Proximity effect and the distribution parameters of multi-conductor transmission line

The effects of the proximity effect and the distribution parameters on the reflection and transmission parameters of a multi-conductor transmission line increase significantly when the gap between two adjacent conductors decreases. Considering the proximity effect, we calculate the distribution inductance and the magnetic flux density of three typical multi-conductor transmission lines by applying the vector potential finite element method. The first case is a coax with a closed structure. The proposed numerical results agree well with the analytical results, which verify that the proposed method is effective. The second one is a parallel line with an opened structure, of which the infinite calculation domain has been truncated by the infinite element method during calculation. The comparison implies that the proximity effect influences the per-unit-length inductance of multi-conductor lines. The last instance is a coupled microstrip. The distribution of the magnetic flux density around the coupled lines show that it is affected by the proximity effect. The inductance matrix obtained differs from that of the previous work, in which the proximity effect has not been taken into account. All 3 cases imply that the vector potential finite element method is suitable for calculating the distribution parameters of multi-conductor transmission line with the proximity effect.