Differential Microstrip Modes#
This notebook builds a boxed differential microstrip cross-section (substrate + air + ground plane + two PEC strips), solves eigenmodes, and plots the first fields.
from palacetoolkit.mode_solver import WaveguideModeSolver
from palacetoolkit.utils import view_fe_mesh_2d, view_fields_2d, write_and_finalize_gmsh
from palacetoolkit.viz import view_mesh
import gmsh
import numpy as np
def make_differential_microstrip_mesh(
box_w=8.0,
h_sub=1.0,
h_air=3.0,
strip_w=0.8,
strip_gap=0.5,
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("differential_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)
x1 = -(strip_gap / 2 + strip_w)
x2 = strip_gap / 2
strip_p = gmsh.model.occ.addRectangle(x1, 0.0, 0, strip_w, strip_t)
strip_n = gmsh.model.occ.addRectangle(x2, 0.0, 0, strip_w, strip_t)
_, outmap = gmsh.model.occ.fragment([(2, sub), (2, air), (2, strip_p), (2, strip_n)], [])
gmsh.model.occ.remove(list(outmap[2]) + list(outmap[3]), 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)
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_p_edges = []
strip_n_edges = []
ground_edges = []
open_edges = []
c1 = x1 + strip_w / 2
c2 = x2 + strip_w / 2
for et in edge_tags:
ex, ey, _ = gmsh.model.occ.getCenterOfMass(1, et)
on_strip_y = (-1e-6 <= ey <= strip_t + 1e-6)
if on_strip_y and abs(ex - c1) <= strip_w / 2 + 1e-6:
strip_p_edges.append(et)
elif on_strip_y and abs(ex - c2) <= strip_w / 2 + 1e-6:
strip_n_edges.append(et)
elif 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_p_edges:
gmsh.model.addPhysicalGroup(1, strip_p_edges, tag=2, name="strip_p")
if strip_n_edges:
gmsh.model.addPhysicalGroup(1, strip_n_edges, tag=3, name="strip_n")
if open_edges:
gmsh.model.addPhysicalGroup(1, open_edges, tag=4, name="open_boundary")
for _, ptag in gmsh.model.getEntities(0):
x, y, _ = gmsh.model.getValue(0, ptag, [])
near_pair = (abs(x) <= (strip_gap / 2 + strip_w + 0.8) and -0.1 <= y <= strip_t + 0.5)
gmsh.model.mesh.setSize([(0, ptag)], lc_strip if near_pair else lc_bulk)
gmsh.model.mesh.generate(2)
return write_and_finalize_gmsh(filename, prefix="wg_diffms_")
eps_sub = 4.0
eps_air = 1.0
mu_r = 1.0
omega = 16.0
mesh_file = make_differential_microstrip_mesh(
box_w=8.0,
h_sub=1.0,
h_air=3.0,
strip_w=0.8,
strip_gap=0.5,
strip_t=0.06,
)
view_mesh(mesh_file)
mu_inv = {1: 1.0 / mu_r, 2: 1.0 / mu_r}
eps = {1: eps_sub, 2: eps_air}
# Ground and both strips are PEC; top/sides remain non-PEC.
pec_bdr = [1, 2, 3]
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 differential microstrip modes:")
for i, kn in enumerate(results["kn"], start=1):
print(f" Mode {i:2d}: kn={kn.real:+10.6f}{kn.imag:+10.6f}j")
Loading mesh file: /tmp/wg_diffms_str8ia0a.msh
Groups to render transparent: ['air_none', 'air_plastic_enclosure']
Mesh loaded successfully with 2 cell blocks
Found 5826 triangles total
Physical group tags in mesh: {1: 'substrate', 2: 'air'}
FE spaces: ND dofs = 29338, H1 dofs = 11859, total = 41197
Essential DOFs: ND = 234, H1 = 235, total = 469
Solving eigenvalue problem (omega = 16, sigma = -1126.4, size = 41197)...
Found 8 modes:
Mode 1: kn = +3.19729249e+01 -0.00000000e+00j <-- selected
Mode 2: kn = +3.19611499e+01 -0.00000000e+00j
Mode 3: kn = +3.19568982e+01 -0.00000000e+00j
Mode 4: kn = +3.19474805e+01 -0.00000000e+00j
Mode 5: kn = +3.19262270e+01 -0.00000000e+00j
Mode 6: kn = +3.19115007e+01 -0.00000000e+00j
Mode 7: kn = +3.18770498e+01 -0.00000000e+00j
Mode 8: kn = +3.18537901e+01 -0.00000000e+00j
Computed differential microstrip modes:
Mode 1: kn=+31.972925 -0.000000j
Mode 2: kn=+31.961150 -0.000000j
Mode 3: kn=+31.956898 -0.000000j
Mode 4: kn=+31.947481 -0.000000j
Mode 5: kn=+31.926227 -0.000000j
Mode 6: kn=+31.911501 -0.000000j
Mode 7: kn=+31.877050 -0.000000j
Mode 8: kn=+31.853790 -0.000000j
view_fe_mesh_2d(
mesh_file=mesh_file,
eps=eps,
title="Differential Microstrip FE Mesh and Materials",
show_edges=True,
)
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="Differential Microstrip First Modes (Boxed Cross-Section)",
)
MFEM Warning: 16 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: 16 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: 16 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
