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"source": [
"## Coax to waveguide\n",
"This notebook outlines the design and simulation workflow for a horn antenna fed by a standard WR-90 waveguide operating at a target frequency of 10 GHz (λ≈30mm)\n",
"### Design Parameters \n",
"The antenna geometry and probe feed are defined based on the following physical constraints:\n",
"\n",
"Waveguide (WR-90): \n",
"- 22.86 mm (width) \n",
"- 10.16 mm (height) \n",
"- 40 mm (length)\n",
"\n",
"Probe Feed:\n",
"- Probe Length: 5.89 mm (≈λ/5) to ensure optimal impedance matching.\n",
"- Coaxial Geometry: 3.6 mm (outer diameter) and 1.28 mm (inner diameter).\n",
"\n",
"These parameters serve as the foundation for our geometric construction and subsequent discretization, ensuring the antenna is tuned for its intended frequency of operation."
]
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"import gmsh\n",
"import math\n",
"import os\n",
"import json\n",
"\n",
"from palacetoolkit.viz import view_mesh\n",
"from palacetoolkit.geometry import extract_tag, xmin, xmax, ymin, ymax, zmin, zmax\n",
"from palacetoolkit.mesh import create_graded_mesh, run_for_docs\n",
"from palacetoolkit.viz import view_mesh\n",
"from palacetoolkit.mesh import (\n",
" create_graded_mesh\n",
")"
]
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"### Parameters:\n",
"- inner_diameter_mm: Inner diameter of the coaxial cable in millimeters.\n",
"- outer_diameter_mm: Outer diameter of the coaxial cable in millimeters.\n",
"- probe_length_mm : Length of the probe in milimiters.\n",
"- length_mm: Length of the coaxial cable section in millimeters.\n",
"- wg_height: Height of the rectangular waveguide in millimeters.\n",
"- wg_length: Length of the rectangular waveguide in millimeters.\n",
"- wg_width: Width of the rectangular waveguide in millimeters.\n",
"- freq_ghz: Frequency of the wave in gigahertz.\n",
"- verbose: Verbosity level for Gmsh output\n",
"- filename: Name of the output mesh file."
]
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"inner_diameter_mm: float = 1.28\n",
"outer_diameter_mm: float = 3.6 \n",
"probe_length_mm = 5.89\n",
"length_mm: float = 5\n",
"wg_height: float = 10.16\n",
"wg_length: float = 40\n",
"wg_width: float = 22.86\n",
"freq_ghz: float = 10.0\n",
"verbose: int = 2\n",
"filename: str = \"coax_to_waveguide.msh\"\n",
"mesh_order = 1\n",
"gui = False\n",
"order = 1"
]
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"source": [
"### Initializing the Modeling Environment"
]
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"source": [
"gmsh.initialize()\n",
"gmsh.option.setNumber(\"General.Verbosity\", 5)\n",
"gmsh.model.add(\"coax_to_waveguide\")\n",
"kernel = gmsh.model.occ"
]
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"source": [
"### Design Parameter Calculation\n",
"We calculate the operating wavelength (λ) and derive the critical dimensions for the coaxial probe and backshort position. By basing these values on the 10 GHz design frequency, we ensure the geometry is physically optimized for efficient power transfer within the waveguide structure."
]
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"name": "stdout",
"output_type": "stream",
"text": [
"Wavelength: 30.00 mm\n",
"Probe length: 5.89 mm\n",
"Backshort Z position: 6.00 mm\n"
]
}
],
"source": [
"c = 3e8 \n",
"lamda = (c / (freq_ghz * 1e9)) * 1e3 \n",
"\n",
"inner_radius = inner_diameter_mm / 2\n",
"outer_radius = outer_diameter_mm / 2\n",
"\n",
"# y_top is the y-coordinate of the center of the coax probe, \n",
"# which is typically placed at the center of the waveguide height\n",
"y_top = wg_height / 2\n",
"coax_y_max = y_top + length_mm\n",
"\n",
"# backshort_z is the distance from the probe tip to the backshort plane, \n",
"# which is typically around λ/5 for good impedance matching\n",
"backshort_z = lamda / 5\n",
"\n",
"print(f\"Wavelength: {lamda:.2f} mm\")\n",
"print(f\"Probe length: {probe_length_mm:.2f} mm\")\n",
"print(f\"Backshort Z position: {backshort_z:.2f} mm\")"
]
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"source": [
"### Geometry Construction and Boolean Operations\n",
"In this step, we construct the CAD model by defining the waveguide box and the coaxial feed components. We use Boolean cut operations to integrate the probe into the waveguide and define the dielectric region. Finally, we perform a global fragment operation to ensure all geometric volumes are properly connected, forming a unified topology ready for discretization."
]
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"name": "stdout",
"output_type": "stream",
"text": [
"Info : [ 0%] Difference \r",
"Info : [ 10%] Difference \r",
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"Info : [ 40%] Difference \r",
"Info : [ 50%] Difference \r",
"Info : [ 60%] Difference \r",
"Info : [ 70%] Difference - Filling splits of edges \r",
"Info : [ 80%] Difference - Making faces \r",
"Info : [ 90%] Difference - Classify solids \r",
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" \r",
"Info : [ 0%] Fragments \r",
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"Info : [ 70%] Fragments \r",
"Info : [ 80%] Fragments - Adding holes \r",
"Info : [ 90%] Fragments \r",
" \r"
]
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"source": [
"# Waveguide box\n",
"waveguide = kernel.addBox(\n",
" -wg_width/2, -wg_height/2, 0,\n",
" wg_width, wg_height, wg_length\n",
")\n",
"\n",
"# Outer coax cylinder\n",
"outer_cyl = kernel.addCylinder(0, y_top, backshort_z, \n",
" 0, length_mm, 0, outer_radius)\n",
"\n",
"# Inner conductor\n",
"inner_cyl = kernel.addCylinder(0, coax_y_max, backshort_z, \n",
" 0, -(length_mm + probe_length_mm), 0, inner_radius)\n",
"\n",
"kernel.synchronize()\n",
"\n",
"coax_dielectric, _ = kernel.cut([(3, outer_cyl)], [(3, inner_cyl)],\n",
" removeObject=True, removeTool=False)\n",
"\n",
"waveguide_cut, _ = kernel.cut([(3, waveguide)], [(3, inner_cyl)],\n",
" removeObject=True, removeTool= True)\n",
"\n",
"kernel.synchronize()\n",
"\n",
"all_volumes = gmsh.model.getEntities(3)\n",
"kernel.fragment(all_volumes, [])\n",
"kernel.synchronize()"
]
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"source": [
"### Geometric Entity Classification\n",
"Here, we categorize the fragmented CAD entities into functional groups based on their spatial coordinates. We define logical filters to isolate the waveguide walls, coaxial conductors, waveports, and internal volumes. This classification step is essential for mapping the geometry to the specific physical boundary conditions required by the Palace solver"
]
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"source": [
"all_2d_entities = gmsh.model.getEntities(2)\n",
"all_3d_entities = gmsh.model.getEntities(3)\n",
"\n",
"def is_interface(x):\n",
" return (math.isclose(ymin(x), y_top, abs_tol=1e-4) and\n",
" math.isclose(ymax(x), y_top, abs_tol=1e-4) and\n",
" math.isclose(xmax(x), outer_radius, abs_tol=1e-4))\n",
"\n",
"def is_coax_port(x):\n",
" return (math.isclose(ymin(x), coax_y_max, abs_tol=1e-4) and\n",
" math.isclose(ymax(x), coax_y_max, abs_tol=1e-4) and\n",
" math.isclose(xmax(x), outer_radius, abs_tol=1e-4))\n",
"\n",
"def is_inner_conductor(x):\n",
" return (math.isclose(xmax(x), inner_radius, abs_tol=1e-4) and \n",
" not is_interface(x))\n",
"\n",
"def is_outer_conductor(x):\n",
" return (math.isclose(xmax(x), outer_radius, abs_tol=1e-4) and\n",
" ymin(x) >= y_top - 1e-4 and\n",
" not is_coax_port(x) and\n",
" not is_interface(x))\n",
"\n",
"def is_waveport(x):\n",
" return( math.isclose(zmax(x), wg_length, abs_tol=1e-4) and\n",
" math.isclose(zmin(x), wg_length, abs_tol=1e-4))\n",
"\n",
"def is_waveguide_wall(x):\n",
" return (not is_coax_port(x) and\n",
" not is_inner_conductor(x) and\n",
" not is_outer_conductor(x) and\n",
" not is_waveport(x) and \n",
" not is_interface(x)) \n",
"\n",
"def is_coax_volume(x):\n",
" return ymin(x) >= y_top - 1e-4\n",
"\n",
"def is_waveguide_volume(x):\n",
" return ymax(x) <= y_top + 1e-4 \n",
"\n",
"coax_port_surfs = [x for x in all_2d_entities if is_coax_port(x)]\n",
"inner_cond_surfs = [x for x in all_2d_entities if is_inner_conductor(x)]\n",
"outer_cond_surfs = [x for x in all_2d_entities if is_outer_conductor(x)]\n",
"waveguide_wall_surfs = [x for x in all_2d_entities if is_waveguide_wall(x)]\n",
"waveport_surfs = [x for x in all_2d_entities if is_waveport(x)] \n",
"coax_vols = [x for x in all_3d_entities if is_coax_volume(x)]\n",
"waveguide_vols = [x for x in all_3d_entities if is_waveguide_volume(x)]\n"
]
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"source": [
"### Physical Group Assignment\n",
"In this block, we map the classified geometric entities to Physical Groups. Assigning these unique identifiers allows the Palace solver to distinguish between different materials and boundary conditions, such as the waveguide walls (PEC), the coaxial probe, and the internal air and dielectric volumes. Finally, we store these identifiers in a pg_map dictionary for streamlined reference during the simulation configuration."
]
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"source": [
"pg_coax_port = gmsh.model.addPhysicalGroup(2, [x[1] for x in coax_port_surfs], -1, \"coax_port\")\n",
"pg_probe = gmsh.model.addPhysicalGroup(2, [x[1] for x in inner_cond_surfs], -1, \"inner_conductor\")\n",
"pg_outer_cyl = gmsh.model.addPhysicalGroup(2, [x[1] for x in outer_cond_surfs], -1, \"outer_conductor\")\n",
"pg_waveguide = gmsh.model.addPhysicalGroup(2, [x[1] for x in waveguide_wall_surfs], -1, \"waveguide_walls\")\n",
"pg_waveport = gmsh.model.addPhysicalGroup(2, [x[1] for x in waveport_surfs], -1, \"waveport\")\n",
"pg_dieletric = gmsh.model.addPhysicalGroup(3, [x[1] for x in coax_vols], -1, \"coax_volume\")\n",
"pg_air = gmsh.model.addPhysicalGroup(3, [x[1] for x in waveguide_vols], -1, \"waveguide_volume\")\n",
"\n",
"pg_map = {\n",
" \"coax_port\": pg_coax_port,\n",
" \"waveport\": pg_waveport,\n",
" \"waveguide_surface\": pg_waveguide,\n",
" \"waveguide_volume\": pg_air,\n",
" \"probe\": pg_probe,\n",
" \"outer_cyl\": pg_outer_cyl,\n",
" \"dielectric\": pg_dieletric\n",
" }"
]
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"source": [
"### Mesh Generation, Refinement, and Export\n",
"We conclude the workflow by applying a graded mesh refinement strategy, concentrating element density near the coaxial feed and waveport to accurately resolve the high-frequency electromagnetic field gradients. "
]
},
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