Microstrip Modes (2D Cross-Section)¶
This notebook builds a simple boxed microstrip cross-section (substrate + air + PEC strip conductor), solves eigenmodes with WaveguideModeSolver, and plots the first fields.
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from palacetoolkit.mode_solver import WaveguideModeSolver
from palacetoolkit.viz import run_with_scrollable_output, view_mesh
import importlib
import inspect
import gmsh
import matplotlib.pyplot as plt
import numpy as np
import palacetoolkit.utils as ptk_utils
importlib.reload(ptk_utils)
view_fe_mesh_2d = ptk_utils.view_fe_mesh_2d
view_fields_2d = ptk_utils.view_fields_2d
write_and_finalize_gmsh = ptk_utils.write_and_finalize_gmsh
from palacetoolkit.mode_solver import WaveguideModeSolver
from palacetoolkit.viz import run_with_scrollable_output, view_mesh
import importlib
import inspect
import gmsh
import matplotlib.pyplot as plt
import numpy as np
import palacetoolkit.utils as ptk_utils
importlib.reload(ptk_utils)
view_fe_mesh_2d = ptk_utils.view_fe_mesh_2d
view_fields_2d = ptk_utils.view_fields_2d
write_and_finalize_gmsh = ptk_utils.write_and_finalize_gmsh
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sig = inspect.signature(WaveguideModeSolver.__init__)
print("WaveguideModeSolver.__init__ signature:")
print(sig)
print("\nPEC conductor support via boundary attributes:", "pec_bdr" in sig.parameters)
print("The solver enforces PEC by essential DOF elimination on selected boundary attributes.")
sig = inspect.signature(WaveguideModeSolver.__init__)
print("WaveguideModeSolver.__init__ signature:")
print(sig)
print("\nPEC conductor support via boundary attributes:", "pec_bdr" in sig.parameters)
print("The solver enforces PEC by essential DOF elimination on selected boundary attributes.")
WaveguideModeSolver.__init__ signature: (self, mesh, order=1, mu_inv=1.0, eps=1.0, pec_bdr='all') PEC conductor support via boundary attributes: True The solver enforces PEC by essential DOF elimination on selected boundary attributes.
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def make_microstrip_mesh(
box_w=8.0,
h_sub=1.0,
h_air=3.0,
strip_w=1.8,
strip_t=0.06,
lc_bulk=0.18,
lc_strip=0.05,
filename=None,
):
gmsh.initialize()
gmsh.option.setNumber("General.Verbosity", 0)
gmsh.model.add("microstrip_modes")
sub = gmsh.model.occ.addRectangle(-box_w / 2, -h_sub, 0, box_w, h_sub)
air = gmsh.model.occ.addRectangle(-box_w / 2, 0.0, 0, box_w, h_air)
strip = gmsh.model.occ.addRectangle(-strip_w / 2, 0.0, 0, strip_w, strip_t)
_, outmap = gmsh.model.occ.fragment([(2, sub), (2, air), (2, strip)], [])
strip_parts = list(outmap[2])
gmsh.model.occ.remove(strip_parts, recursive=True)
gmsh.model.occ.synchronize()
all_surfs = [t for _, t in gmsh.model.getEntities(2)]
substrate_surfs = []
air_surfs = []
for tag in all_surfs:
_, cy, _ = gmsh.model.occ.getCenterOfMass(2, tag)
if cy < -1e-9:
substrate_surfs.append(tag)
else:
air_surfs.append(tag)
if not substrate_surfs or not air_surfs:
gmsh.finalize()
raise RuntimeError("Failed to classify substrate/air surfaces for microstrip mesh")
gmsh.model.addPhysicalGroup(2, substrate_surfs, tag=1, name="substrate")
gmsh.model.addPhysicalGroup(2, air_surfs, tag=2, name="air")
bnd = gmsh.model.getBoundary([(2, t) for t in substrate_surfs + air_surfs], oriented=False, combined=False)
edge_tags = sorted({abs(t) for _, t in bnd})
strip_edges = []
ground_edges = []
open_edges = []
for et in edge_tags:
ex, ey, _ = gmsh.model.occ.getCenterOfMass(1, et)
on_strip_x = abs(ex) <= strip_w / 2 + 1e-6
on_strip_y = (-1e-6 <= ey <= strip_t + 1e-6)
if on_strip_x and on_strip_y:
strip_edges.append(et)
continue
# Ground plane is the lower boundary of the simulation box.
if abs(ey + h_sub) <= 1e-6:
ground_edges.append(et)
else:
open_edges.append(et)
if ground_edges:
gmsh.model.addPhysicalGroup(1, ground_edges, tag=1, name="ground_plane")
if strip_edges:
gmsh.model.addPhysicalGroup(1, strip_edges, tag=2, name="strip_conductor")
if open_edges:
gmsh.model.addPhysicalGroup(1, open_edges, tag=3, name="open_boundary")
for _, ptag in gmsh.model.getEntities(0):
x, y, _ = gmsh.model.getValue(0, ptag, [])
near_strip = (abs(x) <= strip_w / 2 + 0.4 and -0.1 <= y <= strip_t + 0.5)
gmsh.model.mesh.setSize([(0, ptag)], lc_strip if near_strip else lc_bulk)
gmsh.model.mesh.generate(2)
return write_and_finalize_gmsh(filename, prefix="wg_microstrip_")
def make_microstrip_mesh(
box_w=8.0,
h_sub=1.0,
h_air=3.0,
strip_w=1.8,
strip_t=0.06,
lc_bulk=0.18,
lc_strip=0.05,
filename=None,
):
gmsh.initialize()
gmsh.option.setNumber("General.Verbosity", 0)
gmsh.model.add("microstrip_modes")
sub = gmsh.model.occ.addRectangle(-box_w / 2, -h_sub, 0, box_w, h_sub)
air = gmsh.model.occ.addRectangle(-box_w / 2, 0.0, 0, box_w, h_air)
strip = gmsh.model.occ.addRectangle(-strip_w / 2, 0.0, 0, strip_w, strip_t)
_, outmap = gmsh.model.occ.fragment([(2, sub), (2, air), (2, strip)], [])
strip_parts = list(outmap[2])
gmsh.model.occ.remove(strip_parts, recursive=True)
gmsh.model.occ.synchronize()
all_surfs = [t for _, t in gmsh.model.getEntities(2)]
substrate_surfs = []
air_surfs = []
for tag in all_surfs:
_, cy, _ = gmsh.model.occ.getCenterOfMass(2, tag)
if cy < -1e-9:
substrate_surfs.append(tag)
else:
air_surfs.append(tag)
if not substrate_surfs or not air_surfs:
gmsh.finalize()
raise RuntimeError("Failed to classify substrate/air surfaces for microstrip mesh")
gmsh.model.addPhysicalGroup(2, substrate_surfs, tag=1, name="substrate")
gmsh.model.addPhysicalGroup(2, air_surfs, tag=2, name="air")
bnd = gmsh.model.getBoundary([(2, t) for t in substrate_surfs + air_surfs], oriented=False, combined=False)
edge_tags = sorted({abs(t) for _, t in bnd})
strip_edges = []
ground_edges = []
open_edges = []
for et in edge_tags:
ex, ey, _ = gmsh.model.occ.getCenterOfMass(1, et)
on_strip_x = abs(ex) <= strip_w / 2 + 1e-6
on_strip_y = (-1e-6 <= ey <= strip_t + 1e-6)
if on_strip_x and on_strip_y:
strip_edges.append(et)
continue
# Ground plane is the lower boundary of the simulation box.
if abs(ey + h_sub) <= 1e-6:
ground_edges.append(et)
else:
open_edges.append(et)
if ground_edges:
gmsh.model.addPhysicalGroup(1, ground_edges, tag=1, name="ground_plane")
if strip_edges:
gmsh.model.addPhysicalGroup(1, strip_edges, tag=2, name="strip_conductor")
if open_edges:
gmsh.model.addPhysicalGroup(1, open_edges, tag=3, name="open_boundary")
for _, ptag in gmsh.model.getEntities(0):
x, y, _ = gmsh.model.getValue(0, ptag, [])
near_strip = (abs(x) <= strip_w / 2 + 0.4 and -0.1 <= y <= strip_t + 0.5)
gmsh.model.mesh.setSize([(0, ptag)], lc_strip if near_strip else lc_bulk)
gmsh.model.mesh.generate(2)
return write_and_finalize_gmsh(filename, prefix="wg_microstrip_")
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eps_sub = 9.8
eps_air = 1.0
mu_r = 1.0
omega = 18.0
kn_air = omega * np.sqrt(mu_r * eps_air)
kn_sub = omega * np.sqrt(mu_r * eps_sub)
print(f"Reference phase window (air to substrate): {kn_air:.4f} < kn < {kn_sub:.4f}")
eps_sub = 9.8
eps_air = 1.0
mu_r = 1.0
omega = 18.0
kn_air = omega * np.sqrt(mu_r * eps_air)
kn_sub = omega * np.sqrt(mu_r * eps_sub)
print(f"Reference phase window (air to substrate): {kn_air:.4f} < kn < {kn_sub:.4f}")
Reference phase window (air to substrate): 18.0000 < kn < 56.3489
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mesh_file = run_with_scrollable_output(
make_microstrip_mesh,
box_w=8.0,
h_sub=1.0,
h_air=3.0,
strip_w=1.8,
strip_t=0.06,
lc_bulk=0.18,
lc_strip=0.05,
title="Microstrip mesh generation",
max_lines=10,
)
view_mesh(mesh_file)
mu_inv = {1: 1.0 / mu_r, 2: 1.0 / mu_r}
eps = {1: eps_sub, 2: eps_air}
# WaveguideModeSolver currently supports PEC marking via pec_bdr; it does not
# provide an absorbing boundary-condition model.
pec_bdr = [1, 2] # ground plane + strip conductor
solver = WaveguideModeSolver(mesh_file, order=2, mu_inv=mu_inv, eps=eps, pec_bdr=pec_bdr)
results = solver.solve(omega, num_modes=8, mode_idx=1)
print("Computed microstrip modes:")
for i, kn in enumerate(results["kn"], start=1):
if kn_air < kn.real < kn_sub and abs(kn.imag) < 0.1 * abs(kn.real):
mode_type = "bound/hybrid"
elif abs(kn.imag) > 0.1 * abs(kn.real):
mode_type = "evanescent"
else:
mode_type = "radiative or box mode"
print(f" Mode {i:2d}: kn={kn.real:+10.6f}{kn.imag:+10.6f}j [{mode_type}]")
mesh_file = run_with_scrollable_output(
make_microstrip_mesh,
box_w=8.0,
h_sub=1.0,
h_air=3.0,
strip_w=1.8,
strip_t=0.06,
lc_bulk=0.18,
lc_strip=0.05,
title="Microstrip mesh generation",
max_lines=10,
)
view_mesh(mesh_file)
mu_inv = {1: 1.0 / mu_r, 2: 1.0 / mu_r}
eps = {1: eps_sub, 2: eps_air}
# WaveguideModeSolver currently supports PEC marking via pec_bdr; it does not
# provide an absorbing boundary-condition model.
pec_bdr = [1, 2] # ground plane + strip conductor
solver = WaveguideModeSolver(mesh_file, order=2, mu_inv=mu_inv, eps=eps, pec_bdr=pec_bdr)
results = solver.solve(omega, num_modes=8, mode_idx=1)
print("Computed microstrip modes:")
for i, kn in enumerate(results["kn"], start=1):
if kn_air < kn.real < kn_sub and abs(kn.imag) < 0.1 * abs(kn.real):
mode_type = "bound/hybrid"
elif abs(kn.imag) > 0.1 * abs(kn.real):
mode_type = "evanescent"
else:
mode_type = "radiative or box mode"
print(f" Mode {i:2d}: kn={kn.real:+10.6f}{kn.imag:+10.6f}j [{mode_type}]")
Loading mesh file: /tmp/wg_microstrip__bov39xb.msh
Groups to render transparent: ['air_none', 'air_plastic_enclosure']
Mesh loaded successfully with 2 cell blocks
Found 5388 triangles total
Physical group tags in mesh: {1: 'substrate', 2: 'air'}
FE spaces: ND dofs = 27152, H1 dofs = 10988, total = 38140 Essential DOFs: ND = 242, H1 = 243, total = 485
Solving eigenvalue problem (omega = 18, sigma = -3492.72, size = 38140)...
Found 8 modes:
Mode 1: kn = +5.63384559e+01 -0.00000000e+00j <-- selected
Mode 2: kn = +5.63261060e+01 -0.00000000e+00j
Mode 3: kn = +5.63247853e+01 -0.00000000e+00j
Mode 4: kn = +5.63172001e+01 -0.00000000e+00j
Mode 5: kn = +5.63089125e+01 -0.00000000e+00j
Mode 6: kn = +5.62972038e+01 -0.00000000e+00j
Mode 7: kn = +5.62816967e+01 -0.00000000e+00j
Mode 8: kn = +5.62655780e+01 -0.00000000e+00j
Computed microstrip modes:
Mode 1: kn=+56.338456 -0.000000j [bound/hybrid]
Mode 2: kn=+56.326106 -0.000000j [bound/hybrid]
Mode 3: kn=+56.324785 -0.000000j [bound/hybrid]
Mode 4: kn=+56.317200 -0.000000j [bound/hybrid]
Mode 5: kn=+56.308912 -0.000000j [bound/hybrid]
Mode 6: kn=+56.297204 -0.000000j [bound/hybrid]
Mode 7: kn=+56.281697 -0.000000j [bound/hybrid]
Mode 8: kn=+56.265578 -0.000000j [bound/hybrid]
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view_fe_mesh_2d(
mesh_file=mesh_file,
eps=eps,
title="Microstrip FE Mesh and Materials",
show_edges=True,
)
view_fe_mesh_2d(
mesh_file=mesh_file,
eps=eps,
title="Microstrip FE Mesh and Materials",
show_edges=True,
)
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view_fields_2d(
solver=solver,
results=results,
mesh_file=mesh_file,
eps=eps,
pec_bdr=pec_bdr,
include_streamplot=True,
streamplot_density=1.2,
streamplot_show_arrows=True,
streamplot_normalize=True,
streamplot_seed_from_field=True,
streamplot_seed_frac=0.1,
streamplot_seed_stride=2,
streamplot_mask_weak=True,
streamplot_min_frac=0.1,
num_modes=3,
nx=80,
ny=60,
cmap="hot",
title="Microstrip First Modes (Boxed Cross-Section)",
)
view_fields_2d(
solver=solver,
results=results,
mesh_file=mesh_file,
eps=eps,
pec_bdr=pec_bdr,
include_streamplot=True,
streamplot_density=1.2,
streamplot_show_arrows=True,
streamplot_normalize=True,
streamplot_seed_from_field=True,
streamplot_seed_frac=0.1,
streamplot_seed_stride=2,
streamplot_mask_weak=True,
streamplot_min_frac=0.1,
num_modes=3,
nx=80,
ny=60,
cmap="hot",
title="Microstrip First Modes (Boxed Cross-Section)",
)
MFEM Warning: 18 points were not found ... in function: virtual int mfem::Mesh::FindPoints(mfem::DenseMatrix&, mfem::Array<int>&, mfem::Array<mfem::IntegrationPoint>&, bool, mfem::InverseElementTransformation*) ... in file: /__w/PyMFEM/PyMFEM/PyMFEM/external/mfem/mesh/mesh.cpp:13515
MFEM Warning: 18 points were not found ... in function: virtual int mfem::Mesh::FindPoints(mfem::DenseMatrix&, mfem::Array<int>&, mfem::Array<mfem::IntegrationPoint>&, bool, mfem::InverseElementTransformation*) ... in file: /__w/PyMFEM/PyMFEM/PyMFEM/external/mfem/mesh/mesh.cpp:13515
MFEM Warning: 18 points were not found ... in function: virtual int mfem::Mesh::FindPoints(mfem::DenseMatrix&, mfem::Array<int>&, mfem::Array<mfem::IntegrationPoint>&, bool, mfem::InverseElementTransformation*) ... in file: /__w/PyMFEM/PyMFEM/PyMFEM/external/mfem/mesh/mesh.cpp:13515
