Resonator frequency estimation models#
This example demonstrates estimating resonance frequencies of superconducting microwave resonators using Jax.
Probelines weakly coupled to \(\lambda/4\) resonator#
Creates a probelines weakly coupled to a quarter-wave resonator.
The resonance frequency is first estimated using the resonator_frequency function and then compared to the frequency in the coupled case.
if __name__ == "__main__":
import matplotlib.pyplot as plt
ep_eff, z0 = cpw_parameters(width=10, gap=6)
print(f"{ep_eff=!r}")
print(f"{z0=!r}") # Characteristic impedance
res_freq = resonator_frequency(
length=4000,
epsilon_eff=float(jnp.real(ep_eff)),
is_quarter_wave=True,
)
print("Resonance frequency (quarter-wave):", res_freq / 1e9, "GHz")
circuit, info = sax.circuit(
netlist={
"instances": {
"R1": "quarter_wave_resonator",
},
"connections": {},
"ports": {
"in": "R1,coupling_o1",
"out": "R1,coupling_o2",
},
},
models={
"quarter_wave_resonator": partial(
quarter_wave_resonator_coupled,
cross_section=coplanar_waveguide(width=10, gap=6),
length=4000,
)
},
)
frequencies = jnp.linspace(1e9, 10e9, 5001)
S = circuit(f=frequencies)
print(info)
plt.plot(frequencies / 1e9, abs(S["in", "out"]) ** 2)
plt.xlabel("f [GHz]")
plt.ylabel("$S_{21}$")
def _mark_resonance_frequency(x_value: float, color: str, label: str):
"""Draws a vertical dashed line on the current matplotlib plot to mark a resonance frequency."""
plt.axvline(
x_value / 1e9, # Convert frequency from Hz to GHz for plotting
color=color,
linestyle="--",
label=label,
)
_mark_resonance_frequency(res_freq, "red", "Predicted resonance Frequency")
actual_freq = frequencies[jnp.argmin(abs(S["in", "out"]))]
print("Coupled resonance frequency:", actual_freq / 1e9, "GHz")
_mark_resonance_frequency(actual_freq, "green", "Coupled resonance Frequency")
plt.legend()
ep_eff=6.065191244680569
z0=49.312798842593466
Resonance frequency (quarter-wave): 7.6081395616176914 GHz
CircuitInfo(dag=<networkx.classes.digraph.DiGraph object at 0x7f1b33d77750>, models={'quarter_wave_resonator': functools.partial(<function quarter_wave_resonator_coupled at 0x7f1b33e63600>, cross_section=CrossSection(sections=(Section(width=10.0, offset=0.0, insets=None, layer=<LayerMapQPDK.M1_DRAW: 1>, port_names=('o1', 'o2'), port_types=('optical', 'optical'), name='_default', hidden=False, simplify=None, width_function=None, offset_function=None), Section(width=6.0, offset=8.0, insets=None, layer=<LayerMapQPDK.M1_ETCH: 47>, port_names=(None, None), port_types=('optical', 'optical'), name='etch_offset_pos', hidden=False, simplify=None, width_function=None, offset_function=None), Section(width=6.0, offset=-8.0, insets=None, layer=<LayerMapQPDK.M1_ETCH: 47>, port_names=(None, None), port_types=('optical', 'optical'), name='etch_offset_neg', hidden=False, simplify=None, width_function=None, offset_function=None), Section(width=10.0, offset=0, insets=None, layer=<LayerMapQPDK.WG: 59>, port_names=(None, None), port_types=('optical', 'optical'), name='waveguide', hidden=False, simplify=None, width_function=None, offset_function=None)), components_along_path=(), radius=100.0, radius_min=11.0, bbox_layers=None, bbox_offsets=None), length=4000), 'top_level': <function _flat_circuit.<locals>._circuit at 0x7f1b302d44a0>}, backend='klu')
Coupled resonance frequency: 7.5718 GHz
Optimizer for given resonance frequency#
Find the resonator length that gives a desired resonance frequency using an optimizer.
if __name__ == "__main__":
import ray
import ray.tune
import ray.tune.search.optuna
frequencies = jnp.linspace(0.5e9, 10e9, 1001)
TARGET_FREQUENCY = 6e9 # Target resonance frequency in Hz
def loss_fn(config: dict[str, float]) -> dict[str, float]:
"""Loss function to minimize the difference between the actual and target resonance frequencies.
Args:
config: Dictionary containing the resonator length in micrometers.
"""
length = config["length"]
# Setup model
S = circuit(f=frequencies, length=length)
# Get frequency at minimum S21
coupled_freq = frequencies[jnp.argmin(abs(S["in", "out"]))]
return {
"l1_loss_ghz": abs(float(coupled_freq) - TARGET_FREQUENCY) / 1e9,
"mse": (float(coupled_freq) - TARGET_FREQUENCY) ** 2,
}
# Test loss function
print(f"{loss_fn(dict(length=4000.0))=}")
print(f"{loss_fn(dict(length=5900.0))=}")
# Initialize Ray (possibly with cluster)
ray.init()
# Optimize length using Ray Tune
tuner = ray.tune.Tuner(
loss_fn,
param_space={
"length": ray.tune.uniform(1000.0, 9000.0),
},
tune_config=ray.tune.TuneConfig(
metric="mse",
mode="min",
num_samples=50,
max_concurrent_trials=math.ceil((os.cpu_count() or 1) / 4),
reuse_actors=True,
search_alg=ray.tune.search.optuna.OptunaSearch(),
),
)
results = tuner.fit()
best_trial = results.get_best_result()
length = best_trial.config["length"]
print(f"Best trial config: {best_trial.config}")
# Initialize optimizer
print(f"Optimized Length: {length:.2f} µm")
optimal_S = circuit(f=frequencies, length=length)
optimal_freq = frequencies[jnp.argmin(abs(optimal_S["in", "out"]))]
print(f"Achieved Resonance Frequency: {optimal_freq / 1e9:.2f} GHz")
# Plot
plt.close()
plt.plot(frequencies / 1e9, abs(optimal_S["in", "out"]) ** 2)
plt.xlabel("f [GHz]")
plt.ylabel("$S_{21}$")
_mark_resonance_frequency(optimal_freq, "blue", "Optimized resonance Frequency")
_mark_resonance_frequency(TARGET_FREQUENCY, "orange", "Target resonance Frequency")
plt.legend()
plt.show()
ruff: enable[E402]