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twan
1 Posts |
 Posted - Nov 06 2015 : 19:13:30
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I am calculating the mutual inductance between 2 conductors placed at a distance apart. From what I understand, the mutual inductance between two conductors should decrease if a third conductor is placed between them. However when I run the simulation, the conductance between conductor 1 and 2 is the same ,regardless of conductor 3 being between them or not. Can somebody point out if where I'm mistaken.Thanks. the code is-
* mutual inductance of two conductors
.units mm
.Default z=0 sigma=5.8e4
*node of conductor1
N1 x=0 y=0
N2 x=0 y=1
*node of conductor 2
N3 x=0.5 y=0
N4 x=0.5 y=1
*node of conductor 3 , placed between 1 and 2
N15 x=0.25 y=0
N16 x=0.25 y=1
*the segment connecting the node
E1 N1 N2 w=0.075 h=0.1
E2 N3 N4 w=0.075 h=0.1
E3 N5 N6 W=0.075 h=0.1
E4 N15 N16 w=0.1 h=0.1
.external n1 n2
.external n3 n4
*frequency points
.freq fmin=1e9 fmax=1e9
.end
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Enrico
545 Posts |
Posted - Nov 08 2015 : 19:49:03
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This is a specific case of a wider topic about inductance shielding.
Very often there is the necessity to shield in some way one conductor from one another to reduce inductance. Unfortunately, inductance coupling does not work like capacitive coupling, for which a grounded line between two signal lines in most cases is enough to provide EM shielding.
The intuitive idea to reduce the inductive coupling is to create some sort of shield between two conductors using a third one in the middle, as it is usually done to reduce the capacitive coupling.
However, this idea not necessary working as expected. Let's start considering how things work at low frequency in capacitance case. Basic electromagnetic theory tell us that at low frequency, when the fields are static, the electric field does not penetrate into conductors. The rationale is, if we had an electric field inside the conductor, the free charges would start moving towards the surface, so there wouldn't be any equilibrium. Therefore, due to the accumulation of charges on the surface, we have a shielding effect for the electric field.
The same concept however is not true for magnetic fields, if we are considering materials with relative permettivity (ur) approaching one (that is, non-ferromagnetic materials). In this case, the field penetrates the conductors, without being significantly disturbed. As a result, shielding two conductors using a third one in the middle simply is not effective.
However, when the frequency increases, things start to change, because of the proximity effect. That is, eddy currents are induced on nearby conductors. These induced currents do have the effect of shielding one conductor from the other; however, one single wire between other two wires hardly produces any difference. A ground plane would provide a more marked shielding effect (though still not very pronounced).
FastHenry2 could be used to perform simulated experiments to clarify the theory and work with some quantitative results.
The first example is the calculation of the inductance of a single wire, over the frequency range from 1KHz to 10GHz, first in free space and then near to a ground plane.
First simulate the lone wire. Then add a ground plane near to the wire. Note that you don’t need to create a port on the ground plane to see its effect on the wire.
Running FastHenry2, it can be observed that at low frequencies the results are the same with or without the insertion of the ground plane. However, when the frequency increases, also the high-frequency effects start playing a significant role. As a consequence, in the presence of the ground plane, the high-frequency resistance increase and inductance drop are more pronounced.
The second example consists in simulating two wires in free space, and then inserting a third one between the first two. Also in this simulation, it is not necessary to create a port over the third wire, to be able to see its effect. By comparing the results at high frequency, we notice some very slight differences in the inductive coupling (off-diagonal) terms. Using a ground plane in between, we could get some more shielding, but this solution is very often not feasible; moreover, remember that this shielding effect not only is small but also is visible only at high frequencies.
However, if it is true that the magnetic fields are not shielded by materials with (almost) unitary ur, it is still possible to reduce the loop impedance of a conductor. The loop impedance depends on where the 'return' path for the current is located; therefore, if you insert a third conductor between the two conductors you are trying to shield from each other and connect it at both ends to a ground plane, a current can flow to reduce the magnetic field. But since you must be able to make current actually flow in your conductors, you cannot appreciate this effect completely from the inductance matrix but it is better seen with a circuit simulator. This concept, however, is very delicate, since shielding depends on where the foreseen 'return' path for the current flowing in your lines is (i.e. in a nearby ground plane, as could happen in a PCB, or very far on some other conductor, as could happen in a dense connector).
(Note: this is an 'old' topic, and many thanks go to Stefan Weber of Fraunhofer-Institut für Zuverlässigkeit und Mikrointegration (IZM) for his comments and the useful discussions we had at the time).
Best Regards,
Enrico
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Mutual Inductance between 2 conductors
