Probes and S-Parameters

rfx provides three probe types for extracting field data, plus several S-parameter extraction methods for different port models.

---

Point probe

Records a single field component at one Yee cell over time. The time series is stored in result.time_series.

sim.add_probe(
    position=(0.025, 0.025, 0.010),  # (x, y, z) in metres
    component="ez",                   # ex / ey / ez / hx / hy / hz
)

After running:

result = sim.run(n_steps=4000)
ts = result.time_series          # shape (n_steps, n_probes)
ez_vs_time = ts[:, 0]            # first probe, all timesteps

Multiple probes are indexed in the order they were registered.

---

Vector probe

Records all six field components (Ex, Ey, Ez, Hx, Hy, Hz) at the same position.

sim.add_vector_probe((0.025, 0.025, 0.010))

Result columns 0–5 correspond to Ex, Ey, Ez, Hx, Hy, Hz in that order.

---

DFT plane probe

Accumulates the frequency-domain field on a 2-D cross-section during the time loop. More memory-efficient than saving full snapshots and avoids FFT leakage of short time windows.

import jax.numpy as jnp

sim.add_dft_plane_probe(
    axis="z",
    coordinate=0.010,           # z-plane at 10 mm
    component="ez",
    freqs=jnp.linspace(1e9, 4e9, 50),
    name="ez_cross_section",
)

Access the result:

result = sim.run(n_steps=4000)
plane = result.dft_planes["ez_cross_section"]
# plane.data : shape (n_freqs, nx, ny) complex

!!! tip Omit freqs and set n_freqs to let rfx choose a frequency array automatically from freq_max / 10 to freq_max.

---

S-parameter extraction

Lumped port S-matrix

When one or more lumped ports are added with add_port(), pass compute_s_params=True:

sim.add_port((0.01, 0.02, 0.01), "ez", impedance=50)
sim.add_port((0.04, 0.02, 0.01), "ez", impedance=50)

result = sim.run(n_steps=3000, compute_s_params=True)
s_matrix = result.s_params           # (2, 2, n_freqs) complex
freqs     = result.freqs             # (n_freqs,) Hz

import numpy as np
s11_db = 20 * np.log10(np.abs(s_matrix[0, 0, :]))
s21_db = 20 * np.log10(np.abs(s_matrix[1, 0, :]))

The S-matrix is normalised to each port’s impedance.

Wire port S-matrix (JIT-DFT)

Wire ports use voltage/current DFT integrals accumulated during the time loop. The extraction is performed inside a JIT-compiled scan, making it faster than post-processing FFTs for long simulations.

sim.add_port(
    (0.01, 0.02, 0.0),
    "ez",
    impedance=50,
    extent=0.0016,               # wire length
)

result = sim.run(n_steps=5000, compute_s_params=True)
s11 = result.s_params[0, 0, :]  # complex, shape (n_freqs,)

Waveguide S-parameters

See Sources & Ports for the waveguide-port setup workflow. After running:

sp = result.waveguide_sparams["port1"]

print(sp.freqs.shape)              # (n_freqs,)
print(sp.s11.shape)                # (n_freqs,) complex
print(sp.calibration_preset)
print(f"Reference plane: {sp.reference_plane*1e3:.1f} mm")
print(f"Probe plane:     {sp.probe_plane*1e3:.1f} mm")

WaveguideSParamResult fields:

Field	Type	Description
freqs	ndarray	Frequency array (Hz)
s11	complex ndarray	Reflection coefficient at port
s21	complex ndarray	Transmission to measurement plane
calibration_preset	str	"measured" or "source_to_probe"
source_plane	float	Actual source injection plane (m)
reference_plane	float	Reported S11 reference plane (m)
probe_plane	float	Reported S21 measurement plane (m)

---

Resonance extraction — Harminv

result.find_resonances() applies the Harminv MUSIC-like algorithm to extract complex resonant frequencies from the probe ring-down signal. It returns a list of HarminvMode objects sorted by amplitude.

modes = result.find_resonances(
    freq_range=(1e9, 5e9),   # search band (Hz)
    probe_idx=0,             # which probe to analyse (default 0)
)

for m in modes:
    print(f"f={m.freq/1e9:.4f} GHz  Q={m.Q:.0f}  amp={m.amplitude:.3e}")

HarminvMode fields:

Field	Description
freq	Resonant frequency (Hz)
decay	Exponential decay rate (1/s)
Q	Quality factor = pi*f/decay
amplitude	Complex mode amplitude
phase	Phase (radians)

Parameters

modes = result.find_resonances(
    freq_range=(1e9, 4e9),
    probe_idx=0,
    source_decay_time=None,  # auto-computed: 2*(3*tau), where tau=1/(f_c*bw*pi)
    bandpass=None,           # auto: True for CPML (removes DC artifacts), False for PEC
)

!!! note Harminv requires the signal to have decayed to ring-down before the analysis window starts. source_decay_time is subtracted from the beginning of the time series. The default auto-computation is appropriate for GaussianPulse excitation.

Standalone Harminv

You can call Harminv directly on any time series:

from rfx import harminv
import numpy as np

dt = 1e-12  # timestep in seconds
signal = np.loadtxt("probe_data.txt")
modes = harminv(signal, dt, f_min=1e9, f_max=5e9)

---

Plotting helpers

from rfx import plot_s_params, plot_time_series, plot_field_slice

plot_s_params(result)           # S11/S21 magnitude and phase
plot_time_series(result)        # all probe time series on one axes
plot_field_slice(result, "ez", axis="z", index=30)  # 2-D Ez cross-section

---

Touchstone I/O

from rfx import write_touchstone, read_touchstone

# Write 2-port S-params to a .s2p file
write_touchstone("patch_antenna.s2p", result.freqs, result.s_params)

# Read back
freqs, s_matrix = read_touchstone("patch_antenna.s2p")