I am studying the operation of Q3D, and found the terminology mutual resistance used in Q3D. From the Help document, it describes loss due to eddy current is modeled in mutual resistance. Combined with the learning from SI and basic understanding about electric power generator, I got confused about these three.

My understanding

  1. Eddy current is generated in conductors when this exists time varying magnetic field. The magnetic field generated by eddy current is to oppose the change of external magnetic field. Eddy current dissipates into heat when circulating in conductors. That's why it is modeled in terms of mutual resistance.
  2. For electric power generator, a loop of wire is put inside a static magnetic field. The mechanical force is exerted to force the motion of the wire loop, usually rotation. Then, the changing magnetic flux through this wire loop induces electric current circulating along the wire loop.
  3. For inductive crosstalk of neighboring transmission line, a sinusoidal signal in one TL propagates from TX to RX. The TL can be approximately regarded as a series of LC, along which the signal propagates step by step (very small step). The signal propagating constitutes local current loop, which generates magnetic field, and in turn induces current loop in the neighbor TL. This induced current propagates forward and backward, contributing to FEXT and NEXT.

My question

  1. These three phenomena result from the same origin, which is magnetic induction, and mutual inductance can be a physical quantity in this phenomenon. Then, what're the differences among these three generated current in different situations? To my limited understanding of electromagnetics, I think they are the same, and the difference is that if there's a way for the current flow away to make impact on others. For the case of power generator, the generated current can be guided out to accumulate the electric power. For the case of TL, the generated current can freely flow along the victim conductor, and finally results in crosstalk affecting TX and RX. For other cases, the generated current just circulates and dissipates. Is this thinking correct?
  2. If the circulating current generated on a current carrying conductor, then what and how does it contribute to the voltage drop on the conductor and the net current received on the terminals?
  3. Passive elements, such as TL, via, etc, can be modeled using S parameters, which can be converted into Z parameters. Therefore, I think the term mutual resistance is actually a part of Z parameters. However, I am not sure if this is correct and how to describe them in more detail, for example, quantitatively describing this phenomenon using a simple setup and plugging in some values.

1 Answer 1


When you have magnetically coupled conductors, the AC losses in each conductor depend on the currents in all of the conductors because all of the currents contribute to the magnetic fields that produce the AC losses.

The inductive and resistive effects can be described in terms of self and mutual inductances and self and mutual resistances.

Self and mutual impedance equations for two windings:

Self and mutual impedance equations for two windings

This can be extended to N windings.

Impedance matrix equation:

Impedance matrix equation

Here is a presentation that discusses modeling transformers with mutual impedances, but the concept could be applied to other coupled conductors.

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    Commented Apr 24, 2022 at 19:17

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