"""Resonators."""
from typing import Any
import jax.numpy as jnp
import sax
from gdsfactory.typings import CrossSectionSpec
from sax.models.rf import capacitor, electrical_open, electrical_short, tee
from qpdk.helper import deprecated
from qpdk.models.constants import DEFAULT_FREQUENCY, c_0
from qpdk.models.couplers import cpw_cpw_coupling_capacitance
from qpdk.models.cpw import (
cpw_parameters,
cpw_z0_from_cross_section,
get_cpw_dimensions,
)
from qpdk.models.waveguides import straight, straight_shorted
[docs]
def quarter_wave_resonator_coupled(
f: sax.FloatArrayLike = DEFAULT_FREQUENCY,
length: float = 5000.0,
coupling_gap: float = 0.27,
coupling_straight_length: float = 20,
cross_section: CrossSectionSpec = "cpw",
) -> sax.SDict:
"""Model for a quarter-wave coplanar waveguide resonator coupled to a probeline.
Args:
cross_section: The cross-section of the CPW.
f: Frequency in Hz at which to evaluate the S-parameters.
length: Total length of the resonator in μm.
coupling_gap: Gap between the resonator and the probeline in μm.
coupling_straight_length: Length of the coupling section in μm.
Returns:
sax.SDict: S-parameters dictionary
"""
f_arr = jnp.asarray(f)
instances = {
"resonator": resonator_coupled(
f=f_arr,
length=length,
coupling_gap=coupling_gap,
coupling_straight_length=coupling_straight_length,
cross_section=cross_section,
open_start=True,
open_end=False,
),
"short": electrical_short(f=f_arr),
}
connections = {
"resonator,resonator_o2": "short,o1",
}
ports = {
"coupling_o1": "resonator,coupling_o1",
"coupling_o2": "resonator,coupling_o2",
"resonator_o1": "resonator,resonator_o1",
}
return sax.evaluate_circuit_fg((connections, ports), instances)
[docs]
def resonator_coupled(
f: sax.FloatArrayLike = DEFAULT_FREQUENCY,
length: float = 5000.0,
coupling_gap: float = 0.27,
coupling_straight_length: float = 20,
cross_section: CrossSectionSpec = "cpw",
open_start: bool = True,
open_end: bool = False,
) -> sax.SDict:
"""Model for a coplanar waveguide resonator coupled to a probeline.
Args:
cross_section: The cross-section of the CPW.
f: Frequency in Hz at which to evaluate the S-parameters.
length: Total length of the resonator in μm.
coupling_gap: Gap between the resonator and the probeline in μm.
coupling_straight_length: Length of the coupling section in μm.
open_start: If True, adds an electrical open at the start.
open_end: If True, adds an electrical open at the end.
Returns:
sax.SDict: S-parameters dictionary with 4 ports.
"""
f_arr = jnp.asarray(f)
capacitor_settings = {
"capacitance": cpw_cpw_coupling_capacitance(
f_arr, coupling_straight_length, coupling_gap, cross_section
),
"z0": cpw_z0_from_cross_section(cross_section, f_arr),
}
instances = {
"coupling_1": straight(
f=f_arr, length=coupling_straight_length / 2, cross_section=cross_section
),
"coupling_2": straight(
f=f_arr, length=coupling_straight_length / 2, cross_section=cross_section
),
"resonator_1": straight(
f=f_arr, length=coupling_straight_length / 2, cross_section=cross_section
),
"resonator_2": straight(
f=f_arr,
length=length - coupling_straight_length / 2,
cross_section=cross_section,
),
"tee_1": tee(f=f_arr),
"tee_2": tee(f=f_arr),
"capacitor": capacitor(f=f_arr, **capacitor_settings),
}
connections = {
"coupling_1,o2": "tee_1,o1",
"coupling_2,o1": "tee_1,o2",
"resonator_1,o2": "tee_2,o1",
"resonator_2,o1": "tee_2,o2",
"tee_1,o3": "capacitor,o1",
"tee_2,o3": "capacitor,o2",
}
ports = {
"coupling_o1": "coupling_1,o1",
"coupling_o2": "coupling_2,o2",
}
if open_start:
instances["open_start_term"] = electrical_open(f=f_arr, n_ports=2)
connections["resonator_1,o1"] = "open_start_term,o1"
ports["resonator_o1"] = "open_start_term,o2"
else:
ports["resonator_o1"] = "resonator_1,o1"
if open_end:
instances["open_end_term"] = electrical_open(f=f_arr, n_ports=2)
connections["resonator_2,o2"] = "open_end_term,o1"
ports["resonator_o2"] = "open_end_term,o2"
else:
ports["resonator_o2"] = "resonator_2,o2"
return sax.evaluate_circuit_fg((connections, ports), instances)
[docs]
def resonator_frequency(
*,
length: float,
epsilon_eff: float | None = None,
media: Any = None,
cross_section: CrossSectionSpec = "cpw",
is_quarter_wave: bool = True,
) -> float:
r"""Calculate the resonance frequency of a quarter- or half-wave CPW resonator.
.. math::
\begin{aligned}
f &= \frac{v_p}{4L} \mathtt{ (quarter-wave resonator)} \\
f &= \frac{v_p}{2L} \mathtt{ (half-wave resonator)}
\end{aligned}
The phase velocity is :math:`v_p = c_0 / \sqrt{\varepsilon_{\mathrm{eff}}}`.
See :cite:`simonsCoplanarWaveguideCircuits2001,m.pozarMicrowaveEngineering2012` for details.
Args:
length: Length of the resonator in μm.
epsilon_eff: Effective permittivity. If ``None`` (default),
computed from *cross_section* using :func:`~qpdk.models.cpw.cpw_parameters`.
media: Deprecated. Use *epsilon_eff* or *cross_section* instead.
cross_section: Cross-section specification (used only when
*epsilon_eff* and *media* are not provided).
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.
"""
if epsilon_eff is None:
if media is not None:
deprecated(
"The 'media' argument is deprecated. Use 'epsilon_eff' or 'cross_section' instead."
)(lambda: None)()
epsilon_eff = float(jnp.real(jnp.mean(media.ep_r)))
else:
width, gap = get_cpw_dimensions(cross_section)
epsilon_eff, _z0 = cpw_parameters(width, gap)
v_p = c_0 / jnp.sqrt(epsilon_eff)
coefficient = 4 if is_quarter_wave else 2
return float(jnp.squeeze(v_p / (coefficient * length * 1e-6)))
[docs]
def resonator(
f: sax.FloatArrayLike = DEFAULT_FREQUENCY,
length: sax.Float = 1000,
cross_section: CrossSectionSpec = "cpw",
) -> sax.SType:
"""S-parameter model for a simple transmission line resonator.
Args:
f: Array of frequency points in Hz
length: Physical length in µm
cross_section: The cross-section of the waveguide.
Returns:
sax.SType: S-parameters dictionary
"""
return straight(f=f, length=length, cross_section=cross_section)
[docs]
def resonator_half_wave(
f: sax.FloatArrayLike = DEFAULT_FREQUENCY,
length: sax.Float = 1000,
cross_section: CrossSectionSpec = "cpw",
) -> sax.SType:
"""S-parameter model for a half-wave resonator (open at both ends).
Args:
f: Array of frequency points in Hz
length: Physical length in µm
cross_section: The cross-section of the waveguide.
Returns:
sax.SType: S-parameters dictionary
"""
return straight(f=f, length=length, cross_section=cross_section)
[docs]
def resonator_quarter_wave(
f: sax.FloatArrayLike = DEFAULT_FREQUENCY,
length: sax.Float = 1000,
cross_section: CrossSectionSpec = "cpw",
) -> sax.SType:
"""S-parameter model for a quarter-wave resonator (shorted at one end).
Args:
f: Array of frequency points in Hz
length: Physical length in µm
cross_section: The cross-section of the waveguide.
Returns:
sax.SType: S-parameters dictionary
"""
return straight_shorted(f=f, length=length, cross_section=cross_section)
