"""Generic Models."""
import jax
import jax.numpy as jnp
import sax
from matplotlib import pyplot as plt
from sax.models.rf import (
admittance,
capacitor,
electrical_open,
electrical_short,
gamma_0_load,
impedance,
inductor,
tee,
)
from qpdk.models.constants import DEFAULT_FREQUENCY
__all__ = [
"admittance",
"capacitor",
"electrical_open",
"electrical_short",
"electrical_short_2_port",
"gamma_0_load",
"impedance",
"inductor",
"lc_resonator",
"lc_resonator_coupled",
"open",
"short",
"short_2_port",
"tee",
]
[docs]
@jax.jit
def electrical_short_2_port(f: sax.FloatArrayLike = DEFAULT_FREQUENCY) -> sax.SDict:
"""Electrical short 2-port connection Sax model.
Args:
f: Array of frequency points in Hz
Returns:
sax.SDict: S-parameters dictionary
"""
return electrical_short(f=f, n_ports=2)
short = electrical_short
open = electrical_open
short_2_port = electrical_short_2_port
[docs]
@jax.jit(static_argnames=["grounded"])
def lc_resonator(
f: sax.FloatArrayLike = DEFAULT_FREQUENCY,
capacitance: float = 100e-15,
inductance: float = 1e-9,
grounded: bool = False,
) -> sax.SDict:
r"""LC resonator Sax model with capacitor and inductor in parallel.
The resonance frequency is given by:
.. svgbob::
o1 ──┬──L──┬── o2
│ │
└──C──┘
If grounded=True, a 2-port short is connected to port o2:
.. svgbob::
o1 ──┬──L──┬──.
│ │ | "2-port ground"
└──C──┘ |
"o2"
.. math::
f_r = \frac{1}{2 \pi \sqrt{LC}}
For theory and relation to superconductors, see :cite:`gaoPhysicsSuperconductingMicrowave2008`.
Args:
f: Array of frequency points in Hz.
capacitance: Capacitance of the resonator in Farads.
inductance: Inductance of the resonator in Henries.
grounded: If True, add a 2-port ground to the second port.
Returns:
sax.SDict: S-parameters dictionary with ports o1 and o2.
"""
f = jnp.asarray(f)
instances = {
"capacitor": capacitor(f=f, capacitance=capacitance),
"inductor": inductor(f=f, inductance=inductance),
"tee_1": tee(f=f),
"tee_2": tee(f=f),
}
connections = {
"tee_1,o2": "capacitor,o1",
"tee_1,o3": "inductor,o1",
"capacitor,o2": "tee_2,o2",
"inductor,o2": "tee_2,o3",
}
if grounded:
instances["ground"] = electrical_short(f=f, n_ports=2)
connections["tee_2,o1"] = "ground,o1"
ports = {
"o1": "tee_1,o1",
"o2": "ground,o2",
}
else:
ports = {
"o1": "tee_1,o1",
"o2": "tee_2,o1",
}
return sax.evaluate_circuit_fg((connections, ports), instances)
[docs]
@jax.jit(static_argnames=["grounded"])
def lc_resonator_coupled(
f: sax.FloatArrayLike = DEFAULT_FREQUENCY,
capacitance: float = 100e-15,
inductance: float = 1e-9,
grounded: bool = False,
coupling_capacitance: float = 10e-15,
coupling_inductance: float = 0.0,
) -> sax.SDict:
r"""Coupled LC resonator Sax model.
This model extends the basic LC resonator by adding a coupling network
consisting of a parallel capacitor and inductor connected to one port
of the LC resonator via a tee junction.
The resonance frequency of the main LC resonator is given by:
.. math::
f_r = \frac{1}{2 \pi \sqrt{LC}}
The coupling network modifies the effective coupling to the resonator.
.. svgbob::
+──Lc──+ +──L──+
o1 ──────│ │────| │─── o2 or grounded o2
+──Cc──+ +──C──+
"LC resonator"
Where :math:`L_\text{c}` and :math:`C_\text{c}` are the coupling inductance and capacitance, respectively.
Args:
f: Array of frequency points in Hz.
capacitance: Capacitance of the main resonator in Farads.
inductance: Inductance of the main resonator in Henries.
grounded: If True, the resonator is grounded.
coupling_capacitance: Coupling capacitance in Farads.
coupling_inductance: Coupling inductance in Henries.
Returns:
sax.SDict: S-parameters dictionary with ports o1 and o2.
"""
f = jnp.asarray(f)
resonator = lc_resonator(
f=f, capacitance=capacitance, inductance=inductance, grounded=grounded
)
# Always use the full tee network topology for consistent behavior
# When an element has zero value, it naturally produces the correct S-parameters
instances: dict[str, sax.SType] = {
"resonator": resonator,
"tee_between": tee(f=f),
"tee_outer": tee(f=f),
"inductive_coupling": inductor(f=f, inductance=coupling_inductance),
"capacitive_coupling": capacitor(f=f, capacitance=coupling_capacitance),
}
connections = {
"tee_outer,o2": "inductive_coupling,o1",
"tee_outer,o3": "capacitive_coupling,o1",
"inductive_coupling,o2": "tee_between,o2",
"capacitive_coupling,o2": "tee_between,o3",
"tee_between,o1": "resonator,o1",
}
ports = {
"o1": "tee_outer,o1",
"o2": "resonator,o2",
}
return sax.evaluate_circuit_fg((connections, ports), instances)
if __name__ == "__main__":
f = jnp.linspace(1e9, 25e9, 201)
S = gamma_0_load(f=f, gamma_0=0.5 + 0.5j, n_ports=2)
for key in S:
plt.plot(f / 1e9, abs(S[key]) ** 2, label=key)
plt.ylim(-0.05, 1.05)
plt.xlabel("Frequency [GHz]")
plt.ylabel("S")
plt.grid(True)
plt.legend()
plt.show(block=False)
S_cap = capacitor(f=f, capacitance=(capacitance := 100e-15))
# print(S_cap)
plt.figure()
# Polar plot of S21 and S11
plt.subplot(121, projection="polar")
plt.plot(jnp.angle(S_cap[("o1", "o1")]), abs(S_cap[("o1", "o1")]), label="$S_{11}$")
plt.plot(jnp.angle(S_cap[("o1", "o2")]), abs(S_cap[("o2", "o1")]), label="$S_{21}$")
plt.title("S-parameters capacitor")
plt.legend()
# Magnitude and phase vs frequency
ax1 = plt.subplot(122)
ax1.plot(f / 1e9, abs(S_cap[("o1", "o1")]), label="|S11|", color="C0")
ax1.plot(f / 1e9, abs(S_cap[("o1", "o2")]), label="|S21|", color="C1")
ax1.set_xlabel("Frequency [GHz]")
ax1.set_ylabel("Magnitude [unitless]")
ax1.grid(True)
ax1.legend(loc="upper left")
ax2 = ax1.twinx()
ax2.plot(
f / 1e9,
jnp.angle(S_cap[("o1", "o1")]),
label="∠S11",
color="C0",
linestyle="--",
)
ax2.plot(
f / 1e9,
jnp.angle(S_cap[("o1", "o2")]),
label="∠S21",
color="C1",
linestyle="--",
)
ax2.set_ylabel("Phase [rad]")
ax2.legend(loc="upper right")
plt.title(f"Capacitor $S$-parameters ($C={capacitance * 1e15}\\,$fF)")
plt.show(block=False)
S_ind = inductor(f=f, inductance=(inductance := 1e-9))
# print(S_ind)
plt.figure()
plt.subplot(121, projection="polar")
plt.plot(jnp.angle(S_ind[("o1", "o1")]), abs(S_ind[("o1", "o1")]), label="$S_{11}$")
plt.plot(jnp.angle(S_ind[("o1", "o2")]), abs(S_ind[("o2", "o1")]), label="$S_{21}$")
plt.title("S-parameters inductor")
plt.legend()
ax1 = plt.subplot(122)
ax1.plot(f / 1e9, abs(S_ind[("o1", "o1")]), label="|S11|", color="C0")
ax1.plot(f / 1e9, abs(S_ind[("o1", "o2")]), label="|S21|", color="C1")
ax1.set_xlabel("Frequency [GHz]")
ax1.set_ylabel("Magnitude [unitless]")
ax1.grid(True)
ax1.legend(loc="upper left")
ax2 = ax1.twinx()
ax2.plot(
f / 1e9,
jnp.angle(S_ind[("o1", "o1")]),
label="∠S11",
color="C0",
linestyle="--",
)
ax2.plot(
f / 1e9,
jnp.angle(S_ind[("o1", "o2")]),
label="∠S21",
color="C1",
linestyle="--",
)
ax2.set_ylabel("Phase [rad]")
ax2.legend(loc="upper right")
plt.title(f"Inductor $S$-parameters ($L={inductance * 1e9}\\,$nH)")
plt.show()
