footnote #1 on p. 21 provides the following citation:

H. Barkhausen; Zwei mit Hilfe der neuen Verstarker entdeckte Erscheinungen {Two discovered phenomena with help of new amplifiers}; Physikalische Zeitschrift; Vol. 20; No. 17; 1 September 1919; pp. 401-403.]

Regards,

Tom Cuff

Hello Thomas Cuff

The Rogowski coil is made with an air core (Rubber). But you explained about the Barkhausen effect in the iron core. Do you have experience in making Rogowski coils? Do you know how much distortion a Rogowski coil secondary can have? Do you know the reason for the distortion in the air core?

Thank you for continuing to help me with this problem.

Zahra Pourmoghian

Hello Zahra Pourmoghian ,

I understand that the Rogowski coil is an air-core coil or dielelctric-core coil, but from the photograph of your experimental setup, it appears as if the busbars, around which you have arranged the Rogowski coil, are coming from the iron-core [core made from laminated sheets of cold-reduced, grain-oriented silicon steel, chemically treated to electrically insulate each sheet to reduce eddy current losses] transformer inside the large, gray box (EQ14-6?) in the background; the multichannel Tektronix (?) digital oscilloscope is in the foreground, on a stool, with one channel attached to the current viewing resistor and the other channel attached to the Rogowski coil by 10X probes (?). I am assuming that the 500 A current at 50 Hz, which you mentioned, was feeding the primary winding of this iron-core transformer, and is the magnetization current (+ extra current for whatever load (?) might be attached to the secondary winding of the transformer) for this iron-core transformer. It is this current which will be contaminated by the Barkhausen noise depending on the exact details of the iron-core hysteresis curve. I am only going by your photograph and your brief textual description. If I am incorrect about my understanding of your setup, I apologize.

Good luck with your project,

Tom Cuff

Hello Zahra Pourmoghian ,

Sorry to bother you, again, but I think I finally understand your experimental setup. On the table directly behind the transformer, EQ14-6, there are three gray, cylindrical objects, each with a large black knob on their top and each with an LED display on their side. I believe these are some type of Variac providing excitation to the three primary windings of your transformer, one for each phase, I think. The two braided busbars coming out of the sides of the transformer, EQ14-6, are connected to the secondary winding of the transformer. I believe this transformer, EQ14-6, is a stepdown transformer providing a single phase, high current, 500 A, at a very low voltage. The two braided busbars appear to be connected to a load resistance on the wooden pallets in the foreground. The right busbar is connected to a thick copper cylinder which passes through the center of your Rogowski coil, and is connected via 10X (?) probe to one channel of your GPS Limited model 1000 (?) Digital Storage Oscilloscope. The left busbar connects to 7 or 8 (?) thin copper cylinders, which are the load and connect to the thick copper cylinder coming in from the right; the other channel of your oscilloscope is connected across this load resistor, via another 10X (?) probe, and serves as your current viewing resistor.

I believe the distortion on the dI(t)/dt signal from the Rogowski coil is a genuine effect - not a measurement artifact. The distortion could be due to how the hysteresis curve of the steel core of the transformer, EQ14-6, is being traversed, it could also be due to some nonlinearity in the load resistor due to heating or some other effect, and/or may be even a manifiestation of the Barkhausen noise, etc.

Sorry it took me so long to, I hope, understand your experimental setup, but I needed to find a large screenTV on which to view your photograph.

Regards,

Tom Cuff

Hi Zahra Pourmoghian ,

I finally know where the nonlinearities are in your system: the mechanical junctions in the circuit connected to the secondary winding of transformer EQ14-6. Copper oxidizes, on its outer surface at room temperature, forming crude copper oxide rectifiers, which have a nonlinear I-V curve, especially at low voltage differences. I don't, of course, know what the exact value is of the peak open-circuit voltage difference across the secondary winding of transformer EQ14-6, but it must be fairly low to allow you to drape the braided busbars over the floor without them being an electrical hazard. I can see that many of the mechanical junctions are made with multiple bolts and thick endplates, but no mechanical junction is perfect, electrically speaking. Your dI(t)/dt signal is simply recording this fact.

Every thing I needed was in the photograph of your experimental setup, but I just needed to look at it more closely. Sorry, for taking so long. Also, I apologize for mentioning the Barkhausen effect, which is real, but much smaller than the electrical effect of imperfect mechanical junctions. Thanks for an interesting question.

Regards,

Tom Cuff