Curved vs. Straight Segments

The choice between using curved segments or straight-wire approximations is fundamental to the accuracy and efficiency of electromagnetic simulations. The following study illustrates the advantages of curved segments regarding the stability and convergence properties of numerical solutions.

Helix Antenna Model

To compare these two approaches, we examine a center-fed helical antenna (see Fig. 1) operating in free space (normal mode). The specific dimensions of the model are the following:

• Helix Radius: $0.0273\lambda$
• Pitch: $0.0363\lambda$
• Number of Turns: 10
• Wire Radius: $0.001\lambda$

Input Impedance Convergence

The performance of the Conformal Method of Moments (CMoM) in AN-SOF is compared against a standard straight-wire approximation. We investigate the convergence of the input impedance as the number of segments ($N$) increases.

Figure 2(a) shows the Input Resistance convergence. The straight-wire approximation converges much more slowly than the AN-SOF curve, which settles rapidly into a stable value.

Figure 2(b) displays the Input Reactance convergence. The difference is even more pronounced here: the straight-wire model converges very slowly toward a value below the asymptote of the AN-SOF curve. In contrast, the curved segment model in AN-SOF demonstrates smooth, monotonic, and rapid convergence.

Input Admittance Convergence

The same comparison is applied to the input admittance (conductance and susceptance) to further validate the results.

In Fig. 3(a), the Input Conductance results are plotted. The straight-wire approximation starts to increase smoothly as the number of segments increases and then diverges rapidly. In contrast, the AN-SOF curve decays fast to a convergent value.

In Fig. 3(b), the Input Susceptance is shown. Again, the improved convergence rate of the curved segments is evident, while the straight-wire approximation diverges.

Practical Advantages

As demonstrated by these benchmarks, the use of curved segments provides three critical advantages:

• Convergent Input Impedance and Admittance: As the number of segments is increased, the input impedance and admittance for the CMoM implemented in AN-SOF converge. In contrast, the legacy straight-wire segment approximation does not guarantee convergence, and in the case of the normal-mode helix, it diverges.
• Reduced Simulation Time: Accurate results are obtained with fewer segments, leading to faster computation.
• Memory Efficiency: Because fewer unknowns are required to describe complex geometries like helices, memory overhead is greatly reduced.

By modeling the true physical contour of the structure through the CMoM, AN-SOF ensures that the numerical solution remains stable and reliable, avoiding the artifacts and slow convergence associated with traditional linear approximations.