"""Resonator models."""
from collections.abc import Callable
from functools import partial
import jax.numpy as jnp
import sax
import skrf
from numpy.typing import NDArray
from skrf.media import CPW, Media
from qpdk import LAYER_STACK
from qpdk.tech import material_properties
def cpw_media_skrf(width: float, gap: float) -> partial[CPW]:
"""Create a partial coplanar waveguide (CPW) media object using scikit-rf.
Args:
width: Width of the center conductor in μm.
gap: Width of the gap between the center conductor and ground planes in μm.
Returns:
partial[skrf.media.CPW]: A CPW media object with specified dimensions.
"""
# Convert μm to m for skrf
return partial(
CPW,
w=width * 1e-6,
s=gap * 1e-6,
h=LAYER_STACK.layers["Substrate"].thickness * 1e-6,
t=LAYER_STACK.layers["M1"].thickness * 1e-6,
ep_r=material_properties[LAYER_STACK.layers["Substrate"].material][
"relative_permittivity"
],
rho=1e-100, # set to a very low value to avoid warnings
tand=0,
)
[docs]
def resonator_frequency(
length: float, media: Media, is_quarter_wave: bool = True
) -> NDArray:
r"""Calculate the resonance frequency of a quarter-wave resonator.
.. math::
f &= \frac{v_p}{4L} \text{ (quarter-wave resonator)} \\
f &= \frac{v_p}{2L} \text{ (half-wave resonator)}
There is some variation according to the frequency range specified for ``media`` due to how
:math:`v_p` is calculated in skrf. The phase velocity is given by :math:`v_p = i \cdot \omega / \gamma`,
where :math:`\gamma` is the complex propagation constant and :math:`\omega` is the angular frequency.
See :cite:`simonsCoplanarWaveguideCircuits2001,m.pozarMicrowaveEngineering2012` for details.
Args:
length: Length of the resonator in μm.
media: skrf media object defining the CPW (or other) properties.
is_quarter_wave: If True, calculates for a quarter-wave resonator; if False, for a half-wave resonator.
default is True.
Returns:
float: Resonance frequency in Hz.
"""
coefficient = 4 if is_quarter_wave else 2 # Quarter-wave resonator
a = media.v_p / (coefficient * length * 1e-6)
return a.mean().real
def quarter_wave_resonator_coupled_to_probeline(
media: Callable[[skrf.Frequency], Media],
f: NDArray | None = None,
coupling_capacitance: float = 15e-15,
length: float = 4000,
) -> sax.SDict:
"""Model for a quarter-wave coplanar waveguide resonator coupled to a probeline.
Args:
media: skrf media object defining the CPW (or other) properties.
f: Frequency in Hz at which to evaluate the S-parameters.
coupling_capacitance: Coupling capacitance in Farads.
length: Length of the resonator in μm.
Returns:
sax.SDict: S-parameters dictionary
"""
f = f if f is not None else jnp.array([1e9, 5e9])
media = media(frequency=skrf.Frequency.from_f(f, unit="Hz")) # type: ignore
transmission_line = media.line(d=length, unit="um")
quarter_wave_resonator = transmission_line ** media.short()
coupling_capacitor = media.capacitor(coupling_capacitance, name="C_coupling")
resonator_coupled = coupling_capacitor**quarter_wave_resonator
probeline_factory = partial(media.line, d=5000, unit="um")
probeline = skrf.connect(
skrf.connect(probeline_factory(), 1, media.tee(), 0), 2, probeline_factory(), 0
)
all_network = skrf.connect(probeline, 1, resonator_coupled, 0)
sdict = {
("o1", "o1"): jnp.array(all_network.s[:, 0, 0]),
("o1", "o2"): jnp.array(all_network.s[:, 0, 1]),
}
return sax.reciprocal(sdict)
if __name__ == "__main__":
cpw = cpw_media_skrf(width=10, gap=6)(
frequency=skrf.Frequency(2, 9, 101, unit="GHz")
)
print(f"{cpw=!r}")
print(f"{cpw.z0.mean().real=!r}") # Characteristic impedance
res_freq = resonator_frequency(length=4000, media=cpw, is_quarter_wave=True)
print("Resonance frequency (quarter-wave):", res_freq / 1e9, "GHz")
