A guy I worked with years ago (~2015) who is an EE said that "an electric motor was just another form of a transformer". I'm not an EE, so I didn't do things with transformers. I think he meant that it turns energy from one form into another, but that he also meant there was a mathematical parallel in the modeling. Maybe something presuming steady-state, not accounting for spin-up of the armature?

Note: he loved 3-phase, for what that is worth.

Can you show the basic circuit and mathematical model of a simple electrical transformer, and then show a simple model for an equivalent electrical motor. Ideally there should be some python (numpy/scipy) with an ODE45 and a graph of current, voltage, accounting for windings, and somehow relating that to motor rotation or something.

Showing my homework:
I tried searching this forum and found no result that seemed to answer the question.


  • 2
    \$\begingroup\$ Thought experiment: how would you tell the difference, in circuit, of a changing flux vs. moving flux, cutting a winding? \$\endgroup\$ Aug 16, 2023 at 18:33

1 Answer 1


You'd want to start with a reference book on electrical machines. It'll have the state equations to get you going.

The simplest form of a "motor transformer" is a two-phase stepper or BLDC motor. Apply a sine wave close to the electromechanical resonance frequency to phase 1 winding. Lock the rotor. Phase 2 winding will output "close to nothing". Now unlock the rotor. Phase 2 winding will output a phase-shifted version of the input to phase 1.

Compared to a regular transformer, there's additional phase shift due to rotor slip angle. The motor acts just like a 1:1 transformer would, less phase shift, with two additional transductions in series with energy flow: magnetic to mechanical on phase 1 ("primary"), and mechanical to magnetic on phase 2 ("secondary").

A BLDC/stepper with stator poles 180 electrical degrees apart will work very similarly to a 1:1 transformer.

A three-phase induction motor works similarly, except that the rotor magnetic field is due to current flow in the cage, induced by the stator.

  • \$\begingroup\$ I have 4 or 5 texts but they must be the wrong ones. If you have one in mind then I would be grateful if you could share. \$\endgroup\$ Aug 17, 2023 at 2:48

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.