Finding inductance is one of the main uses of magnetic field software. We've posted a tutorial that shows how to use PerMag to find the inductance/length of transmission lines. The report starts with the benchmark example of a coaxial transmission line in the low frequency limit. Here, the current is distributed uniformly over the conductors to minimize the resistance. Figure 1 shows the distribution of magnetic field. The example shows how to set up the solution and to determine the inductance from an integral of magnetic field energy. The next example is more familiar, a coaxial line in the high-frequency limit where fields are excluded from the conductors. This example illustrates two techniques: 1) representing field-excluding materials as surfaces of constant vector potential and 2) finding the total current carried by a field-excluding wire using an Ampere-law integral. Even with moderate-sized elements, the conformal mesh approach gives agreement with theoretical results to within a fraction of a percent. The method is easily applied to more practical applications such as non-circular conductors or a displaced center conductor.
Figure 1. Plot of |B| in a coaxial transmission line, low-frequency limit.
A third example is a two-wire transmission line in free space in the high-frequency limit. It gives the opportunity to discuss how to approximate infinite space in a finite-element calculation. Again, the numerical results are in excellent agreement with theory. It is easy to extend the calculation to a practical application where the numerical approach has significant advantages. Figure 2 shows lines of magnetic flux density for a two-wire transmission line close to a conducting substrate. The presence of the metal sheet reduces the inductance/length of the line by 6%.
The full tutorial summarizes useful equations for inductance calculations. Download: Inductance_calculations.pdf
Figure 2. Lines of magnetic flux density for a two-wire transmission line near a conducting sheet.
LINKS
