1
\$\begingroup\$

I want to understand how to skecth an equivalent circuit model circuit composed of a load (resistor to make it simple) connected to a soruce bia two long paralel wires. Take the following figure as a reference.

![enter image description here

I understand that the coupling of the paralel wires can be modeled as an inductance aswell according to the following formula.

$$\ L_m = \frac{\mu _0 l}{\pi}ln\frac{d-r}{r} $$

How do I represent this incuctance in the equivalent circuit?

To clarify, this cables will also have a partial self inductance and I understand that this L cand be modeled as a series inductance. But I have trouble understanding how to represent the mutual inductance between the two cables.

Would this be a reasonable model?

For the value of M12 I would use the mutual inductance described above L_m

enter image description here

\$\endgroup\$
5
  • 1
    \$\begingroup\$ You do realize that the device is a varistor and that the inductance of the leads is probably irrelevant if you look at the bigger picture. \$\endgroup\$
    – Andy aka
    Nov 6, 2023 at 13:42
  • 1
    \$\begingroup\$ Yes! I agree with you. I was pondering it a bout, in general, and sice this is what I have in my desk I used it as an example haha But I also imagine this situation in a bigger circuit, lets say two 10 meter paralel wires between the MOV (or another electric component) and the source. Then the effect would be much greater. Now that I think about it, this latter examplo could have been better xd \$\endgroup\$ Nov 6, 2023 at 13:46
  • \$\begingroup\$ @winny Its true but there can exist resonant effect due to the total inducance and capacitance of the MOV. Eitherway I think I going to remake the question since It doest illustrate my real question in point. Thanks though! \$\endgroup\$ Nov 6, 2023 at 13:52
  • \$\begingroup\$ @winny For clarification, I was refering this effect to surge scenarios. Since the resonance of that low inductance and capacitance combo will happen at very high frequencies. \$\endgroup\$ Nov 6, 2023 at 14:17
  • \$\begingroup\$ The inductance of the loop is the same whether you have a resistor or not. Just as the loop were made from a non-perfect conductor; inductance doesn't care about the conductivity of the wire. Inductance is an area/shape phenomena. Try this loop inductance calculator: eeweb.com/tools/rectangle-loop-inductance \$\endgroup\$
    – Andy aka
    Nov 6, 2023 at 16:17

1 Answer 1

2
\$\begingroup\$

If you have two long, parallel wires that are reasonably uniform, then the best way to take their effect into account is to model them as a transmission line. This models the finite speed of light, and the inductance and capacitance of the lines.

Generally if the line is shorter than λ/10 or so of the highest frequency you are using, you can ignore the transmission effects of the line. With this short line, you still get a very good model for the lumped C and L model of the stray effects of the wires, from a length of line with a distributed C and L per length given by their characteristic transmission line impedance.

The inductance of the line is just that, a loop inductance of the two conductors in the line. If you want to consider mutual inductance, then you have to elaborate your model to include more conductors, generally a ground conductor with coupling to both lines. This is obviously more a complicated circuit than shown.

\$\endgroup\$
5
  • \$\begingroup\$ Is there a way to avoid this complex model? If I were to use the Mutual inductance formula, for example, should I put a series inductance with the calculated mutual inductance? For reference, the cables that I want to use could go up to 30 meters and could be subjected to frequencies up to 50kHz \$\endgroup\$ Nov 6, 2023 at 15:07
  • \$\begingroup\$ Your schematic does not have mutual inductance terms. Real life does. If you want your model to model more of real life behaviour than it does at the moment, then unfortunately the model will become more complex. \$\endgroup\$
    – Neil_UK
    Nov 6, 2023 at 15:23
  • \$\begingroup\$ I see... So so simples I can go with the lumped parameter model is to model the partial self inductance of both straigh wires right? The only thing that bothers me is that I would thing that the magnetic field produced by each wire is interacting with the other, so in a sense is like the wires are coupled by an inductance isn't that correct? \$\endgroup\$ Nov 6, 2023 at 15:30
  • \$\begingroup\$ I updated my question with the circuit that I was proposing to you in my latest comment \$\endgroup\$ Nov 6, 2023 at 15:41
  • \$\begingroup\$ @SantiOspina The mutual inductance serves only to decrease or increase the total inductance of the loop (increase in this case), note that the current through both inductors is equal, as they are in series. Its effect is indistinguishable from having the correct inductance for the loop in the first place. You get the correct loop inductance by treating the parallel wires as a transmission line. If you want to be able to measure the mutual inductance separately, then you need the more complex circuit. \$\endgroup\$
    – Neil_UK
    Nov 6, 2023 at 17:36

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.