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Results and export

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How results are computed

  • Excitation. By default this is a DC-free Gaussian-derivative pulse, -20 dB at f_max. openEMS' modulated Gaussian carries a DC component when f_min/f_max is small (for example 0.5-8 GHz). The static field it leaves behind keeps the energy above the end criterion, so the run continues to the timestep limit. S-parameters are unaffected, but the run takes about 10x longer. On the Sierpinski model the derivative pulse took the run from about 150 s (not converged) to about 13 s (converged at -47 to -61 dB). Simulation(..., excitation="gauss") restores openEMS' pulse.
  • End criterion. A run stops when the field energy has decayed to the end criterion, −60 dB by default, evaluated every Nyquist period (exact_endcriteria, so the stopping point does not depend on machine speed; --no-exact restores openEMS' ~4 s wall-clock check). Resonance frequency and Dmax are already settled at −40 dB, but S11 depth and radiation efficiency of high-Q structures are not: on the patch, −40 dB gives |S11| −24 dB and η 0.86, −60 dB gives −37 dB and 0.95, −70 dB gives −39 dB and 0.96 (un-radiated ring-down energy corrupts P_acc). Override per run with --end-db.
  • S11 and Zin come from the excited lumped port: S11 = u_ref / u_inc and Zin = u_tot / i_tot, evaluated at --points frequencies between f_min and f_max.
  • Bands are contiguous frequency ranges with |S11| < -10 dB. Each band reports its edges, the frequency of minimum S11 (f_center in the bundle), fractional bandwidth, and whether it touches the edge of the simulated range. The app's band tables (Summary, the S-parameter side panel, the Examples panel) name two frequencies: the Center is the middle of the edges, (f_lo + f_hi) / 2, and the Best match is the frequency of minimum S11. The fractional bandwidth they show, and the Summary's Bandwidth (%), is the width divided by that center; the bundle's fractional_bw divides by f_center. CSV/TSV exports use the tables' definitions: f_center_GHz is the band middle, f_best_GHz is best match, and exported fractional_bw divides by the middle (CSV columns and open-band flags). A band that touches the edge of the simulated range continues past it: its open edge is marked ≤ or ≥, its width is a lower bound, and the example picker names it by its range ("≥ 8–12 GHz") instead of a single frequency.
  • Far field. openEMS records the fields on a near-field box and applies the NF2FF transform at the band centers (or at --pattern). The grid is θ 0-180° in 3° steps and φ 0-360° in 5° steps, with the phase center at nf2ff_center. With PEC or PMC boundaries, openEMS mirrors the recording surface and integrates over the image as well. Fairbeam therefore divides Prad by 2^m and multiplies Dmax by 2^m, where m is the number of PEC/PMC boundaries. Directivity then refers to the physical half space, for example a monopole over an infinite ground plane.
  • Radiation efficiency = Prad / P_acc. P_acc = ½·Re(u·i*) is the power accepted at the port. It is stored at the far-field frequencies and, with --efficiency [N] (a design's monitors.efficiency), at N frequencies across the band, with a reliability flag per frequency (Project bundle format). A model declared lossless (sim.lossless = True) reports 1 while Prad / P_acc is within 5 % of 1 (Project bundle format).
  • Gain = efficiency · Dmax. Realized gain = gain · (1 − |S11|²).

Accuracy notes

  • openEMS uses a staircase (Yee) FDTD mesh. Slanted and curved edges snap to mesh lines, and zero-thickness sheets sit on grid planes. Expect resonances to shift by a few percent unless the openEMS mesh is fine on the metal edges.
  • Check mesh convergence before trusting a number. For a designer file: fairbeam converge <design.json> (or Simulation › Mesh convergence… in the designer) reruns it at 15, 20, 30, 40 cells per wavelength and stops when the resonance, |S11| and Dmax settle (Sweeps and studies). For a Python model: fairbeam converge <model> --param mesh_div=15,20,30 (or cell=0.8,0.6,0.45 on the Sierpinski model); confirm that band centers move by less than your tolerance. How metal edges and zero-thickness sheets are meshed matters more than the global cell size: see Validation. The smallest cell sets the timestep for the whole domain, so avoid slivers (fairbeam.mesh.merge_lines).
  • Conductor loss: metals are perfect conductors unless a design metal has a conductivity (S/m) or a model uses sim.metal(..., conductivity=); then sheets are openEMS conducting sheets of the given thickness (default 0.035 mm) and the efficiency includes the copper loss (Writing models).
  • Literature check, Sierpinski monopole, iteration 3, 48 mm: simulated bands at 3.303 and 6.219 GHz. Puente et al. (1998) measured an 89 mm gasket; scaled to 48 mm, their bands fall at 3.226 and 6.508 GHz. The deviations are +2.4 % and −4.4 %, which is plausible given the staircase mesh, the contact bridges and the idealised infinite ground.
  • Patch antenna: the converged resonance is 2.455 GHz (mesh_div 30-40). The transmission-line model (fairbeam.analytic.patch_resonance: Hammerstad ε_eff and ΔL) gives 2.513 GHz (-2.3 %). The simplified formula ignores the finite ground and the probe, so this agreement is within its expected accuracy.
  • Half-wave dipole: resonance 1.3-1.4 % below the closed-form induced-EMF resonance, R_in 72-73 Ω, Dmax 2.13-2.15 dBi, efficiency 0.999. Full tables, the end-criterion study and recommended settings are in Validation.

The RunHistory sweep CSV follows the same band definitions with lowercase column names: band_lo_ghz and band_hi_ghz are the edges, band_center_ghz is their middle, and band_best_ghz is the |S11| minimum frequency. It uses the first band of each job; missing edges leave the center blank. RunHistory labels the minimum frequency Best match.