"""S-parameter models for generic components."""
from functools import partial
from pprint import pprint
import jax
import jax.numpy as jnp
import sax
from jax.typing import ArrayLike
[docs]
@partial(jax.jit, inline=True, static_argnames=("n_ports"))
def gamma_0_load(
f: ArrayLike = jnp.array([5e9]),
gamma_0: int | float | complex = 0,
n_ports: int = 1,
) -> sax.SType:
r"""Connection with given reflection coefficient.
Args:
f: Array of frequency points in Hz
gamma_0: Reflection coefficient Γ₀ of connection
n_ports: Number of ports in component. The diagonal ports of the matrix
are set to Γ₀ and the off-diagonal ports to 0.
Returns:
sax.SType: S-parameters dictionary where :math:`S = \Gamma_0I_\text{n\_ports}`
"""
sdict = {
(f"o{i}", f"o{i}"): jnp.full(len(f), gamma_0) for i in range(1, n_ports + 1)
}
sdict |= {
(f"o{i}", f"o{j}"): jnp.zeros(len(f), dtype=complex)
for i in range(1, n_ports + 1)
for j in range(i + 1, n_ports + 1)
}
return sax.reciprocal(sdict)
[docs]
@partial(jax.jit, inline=True, static_argnames=("n_ports"))
def short(
f: ArrayLike = jnp.array([5e9]),
n_ports: int = 1,
) -> sax.SType:
r"""Electrical short connections Sax model.
Args:
f: Array of frequency points in Hz
n_ports: Number of ports to set as shorted
Returns:
sax.SType: S-parameters dictionary where :math:`S = -I_\text{n\_ports}`
"""
return gamma_0_load(f=f, gamma_0=-1, n_ports=n_ports)
[docs]
@partial(jax.jit, inline=True, static_argnames=("n_ports"))
def open(
f: ArrayLike = jnp.array([5e9]),
n_ports: int = 1,
) -> sax.SType:
r"""Electrical open connection Sax model.
Args:
f: Array of frequency points in Hz
n_ports: Number of ports to set as opened
Returns:
sax.SType: S-parameters dictionary where :math:`S = I_\text{n\_ports}`
"""
return gamma_0_load(f=f, gamma_0=1, n_ports=n_ports)
[docs]
@partial(jax.jit, inline=True)
def tee(f: ArrayLike = jnp.array([5e9])) -> sax.SType:
"""Ideal 3-port power divider/combiner (T-junction).
Args:
f: Array of frequency points in Hz
Returns:
sax.SType: S-parameters dictionary
"""
sdict = {(f"o{i}", f"o{i}"): jnp.full(len(f), -1 / 3) for i in range(1, 4)}
sdict |= {
(f"o{i}", f"o{j}"): jnp.full(len(f), 2 / 3)
for i in range(1, 4)
for j in range(i + 1, 4)
}
return sax.reciprocal(sdict)
# return sax.models.splitters.splitter_ideal(wl=f)
[docs]
@partial(jax.jit, inline=True)
def single_impedance_element(
z: int | float | complex = 50,
z0: int | float | complex = 50,
) -> sax.SType:
r"""Single impedance element Sax model.
See :cite:`m.pozarMicrowaveEngineering2012` for details.
Args:
z: Impedance in Ω
z0: Reference impedance in Ω. This may be retrieved from a scikit-rf
Media object using `z0 = media.z0`.
Returns:
sax.SType: S-parameters dictionary
"""
sdict = {
("o1", "o1"): z / (z + 2 * z0),
("o1", "o2"): 2 * z0 / (2 * z0 + z),
("o2", "o2"): z / (z + 2 * z0),
}
return sax.reciprocal(sdict)
[docs]
@partial(jax.jit, inline=True)
def single_admittance_element(
y: int | float | complex = 1 / 50,
) -> sax.SType:
r"""Single admittance element Sax model.
See :cite:`m.pozarMicrowaveEngineering2012` for details.
Args:
y: Admittance
Returns:
sax.SType: S-parameters dictionary
"""
sdict = {
("o1", "o1"): 1 / (1 + y),
("o1", "o2"): y / (1 + y),
("o2", "o2"): 1 / (1 + y),
}
return sax.reciprocal(sdict)
[docs]
@partial(jax.jit, inline=True)
def capacitor(
f: ArrayLike = jnp.array([5e9]),
capacitance: float = 1e-15,
z0: int | float | complex = 50,
) -> sax.SType:
r"""Ideal capacitor () Sax model.
See :cite:`m.pozarMicrowaveEngineering2012` for details.
Args:
f: Array of frequency points in Hz
capacitance: Capacitance in Farads
z0: Reference impedance in Ω. This may be retrieved from a scikit-rf
Media object using `z0 = media.z0`.
Returns:
sax.SType: S-parameters dictionary
"""
ω = 2 * jnp.pi * jnp.asarray(f)
# Y = 2 * (1j * ω * capacitance * z0)
# return single_admittance_element(y=Y)
Z𞁞 = 1 / (1j * ω * capacitance)
return single_impedance_element(z=Z𞁞, z0=z0)
[docs]
@partial(jax.jit, inline=True)
def inductor(
f: ArrayLike = jnp.array([5e9]),
inductance: float = 1e-12,
z0: int | float | complex = 50,
) -> sax.SType:
r"""Ideal inductor () Sax model.
See :cite:`m.pozarMicrowaveEngineering2012` for details.
Args:
f: Array of frequency points in Hz
inductance: Inductance in Henries
z0: Reference impedance in Ω. This may be retrieved from a scikit-rf
Media object using `z0 = media.z0`.
Returns:
sax.SType: S-parameters dictionary
"""
ω = 2 * jnp.pi * jnp.asarray(f)
Zᵢ = 1j * ω * inductance
return single_impedance_element(z=Zᵢ, z0=z0)
if __name__ == "__main__":
from matplotlib import pyplot as plt
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, capacitance=(capacitance := 100e-15))
pprint(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, inductance=(inductance := 1e-9))
pprint(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()
