"""Tool for generating an S matrix automatically from a Tidy3d simulation and lumped port definitions."""
from __future__ import annotations
from typing import Dict, Tuple, Union
import numpy as np
import pydantic.v1 as pd
from ....components.base import cached_property
from ....components.data.data_array import (
DataArray,
FreqDataArray,
)
from ....components.data.monitor_data import (
MonitorData,
)
from ....components.data.sim_data import SimulationData
from ....components.geometry.utils_2d import snap_coordinate_to_grid
from ....components.microwave.data.monitor_data import AntennaMetricsData
from ....components.monitor import DirectivityMonitor
from ....components.simulation import Simulation
from ....components.source.time import GaussianPulse
from ....components.types import Ax
from ....components.viz import add_ax_if_none, equal_aspect
from ....constants import C_0, OHM
from ....exceptions import Tidy3dError, Tidy3dKeyError, ValidationError
from ....web.api.container import BatchData
from ..data.terminal import PortDataArray, TerminalPortDataArray
from ..ports.base_lumped import AbstractLumpedPort
from ..ports.coaxial_lumped import CoaxialLumpedPort
from ..ports.rectangular_lumped import LumpedPort
from ..ports.wave import WavePort
from .base import FWIDTH_FRAC, AbstractComponentModeler, TerminalPortType
[docs]
class TerminalComponentModeler(AbstractComponentModeler):
"""Tool for modeling two-terminal multiport devices and computing port parameters
with lumped and wave ports."""
ports: Tuple[TerminalPortType, ...] = pd.Field(
(),
title="Terminal Ports",
description="Collection of lumped and wave ports associated with the network. "
"For each port, one simulation will be run with a source that is associated with the port.",
)
radiation_monitors: tuple[DirectivityMonitor, ...] = pd.Field(
(),
title="Radiation Monitors",
description="Facilitates the calculation of figures-of-merit for antennas. "
"These monitor will be included in every simulation and record the radiated fields. ",
)
[docs]
@equal_aspect
@add_ax_if_none
def plot_sim(
self, x: float = None, y: float = None, z: float = None, ax: Ax = None, **kwargs
) -> Ax:
"""Plot a :class:`.Simulation` with all sources added for each port, for troubleshooting."""
plot_sources = []
for port_source in self.ports:
source_0 = port_source.to_source(self._source_time)
plot_sources.append(source_0)
sim_plot = self.simulation.copy(update=dict(sources=plot_sources))
return sim_plot.plot(x=x, y=y, z=z, ax=ax, **kwargs)
[docs]
@equal_aspect
@add_ax_if_none
def plot_sim_eps(
self, x: float = None, y: float = None, z: float = None, ax: Ax = None, **kwargs
) -> Ax:
"""Plot permittivity of the :class:`.Simulation` with all sources added for each port."""
plot_sources = []
for port_source in self.ports:
source_0 = port_source.to_source(self._source_time)
plot_sources.append(source_0)
sim_plot = self.simulation.copy(update=dict(sources=plot_sources))
return sim_plot.plot_eps(x=x, y=y, z=z, ax=ax, **kwargs)
@cached_property
def sim_dict(self) -> Dict[str, Simulation]:
"""Generate all the :class:`.Simulation` objects for the port parameter calculation."""
sim_dict = {}
# internal mesh override and snapping points are automatically generated from lumped elements.
lumped_resistors = [port.to_load() for port in self._lumped_ports]
# Apply the highest frequency in the simulation to define the grid, rather than the
# source's central frequency, to ensure an accurate solution over the entire range
grid_spec = self.simulation.grid_spec.copy(
update={
"wavelength": C_0 / np.max(self.freqs),
}
)
# Make an initial simulation with new grid_spec to determine where LumpedPorts are snapped
sim_wo_source = self.simulation.updated_copy(
grid_spec=grid_spec, lumped_elements=lumped_resistors
)
snap_centers = dict()
for port in self._lumped_ports:
port_center_on_axis = port.center[port.injection_axis]
new_port_center = snap_coordinate_to_grid(
sim_wo_source.grid, port_center_on_axis, port.injection_axis
)
snap_centers[port.name] = new_port_center
# Create monitors and snap to the center positions
field_monitors = [
mon
for port in self.ports
for mon in port.to_field_monitors(
self.freqs, snap_center=snap_centers.get(port.name), grid=sim_wo_source.grid
)
]
new_mnts = list(self.simulation.monitors) + field_monitors
if self.radiation_monitors is not None:
new_mnts = new_mnts + list(self.radiation_monitors)
new_lumped_elements = list(self.simulation.lumped_elements) + [
port.to_load(snap_center=snap_centers[port.name]) for port in self._lumped_ports
]
update_dict = dict(
monitors=new_mnts,
lumped_elements=new_lumped_elements,
)
# This is the new default simulation will all shared components added
sim_wo_source = sim_wo_source.copy(update=update_dict)
# Next, simulations are generated that include the source corresponding with the excitation port
for port in self._lumped_ports:
port_source = port.to_source(
self._source_time, snap_center=snap_centers[port.name], grid=sim_wo_source.grid
)
task_name = self._task_name(port=port)
sim_dict[task_name] = sim_wo_source.updated_copy(sources=[port_source])
# Check final simulations for grid size at lumped ports
for _, sim in sim_dict.items():
TerminalComponentModeler._check_grid_size_at_ports(sim, self._lumped_ports)
# Now, create simulations with wave port sources and mode solver monitors for computing port modes
for wave_port in self._wave_ports:
mode_monitor = wave_port.to_mode_solver_monitor(freqs=self.freqs)
# Source is placed just before the field monitor of the port
mode_src_pos = wave_port.center[wave_port.injection_axis] + self._shift_value_signed(
wave_port
)
port_source = wave_port.to_source(self._source_time, snap_center=mode_src_pos)
new_mnts_for_wave = new_mnts + [mode_monitor]
update_dict = dict(monitors=new_mnts_for_wave, sources=[port_source])
task_name = self._task_name(port=wave_port)
sim_dict[task_name] = sim_wo_source.copy(update=update_dict)
return sim_dict
@cached_property
def _source_time(self):
"""Helper to create a time domain pulse for the frequency range of interest."""
freq0 = np.mean(self.freqs)
fdiff = max(self.freqs) - min(self.freqs)
fwidth = max(fdiff, freq0 * FWIDTH_FRAC)
return GaussianPulse(
freq0=freq0, fwidth=fwidth, remove_dc_component=self.remove_dc_component
)
def _construct_smatrix(self) -> TerminalPortDataArray:
"""Post process :class:`.BatchData` to generate scattering matrix."""
return self._internal_construct_smatrix(batch_data=self.batch_data)
def _internal_construct_smatrix(self, batch_data: BatchData) -> TerminalPortDataArray:
"""Post process :class:`.BatchData` to generate scattering matrix, for internal use only."""
port_names = [port.name for port in self.ports]
values = np.zeros(
(len(self.freqs), len(port_names), len(port_names)),
dtype=complex,
)
coords = dict(
f=np.array(self.freqs),
port_out=port_names,
port_in=port_names,
)
a_matrix = TerminalPortDataArray(values, coords=coords)
b_matrix = a_matrix.copy(deep=True)
# Tabulate the reference impedances at each port and frequency
port_impedances = self._port_reference_impedances(batch_data=batch_data)
# loop through source ports
for port_in in self.ports:
sim_data = batch_data[self._task_name(port=port_in)]
a, b = self.compute_power_wave_amplitudes_at_each_port(port_impedances, sim_data)
indexer = dict(f=a.f, port_in=port_in.name, port_out=a.port)
a_matrix.loc[indexer] = a
b_matrix.loc[indexer] = b
s_matrix = self.ab_to_s(a_matrix, b_matrix)
return s_matrix
@pd.validator("simulation")
def _validate_3d_simulation(cls, val):
"""Error if :class:`.Simulation` is not a 3D simulation"""
if val.size.count(0.0) > 0:
raise ValidationError(
f"'{cls.__name__}' must be setup with a 3D simulation with all sizes greater than 0."
)
return val
@pd.validator("radiation_monitors")
def _validate_radiation_monitors(cls, val, values):
freqs = set(values.get("freqs"))
for rad_mon in val:
mon_freqs = rad_mon.freqs
is_subset = freqs.issuperset(mon_freqs)
if not is_subset:
raise ValidationError(
f"The frequencies in the radiation monitor '{rad_mon.name}' "
f"must be equal to or a subset of the frequencies in the '{cls.__name__}'."
)
return val
@staticmethod
def _check_grid_size_at_ports(simulation: Simulation, ports: list[Union[AbstractLumpedPort]]):
"""Raises :class:`.SetupError` if the grid is too coarse at port locations"""
yee_grid = simulation.grid.yee
for port in ports:
port._check_grid_size(yee_grid)
[docs]
def compute_power_wave_amplitudes_at_each_port(
self, port_reference_impedances: PortDataArray, sim_data: SimulationData
) -> tuple[PortDataArray, PortDataArray]:
"""Compute the incident and reflected power wave amplitudes at each port.
The computed amplitudes have not been normalized.
Parameters
----------
port_reference_impedances : :class:`.PortDataArray`
Reference impedance at each port.
sim_data : :class:`.SimulationData`
Results from the simulation.
Returns
-------
tuple[:class:`.PortDataArray`, :class:`.PortDataArray`]
Incident (a) and reflected (b) power wave amplitudes at each port.
"""
port_names = [port.name for port in self.ports]
values = np.zeros(
(len(self.freqs), len(port_names)),
dtype=complex,
)
coords = dict(
f=np.array(self.freqs),
port=port_names,
)
V_matrix = PortDataArray(values, coords=coords)
I_matrix = V_matrix.copy(deep=True)
a = V_matrix.copy(deep=True)
b = V_matrix.copy(deep=True)
for port_out in self.ports:
V_out, I_out = self.compute_port_VI(port_out, sim_data)
indexer = dict(port=port_out.name)
V_matrix.loc[indexer] = V_out
I_matrix.loc[indexer] = I_out
V_numpy = V_matrix.values
I_numpy = I_matrix.values
Z_numpy = port_reference_impedances.values
# Check to make sure sign is consistent for all impedance values
self._check_port_impedance_sign(Z_numpy)
# # Check for negative real part of port impedance and flip the V and Z signs accordingly
negative_real_Z = np.real(Z_numpy) < 0
V_numpy = np.where(negative_real_Z, -V_numpy, V_numpy)
Z_numpy = np.where(negative_real_Z, -Z_numpy, Z_numpy)
F_numpy = TerminalComponentModeler._compute_F(Z_numpy)
# Equation 4.67 - Pozar - Microwave Engineering 4ed
a.values = F_numpy * (V_numpy + Z_numpy * I_numpy)
b.values = F_numpy * (V_numpy - np.conj(Z_numpy) * I_numpy)
return a, b
[docs]
@staticmethod
def compute_port_VI(
port_out: TerminalPortType, sim_data: SimulationData
) -> tuple[FreqDataArray, FreqDataArray]:
"""Compute the port voltages and currents.
Parameters
----------
port_out : ``TerminalPortType``
Port for computing voltage and current.
sim_data : :class:`.SimulationData`
Results from simulation containing field data.
Returns
-------
tuple[FreqDataArray, FreqDataArray]
Voltage and current values at the port as frequency arrays.
"""
voltage = port_out.compute_voltage(sim_data)
current = port_out.compute_current(sim_data)
return voltage, current
[docs]
@staticmethod
def compute_power_wave_amplitudes(
port: Union[LumpedPort, CoaxialLumpedPort], sim_data: SimulationData
) -> tuple[FreqDataArray, FreqDataArray]:
"""Compute the incident and reflected power wave amplitudes at a lumped port.
The computed amplitudes have not been normalized.
Parameters
----------
port : Union[:class:`.LumpedPort`, :class:`.CoaxialLumpedPort`]
Port for computing voltage and current.
sim_data : :class:`.SimulationData`
Results from the simulation.
Returns
-------
tuple[FreqDataArray, FreqDataArray]
Incident (a) and reflected (b) power wave amplitude frequency arrays.
"""
voltage, current = TerminalComponentModeler.compute_port_VI(port, sim_data)
# Amplitudes for the incident and reflected power waves
a = (voltage + port.impedance * current) / 2 / np.sqrt(np.real(port.impedance))
b = (voltage - port.impedance * current) / 2 / np.sqrt(np.real(port.impedance))
return a, b
[docs]
@staticmethod
def compute_power_delivered_by_port(
port: Union[LumpedPort, CoaxialLumpedPort], sim_data: SimulationData
) -> FreqDataArray:
"""Compute the power delivered to the network by a lumped port.
Parameters
----------
port : Union[:class:`.LumpedPort`, :class:`.CoaxialLumpedPort`]
Port for computing voltage and current.
sim_data : :class:`.SimulationData`
Results from the simulation.
Returns
-------
FreqDataArray
Power in units of Watts as a frequency array.
"""
a, b = TerminalComponentModeler.compute_power_wave_amplitudes(sim_data=sim_data, port=port)
# Power delivered is the incident power minus the reflected power
return 0.5 * (np.abs(a) ** 2 - np.abs(b) ** 2)
[docs]
@staticmethod
def ab_to_s(
a_matrix: TerminalPortDataArray, b_matrix: TerminalPortDataArray
) -> TerminalPortDataArray:
"""Get the scattering matrix given the power wave matrices."""
# Ensure dimensions are ordered properly
a_matrix = a_matrix.transpose(*TerminalPortDataArray._dims)
b_matrix = b_matrix.transpose(*TerminalPortDataArray._dims)
s_matrix = a_matrix.copy(deep=True)
a_vals = s_matrix.copy(deep=True).values
b_vals = b_matrix.copy(deep=True).values
s_vals = np.matmul(b_vals, AbstractComponentModeler.inv(a_vals))
s_matrix.data = s_vals
return s_matrix
[docs]
@staticmethod
def s_to_z(
s_matrix: TerminalPortDataArray, reference: Union[complex, PortDataArray]
) -> DataArray:
"""Get the impedance matrix given the scattering matrix and a reference impedance."""
# Ensure dimensions are ordered properly
z_matrix = s_matrix.transpose(*TerminalPortDataArray._dims).copy(deep=True)
s_vals = z_matrix.values
eye = np.eye(len(s_matrix.port_out.values), len(s_matrix.port_in.values))
if isinstance(reference, PortDataArray):
# From Equation 4.68 - Pozar - Microwave Engineering 4ed
# Ensure that Zport, F, and Finv act as diagonal matrices when multiplying by left or right
shape_left = (len(s_matrix.f), len(s_matrix.port_out), 1)
shape_right = (len(s_matrix.f), 1, len(s_matrix.port_in))
Zport = reference.values.reshape(shape_right)
F = TerminalComponentModeler._compute_F(Zport).reshape(shape_right)
Finv = (1.0 / F).reshape(shape_left)
FinvSF = Finv * s_vals * F
RHS = eye * np.conj(Zport) + FinvSF * Zport
LHS = eye - FinvSF
z_vals = np.matmul(AbstractComponentModeler.inv(LHS), RHS)
else:
# Simpler case when all port impedances are the same
z_vals = (
np.matmul(AbstractComponentModeler.inv(eye - s_vals), (eye + s_vals)) * reference
)
z_matrix.data = z_vals
return z_matrix
@cached_property
def port_reference_impedances(self) -> PortDataArray:
"""The reference impedance used at each port for definining power wave amplitudes."""
return self._port_reference_impedances(self.batch_data)
def _port_reference_impedances(self, batch_data: BatchData) -> PortDataArray:
"""Tabulates the reference impedance of each port at each frequency using the
supplied :class:`.BatchData`.
"""
port_names = [port.name for port in self.ports]
values = np.zeros(
(len(self.freqs), len(port_names)),
dtype=complex,
)
coords = dict(f=np.array(self.freqs), port=port_names)
port_impedances = PortDataArray(values, coords=coords)
for port in self.ports:
if isinstance(port, WavePort):
# Mode solver data for each wave port is stored in its associated SimulationData
sim_data_port = batch_data[self._task_name(port=port)]
# WavePorts have a port impedance calculated from its associated modal field distribution
# and is frequency dependent.
impedances = port.compute_port_impedance(sim_data_port).values
port_impedances.loc[dict(port=port.name)] = impedances.squeeze()
else:
# LumpedPorts have a constant reference impedance
port_impedances.loc[dict(port=port.name)] = np.full(len(self.freqs), port.impedance)
port_impedances = TerminalComponentModeler._set_port_data_array_attributes(port_impedances)
return port_impedances
@staticmethod
def _compute_F(Z_numpy: np.array):
"""Helper to convert port impedance matrix to F, which is used for
computing generalized scattering parameters."""
return 1.0 / (2.0 * np.sqrt(np.real(Z_numpy)))
@cached_property
def _lumped_ports(self) -> list[AbstractLumpedPort]:
"""A list of all lumped ports in the ``TerminalComponentModeler``"""
return [port for port in self.ports if isinstance(port, AbstractLumpedPort)]
@cached_property
def _wave_ports(self) -> list[WavePort]:
"""A list of all wave ports in the ``TerminalComponentModeler``"""
return [port for port in self.ports if isinstance(port, WavePort)]
@staticmethod
def _set_port_data_array_attributes(data_array: PortDataArray) -> PortDataArray:
"""Helper to set additional metadata for ``PortDataArray``."""
data_array.name = "Z0"
return data_array.assign_attrs(units=OHM, long_name="characteristic impedance")
@staticmethod
def _check_port_impedance_sign(Z_numpy: np.ndarray):
"""Sanity check for consistent sign of real part of Z for each port across all frequencies."""
for port_idx in range(Z_numpy.shape[1]):
port_Z = Z_numpy[:, port_idx]
signs = np.sign(np.real(port_Z))
if not np.all(signs == signs[0]):
raise Tidy3dError(
f"Inconsistent sign of real part of Z detected for port {port_idx}. "
"If you received this error, please create an issue in the Tidy3D "
"github repository."
)
[docs]
def get_radiation_monitor_by_name(self, monitor_name: str) -> DirectivityMonitor:
"""Find and return a :class:`.DirectivityMonitor` monitor by its name.
Parameters
----------
monitor_name : str
Name of the monitor to find.
Returns
-------
:class:`.DirectivityMonitor`
The monitor matching the given name.
Raises
------
``Tidy3dKeyError``
If no monitor with the given name exists.
"""
for monitor in self.radiation_monitors:
if monitor.name == monitor_name:
return monitor
raise Tidy3dKeyError(f"No radiation monitor named '{monitor_name}'.")
def _monitor_data_at_port_amplitude(
self,
port: TerminalPortType,
sim_data: SimulationData,
monitor_data: MonitorData,
a_port: Union[FreqDataArray, complex],
) -> MonitorData:
"""Normalize the monitor data to a desired complex amplitude of a port,
represented by ``a_port``, where :math:`\\frac{1}{2}|a|^2` is the power
incident from the port into the system.
"""
a_raw, _ = self.compute_power_wave_amplitudes_at_each_port(
self.port_reference_impedances, sim_data
)
a_raw_port = a_raw.sel(port=port.name)
if not isinstance(a_port, FreqDataArray):
freqs = list(monitor_data.monitor.freqs)
array_vals = a_port * np.ones(len(freqs))
a_port = FreqDataArray(array_vals, coords=dict(f=freqs))
scale_array = a_port / a_raw_port
return monitor_data.scale_fields_by_freq_array(scale_array, method="nearest")
[docs]
def get_antenna_metrics_data(
self, port_amplitudes: dict[str, complex] = None, monitor_name: str = None
) -> AntennaMetricsData:
"""Calculate antenna parameters using superposition of fields from multiple port excitations.
The method computes the radiated far fields and port excitation power wave amplitudes
for a superposition of port excitations, which can be used to analyze antenna radiation
characteristics.
Parameters
----------
port_amplitudes : dict[str, complex] = None
Dictionary mapping port names to their desired excitation amplitudes. For each port,
:math:`\\frac{1}{2}|a|^2` represents the incident power from that port into the system.
If None, uses only the first port without any scaling of the raw simulation data.
monitor_name : str = None
Name of the :class:`.DirectivityMonitor` to use for calculating far fields.
If None, uses the first monitor in `radiation_monitors`.
Returns
-------
:class:`.AntennaMetricsData`
Container with antenna parameters including directivity, gain, and radiation efficiency,
computed from the superposition of fields from all excited ports.
"""
# Use the first port as default if none specified
if port_amplitudes is None:
port_amplitudes = {self.ports[0].name: None}
port_names = [port.name for port in self.ports]
# Check port names, and create map from port to amplitude
port_dict = {}
for key in port_amplitudes.keys():
port = self.get_port_by_name(port_name=key)
port_dict[port] = port_amplitudes[key]
# Get the radiation monitor, use first as default
# if none specified
if monitor_name is None:
rad_mon = self.radiation_monitors[0]
else:
rad_mon = self.get_radiation_monitor_by_name(monitor_name)
# Create data arrays for holding the superposition of all port power wave amplitudes
f = list(rad_mon.freqs)
coords = dict(f=f, port=port_names)
a_sum = PortDataArray(np.zeros((len(f), len(port_names)), dtype=complex), coords=coords)
b_sum = a_sum.copy()
# Retrieve associated simulation data
combined_directivity_data = None
for port, amplitude in port_dict.items():
sim_data_port = self.batch_data[self._task_name(port=port)]
radiation_data = sim_data_port[rad_mon.name]
a, b = self.compute_power_wave_amplitudes_at_each_port(
self.port_reference_impedances, sim_data_port
)
# Select a possible subset of frequencies
a = a.sel(f=f)
b = b.sel(f=f)
a_raw = a.sel(port=port.name)
if amplitude is None:
# No scaling performed when amplitude is None
scaled_directivity_data = sim_data_port[rad_mon.name]
scale_factor = 1.0
else:
scaled_directivity_data = self._monitor_data_at_port_amplitude(
port, sim_data_port, radiation_data, amplitude
)
scale_factor = amplitude / a_raw
a = scale_factor * a
b = scale_factor * b
# Combine the possibly scaled directivity data and the power wave amplitudes
if combined_directivity_data is None:
combined_directivity_data = scaled_directivity_data
else:
combined_directivity_data = combined_directivity_data + scaled_directivity_data
a_sum += a
b_sum += b
# Compute and add power measures to results
power_incident = np.real(0.5 * a_sum * np.conj(a_sum)).sum(dim="port")
power_reflected = np.real(0.5 * b_sum * np.conj(b_sum)).sum(dim="port")
return AntennaMetricsData.from_directivity_data(
combined_directivity_data, power_incident, power_reflected
)
