# Energy loss by Hysteresis

I recently did an experiment aiming to verify the magnetization curve of the cores of a single-phase electrical transformer. I applied a sine within one core and I observed this one and the other one responses over the time. The circuit builded for the experiment and the output of this, that is a snapshot from the oscilloscope that I've used to make the measures, we can see at the images below.

I then exported the graphics raw data into CSV files to manipulate it with some computer software, like Matlab or Excel. I mixed the data from both graphs in a manner that I could plot one as being the X-axis (1st CSV column) and the other being the Y-axis (2nd CSV column), and indeed it worked with Matlab. With the data organized I executed the following within Matlab:

Array=csvread('F:\workspace\Matlab\XY.csv');
r1 = Array(:, 1);
r2 = Array(:, 2);
plot(r1,r2);


The result is the transformer hysteresis graph as expected and showed bellow, and we can see a lot of noise within the signal.

Finally, I could calculate the area from the graph through:

trapz(r1,r2);


The obtained result is 4.3768e+09, analyzing the data I would say that, if the X and Y axis was expressed in terms of Volts units, the resulting area would be 0.43768.

## My doubt is:

I know that the encountered area represents somehow the energy loss within the transformer core, but... How do I express it in terms of energy? Is the encountered result (0,43768) expressed in [N/m^2]?

• Is the yellow trace actually the output voltage or the input current? – Andy aka Oct 31 '18 at 12:57
• @Andyaka The yellow is the output one. As we can see this delay and wrong shape are the energy loss. And by what I know, this is exactly what the hysteresis graph shows us. – Gabriel Magri Oct 31 '18 at 15:39
• The thing is, with a transformer, I wouldn't expect to see signs of saturation on the output voltage given that the primary is connected to a voltage sine wave. If the input signal were a current sine wave then yes, this would look more like what you see. I am confused by this. – Andy aka Oct 31 '18 at 16:08
• @Andyaka Sorry, I made a mistake. The yellow signal is the input indeed. I updated the question with an image of the circuit used to make the experiment, on it we can see the points where I made the measures. Thanks. – Gabriel Magri Oct 31 '18 at 21:30