Chapter 9.4.1: Measurement of B-H characteristic
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- čas přidán 5. 09. 2024
- MIT Electromagnetic Fields and Energy, Textbook Components with Video Demonstrations
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Instructor: Markus Zahn, James R. Melcher, Manuel L. Silva
License: Creative Commons BY-NC-SA
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Transcription:
Measurement of the B-H characteristic of a magnetizable core provides the constitutive law that relates the magnetization density M, or equivalently the magnetic flux density B, to the macroscopic magnetic field intensity H within a material.
The objective here is to observe the establishment of H - by an imposed current in accordance with Ampere’s law (relates the integrated magnetic field around a closed loop to the electric current passing through the loop) - and to deduce B from the voltage it induces in accordance with Faraday's law (a magnetic field will induce a current in a circuit - electromagnetic induction. (or Maxwell-Faraday equation where a spacially varying (“or possibly time-varying”) electric field accomplanies a time-varying magnetic field)).
A toroidal coil is tightly wound onto a doughnut shaped magnetizable core. Each turn carries a current I.
For this geometry, ampere’s integral law is enough to relate the current I to the H field in the magnetizable core material. Symmetry about the toroidal axis suggests that H is Phi directed. amperes integral law is written for contour C circulating about the toroidal axis within the core.
Because the major radius R of the torus is large compared to the minor radius, the field is essentially uniform over the cross section of the torus. We approximate the average radius by the radius R, thus the line integral of H is essentially 2 π R · H.
To evaluate the right-hand side of amperes law we see that the surface S spanned by this contour C is pierced by the current I as many times as there are turns N1. So the surface integral of J is n I thus amperes law reduces to the product of h phi in the contour circumference 2 π R, equaling N1 i.
Hϕ 2 π R = N1 i
Here is the excitation winding. the current is supplied by this variac (variac = generic trade name for a variable autotransformer).
The voltage drop across the small resistance, in series with the driving winding, is used to record the driving current I. This voltage drives the horizontal axis of the oscilloscope. Because the H field is proportional to current, the horizontal scope deflection is therefore proportional to the magnetic field intensity H in the core material.
The magnetic flux density M is measured by means of a secondary coil, also wound on the doughnut shaped core. This coil is terminated in a high enough impedance that it carries a negligible current, thus the H field established by the current I of the excitation winding is unchanged.
The flux Φ linked by each turn of the sensing coil is essentially the flux density B multiplied by the cross-sectional area of the core. The flux Φ linked by the N_2 turn coil is then N_2 times the flux linked by each turn. An RC integrating network on this secondary coil integrates the terminal voltage V so that the flux linking the coil is recorded. The circuit acts as an integrator because, at the frequency of operation (60 Hz), the capacitor C has a reactance that is much smaller than the series resistance (Reactance is the opposition of a circuit element to the flow of current, aka lower reactance leads to greater currents for a the same applied voltage).
With the capacitor essentially a short-circuit, the current is approximately v2/R2. From Faraday's law, the terminal voltage of the sensing coil is the time rate of change of the magnetic flux linking the coil. This current then charges the capacitor.
By comparing these last two equations we can see that the voltage V across the capacitor is proportional to the magnetic flux Φ linking the sensing coil V ~ 1/RC · Φ .
Thus, by connecting the terminals of the sensing coil through the integrator to vertical trace of the oscilloscope we make the vertical axis proportional to B. So, we should see a display of B versus H on the oscilloscope.
Here is the experiment. The magnetizable material is in this doughnut shape toroid. The excitation of primary coil connected to these terminals is driven by the current at 60 Hertz from this variac.
The voltage across this series, 1 ohm resistance, then gives a horizontal deflection of the oscilloscope proportional to I, and thus H. The terminals of the sensing coil are connected through the integrating network with resistance 100 kohm in capacitors mF to the vertical deflection terminals of the oscilloscope, thus the vertical deflection is proportional to the integral of the terminal voltage, the flux lambda and hence the B.
We turn up the very AC current. The scope shows the B-H hysteresis loop typical of a magnetically soft material.
Nice, helpful video. It gets me closer to understanding the temporal behavior of magnetic materials. I will have to watch it a few more times to absorb and fully understand. Thank you for uploading this. Even though it is an old video with very old technology, it drives the point home.
I'm using this setup to mesure the hysteresis of a set of large laminated 'E' transformer core pieces. I do not understand how to find what values the componets I am supposed to use.
Both primary and secondary coils are the same number of turns but the count isnt known. Im using 120-130v 60hz ac.
I have a digital scope if that makes any difference.
very informative video, thanks
I have one question though........
how can we measure "H" from calculated "B" manually using BH curve diagram of electric steel....?
What is J? Current?
J is current density ( J = I/A), where I is current and A is cross sectional area through which current flows. Hope that helps