I'm trying to acquire the BH curve of a toroidal current transformer in saturation, having the primary and secondary current.

The formulas I am using are:

B = (1/NsS) Integral(Vs(t)dt)

H = (Ip*Np)/l

$$B = \frac 1 {N_s S} \int V_s(t)dt$$

$$H = \frac {I_p N_p} l$$

Np: turns in primary side
Ns: turns in secondary side
Ip: primary current
S: core cross section
Vs: voltage secondary
l: magnetic path length

So far I have achieved to see the BH shape, however the maximum and minimum values of B do not coincide to the max B for the material(electrical steel), as per next fig:

enter image description here

Any idea of why these values are so far from the theory?

  • 1
    \$\begingroup\$ I've MathJAXed your equations for you. Please check they're still OK and you can delete the plaintext versions or mine! \$\endgroup\$
    – Transistor
    Commented Nov 21, 2023 at 17:31
  • \$\begingroup\$ What kind of material are you testing? Steel? \$\endgroup\$ Commented Nov 21, 2023 at 18:06
  • \$\begingroup\$ "Obtention" is unlikely a very recognizable word to anyone using the English language. \$\endgroup\$
    – Andy aka
    Commented Nov 21, 2023 at 18:46
  • \$\begingroup\$ What are the units in your graph anyway? \$\endgroup\$
    – tobalt
    Commented Nov 21, 2023 at 21:09
  • \$\begingroup\$ You seem to have an integration error: each loop misses the previous one by a fixed (vertical) offset. Have you considered using the differential rather than integral form of the relationship? Alternately, consider adding a ramp error correction term to your analysis. \$\endgroup\$ Commented Nov 21, 2023 at 21:30

1 Answer 1


A quick look at this hysteresis curve reveals that you don't reach saturation.

Saturation has some indicative properties:

  • upsweep and downsweep of the H produce an overlapping curve (absense of hysteresis near the extreme values of H)

  • behavior at positive and negative H is the same

  • the slope of dB/dH is essentially zero

  • \$\begingroup\$ Hello, thanks for your observations. The issue I have is that I introduced a large primary current and connected the CT to a large load too. So in theory and as per the large transformation error, the CT should be saturated. However, as you explained there are some things that do not correspond to this. So I really dont know why I am not seen the characteristic symmetrical bh curve when the CT is saturated. \$\endgroup\$
    – Fe2321
    Commented Nov 21, 2023 at 21:27
  • \$\begingroup\$ @Fe2321 Did you account for frequency? Magnetic core behaviour is obviously dependent on frequency but it is easy to forget about when you are trying to record a BH curve. \$\endgroup\$
    – DKNguyen
    Commented Nov 21, 2023 at 21:35
  • \$\begingroup\$ Hello @DKNguyen. Thanks for your response. How can I consider the frequency when acquiring the BH curve? \$\endgroup\$
    – Fe2321
    Commented Nov 22, 2023 at 16:21
  • \$\begingroup\$ @Fe2321 Frequency dependence would be material dependence so there should be material data, or material parameters with an equation. Beyond that I don't know. You might want to check out significant it actually is though by varying your frequency and seeing if your graph changes enough for it to matter. \$\endgroup\$
    – DKNguyen
    Commented Nov 22, 2023 at 19:14

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