Research website of Vyacheslav Gorchilin
2023-06-05
Finding Coefficients for the Stoletov Curve
Stand RI, Ohm U, B Um, B R: Ohm
Coil L0, mH N La: mH
Core S, mm2 l, mm

μi:

Bs: Tl

Measurement
 t1, µs t2, µs t3, µs U1, B U2, B U3, B
Result

k12: k22: k23:

h12: h22: h23:

τ: µs

ln g:

 current voltage permeability inductance
Details
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This calculator is designed to obtain the coefficients for the Stoletov curve [1] and the graph of this curve itself, built for a coil with a ferromagnetic core without a gap. Also, he can calculate some of the missing data of the coil, for example, find the relative magnetic permeability of its core, the time and induction of its saturation.
To obtain the desired coefficients, a simple stand is required, consisting of a power source U, a key VT1 with a signal generator GG1, shunt RI and, in fact, the investigated coil with core L (read more about the stand). The measurement is made by the oscilloscope OS1 at three points, by cursor measurements (detailed theory). The whole scheme of measurementsion is shown in Figure 1.
 Fig.1. Scheme for obtaining coefficients for the Stoletov curve: a) -- stand, b) -- oscillogram with three measuring points
Comment. Since we measure the current passing in the circuit with an oscilloscope using a shunt (resistor RI), then in fact we get the voltage values ​​on it, which, according to Ohm's law, are converted into current by the calculator.
Stand preparation
The stand has its own internal resistance, consisting of the resistance of the key channel and connecting wires. Also, we include here the active resistance of the wires of the coil itself, collectively called Roth (Fig. 1a). It cannot be determined exactly in a direct way, so it is calculated indirectly in the calculator. To do this, you need to turn on the stand, by adjusting the duty cycle of the GG1 generator pulses, select an oscillogram that approximately corresponds to (Fig. 1b), and store it with an oscilloscope. After that, the stand can be turned off and the study of the received oscillogram can be started.
The GG1 oscillator frequency must be chosen such that all oscillations between transients have time to completely decay. Typically, this frequency is a few kilohertz. The oscilloscope can be synchronized with a second probe connected to the VT1 drain.
To obtain Roth, it is necessary to find Um -- the amplitude of the voltage curve (Fig. 1b), which, obviously , must be less than the supply voltage U. If this is not the case, then your socilloscope probes are not calibrated, and you need to adjust them first. Write the correct reading Um into the calculator. Also, enter there the test bench supply voltage U known to you and the resistance of the shunt RI (the top line of the calculator). After that, the first calculated parameter will appear in the calculator - the total active resistance in the R circuit, which is the sum of: R = RI + Roth.
The measurements in this calculator assume that we know the values of the inductance of the core coil L, the number of its turns N, as well as two parameters of the core itself: its cross-sectional area S and the average length of the magnetic line l. The last two parameters can be obtained from the reference data of the core (example in [2]), or simply by measuring them yourself [3]. All these data are also entered into the calculator (second and third line).
First point
Continuing the study of the saved oscillogram, we find the first measurement point (Fig. 1b). This point is selected approximately halfway through the first section of the oscillogram (details in Fig.6), and the data corresponding to it: t1 and U1, are entered into the calculator. If you only need to obtain the relative magnetic permeability of the core, then this measurement will be enough. But to get the whole picture, you need two more measurement points.
Second and third dots
These points can be obtained on the second section of the previously saved oscillogram, on the top and bottom of the falling curve (details in Fig.6). Their corresponding data: t2 - U2 and t3 - U3 are entered into the calculator. This completes the measurements.
Receiving data
As a result of these studies, we will obtain the following data:
• La - the maximum achievable inductance in the investigated coil;
• μi - initial relative magnetic permeability of the core;
• Bs - core saturation induction;
• τ - core saturation time;
• ln g - natural logarithm of the g coefficient for plotting current versus time ( more);
• k12-k23 - coefficients for the Stoletov curve, which are responsible for the parameters of the core coil;
• h12-h23 - coefficients for the Stoletov curve, responsible for the parameters of the core (without coil); are written in decimal form, for example 2E4 means 2*104.
Also, we get two charts. On the left is a plot of current (or voltage on an oscillogram) versus time. It must correspond to the received oscillogram and the three points measured from it. On the right is a graph of the permeability of the coil core (or its inductance) versus the current passing through it.
If you need to clarify the data obtained in the calculator, then this can be done by pointing to the maximum inductance on the graph of the Stoletov curve, and then comparing it to La. In the case of a strong difference between these data, it is necessary to re-measure the first point again, until these results coincide. Such feedback allows you to achieve any accuracy of the data obtained in this calculator.
Default
Default, the calculator represents the parameters of the TPA4 EFD 30*15*9 core coil, N97 material, no gap, more detailed characteristics of which are presented in [2,4]. A winding of nine turns is wound on the core. A voltage of 11.79 V is applied to the stand, while the shunt resistance is 2 ohms.
Saving Data
This calculator can save the received calculations to your account. To do this, you must be registered on this site. You can save the result of the calculation, which is called the word "project" here, by clicking on the "Save to account" button, and then completely restore the data from the "My Projects" section.
Materials used
1. Wikipedia. Stoletov's Curve.
2. EPCOS ferrite cores. EFD 30*15*9. [PDF]
3. Determining the parameters of the magnetic circuits. [PDF]
4. Ferrite cores. Handbook in Russian and English. [PDF]
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