# Low Frequency Smoothing

Low-frequency smoothing helps when low-frequency wave-port results are under-sampled by the time-domain simulation. For each frequency ff, Tidy3D compares the total simulation time to the period T=1/fT = 1/f:

Nperiods=tsimT=tsimf N_\mathrm{periods} = \frac{t_\mathrm{sim}}{T} = t_\mathrm{sim} f

Frequencies with too few sampled periods are replaced by a polynomial extrapolation from the trusted frequency range. Results with enough sampled periods are left unchanged.

NOTE

For terminal component simulations, low-frequency smoothing affects only wave-port mode decomposition data. Use it when low-frequency S-parameter results are noisy because the simulation does not include enough periods at the lowest frequencies.

# Sampling Window

min_sampling_time: Minimum simulation time, in periods of the corresponding frequency, required for frequency-domain results to be used in the low-frequency extrapolation fit. Results below this threshold are discarded.

  • Type: non-negative floating-point number
  • Unit: periods
  • Default: 1.0
  • Constraint: less than max_sampling_time

max_sampling_time: Maximum simulation time, in periods of the corresponding frequency, used for the low-frequency smoothing range. Results above this threshold are not modified.

  • Type: non-negative floating-point number
  • Unit: periods
  • Default: 5.0
  • Constraint: greater than min_sampling_time

# Extrapolation

order: Polynomial order used for low-frequency extrapolation.

  • Type: integer
  • Options: 0, 1, 2, 3
  • Default: 1

max_deviation: Maximum allowed deviation from trusted values, expressed as a fraction of the trusted values.

  • Type: floating-point number or None
  • Constraint: greater than or equal to 0 when provided
  • Default: 0.5

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