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    Curved vs. Straight Segments

    Created OnOctober 29, 2022
    Updated OnApril 26, 2023
    By:Tony Golden

    Many examples show the advantages of using curved segments with respect to the stability and convergence properties of the solutions. Due to the improved convergence rate, accurate results can be obtained with reduced simulation time and memory space.

    Fig. 1 shows the dimensions of a center-fed helical antenna in free space (normal mode). Figs. 2 and 3 show a comparison between AN-SOF, which uses curved segments, and a straight wire approximation to the helix of Fig. 1. The convergence properties of the input impedance and admittance versus the number of segments are investigated.

    Fig. 1: Helix radius = 0.0273λ. Pitch = 0.0363λ. Number of turns = 10. Wire radius = 0.001λ.
    Fig. 2(a): Resistance convergence plot for the helix of Fig. 1.
    Fig. 2(b): Reactance convergence plot for the helix of Fig. 1.
    Fig. 3(a): Conductance convergence plot for the helix of Fig. 1.
    Fig. 3(b): Susceptance convergence plot for the helix of Fig. 1.

    As can be seen from these results, by using curved segments significantly fewer unknowns are needed to predict the input impedance. However, the admittance convergence is questionable for the straight wire case, while it has a notorious convergent behavior for the curved case.

    The improvement depends on the geometry and frequency, but generally, if N straight segments are needed to obtain a convergent value, then N/p curved segments are needed to obtain the same value, with p = 2…10. For a straight geometry the improvement factor is p = 1, as can be expected, because there are no curved segments in this case.

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