I would like to accurately design and model a current transformer in FEMM. I'm hoping this will enable me to accurately estimate the secondary current in a current transformer, including it's phase relative to the primary current. The model will also help to size the core.

I've used the FEMM software previously to design magnetic concentrators for hall effect sensors. The problem I'm running into is that I cannot induce a current in the secondary winding in FEMM, it seems I have to guess and specify the secondary current.

I've followed David Meeker's example on transformer design, but I cannot follow it exactly because I'm not designing a voltage transformer, i.e. the secondary current is never zero.

These are the 2 equations I'm trying to solve for Is (secondary current): 2 equations
(source: gsu.edu)

I know (or can choose) the following:

  1. Ip - Current in the primary
  2. Rb - Burden resistance
  3. w - Natural frequency of the primary
  4. Vp - Voltage in the primary, reflected burden resistance (from FEMM)
  5. All relevant material properties
  6. All relevant physical properties

this leaves me with 4 unknowns, specifically:

  1. Rp+jwLp - primary coil impedance
  2. jwM - mutual impedance
  3. Rs+Rb+jwLs - secondary coil impedance + burden resistance
  4. Is - current in secondary winding

Currently considering trying the following:

  1. Use super position to independently determine Rp+jwLp and Rs+Rb+jwLs (i.e. remove the each coil and separately calculate these as constants)
  2. Independently calculate values for R, L, M based on idealized equations.

Both of these would be followed by regression to get Is, I'm not certain how to formulate this yet either.

Any help would be greatly appreciated, thanks!


1 Answer 1


Unless I'm missing something subtle in your question then....

Primary impedances Rp+jwLp are irrelevant for a current transformer - the current flows and that's it and if those leakage impedances are too high then it's a really badly designed CT.

Magnetization reactance is also irrelevant if the burden is chosen to be non-excessive i.e. the burden shunts the magnetization inductance so that it can be ignored.

Just do some simple math on typical impedances and you should conclude what I've said above.

  • \$\begingroup\$ Fair point I should add that the mechanical design is driving the magnetic design. I can't simply use a toroidal concentrator and assume the coupling factor is close to 1. The preferred design has to minimize clearances and be installed without disconnecting the bar. I would like to understand how much I can cut corners on the magnetic design well still achieving the accuracy required. \$\endgroup\$ Commented Nov 9, 2016 at 16:50
  • \$\begingroup\$ Well you can make a CT where the coupling factor is less than 1, you just need to calibrate it if the coupling is an unknown factor. Beyond a certain low coupling factor, the secondary leakage inductance might start to make the burden's ability to shunt the magnetization inductance give non-linear errors also but again., if unsure this can be tested and a lower burden chosen. \$\endgroup\$
    – Andy aka
    Commented Nov 9, 2016 at 18:51

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