# Q2D Cross-Section Impedance of a Coplanar Waveguide This notebook demonstrates how to extract the characteristic impedance $Z_0$ of a coplanar waveguide (CPW) cross-section using the Ansys 2D Extractor (Q2D) quasi-static field solver via PyAEDT. The Q2D solver computes per-unit-length RLGC parameters from the cross-sectional geometry, from which the characteristic impedance can be obtained as a function of frequency. We compare the full-wave Q2D result against the analytical conformal-mapping estimate from [`cpw_parameters()`](https://gdsfactory.github.io/quantum-rf-pdk/models.html.md#qpdk.models.cpw_parameters). **Prerequisites:** - Ansys Electronics Desktop installed (requires license) **References:** - PyAEDT Documentation: [https://aedt.docs.pyansys.com/](https://aedt.docs.pyansys.com/) - Q2D Coplanar Waveguide Example: [https://examples.aedt.docs.pyansys.com/version/dev/examples/high_frequency/radiofrequency_mmwave/coplanar_waveguide.html](https://examples.aedt.docs.pyansys.com/version/dev/examples/high_frequency/radiofrequency_mmwave/coplanar_waveguide.html) - Simons, *Coplanar Waveguide Circuits, Components, and Systems* [[Sim01](#id63)] ![CPW cross-section with center width and ground gaps labelled](notebooks/figures/cpw-cross-section.svg) ## Setup and Imports ```ipython3 import sys if "google.colab" in sys.modules: import subprocess print("Running in Google Colab. Installing QPDK...") subprocess.check_call([ sys.executable, "-m", "pip", "install", "-q", "qpdk[models,hfss] @ git+https://github.com/gdsfactory/quantum-rf-pdk.git", ]) ``` ```ipython3 import os import tempfile import time from pathlib import Path from typing import cast import matplotlib.pyplot as plt import numpy as np from ansys.aedt.core import Q2d, settings from ansys.aedt.core.visualization.post.post_common_3d import PostProcessor3D from gplugins.ansys import Q2D, detach_desktop_logging, fit_view from IPython.display import Image, display from qpdk import PDK from qpdk.config import PATH from qpdk.models.cpw import cpw_parameters, get_cpw_dimensions from qpdk.tech import LAYER_STACK, coplanar_waveguide, material_properties PDK.activate() # CPW dimensions cpw_width = 10 # µm cpw_gap = 6 # µm cross_section = coplanar_waveguide(width=cpw_width, gap=cpw_gap) # Analytical impedance estimate ep_eff_analytical, z0_analytical = cpw_parameters(cpw_width, cpw_gap) print(f"CPW dimensions: width = {cpw_width} µm, gap = {cpw_gap} µm") print( f"Analytical estimate: Z₀ = {z0_analytical:.2f} Ω, ε_eff = {ep_eff_analytical:.4f}" ) ``` ## Initialize Q2D Project Set up an Ansys 2D Extractor project. The Q2D solver uses a quasi-static approach to compute per-unit-length transmission-line parameters from the 2D cross-section. **Note:** This section requires Ansys Electronics Desktop to be installed and licensed. ```ipython3 # Configuration for Q2D simulation Q2D_CONFIG = { "sweep_start_ghz": 1.0, # Sweep from 1 GHz "sweep_stop_ghz": 10.0, # to 10 GHz "sweep_step_ghz": 0.1, # 100 MHz step } ``` ```ipython3 # Ensure Ansys path is set so PyAEDT can find it ansys_default_path = "/usr/ansys_inc/v252/AnsysEM" if "ANSYSEM_ROOT252" not in os.environ and Path(ansys_default_path).exists(): os.environ["ANSYSEM_ROOT252"] = ansys_default_path settings.use_grpc_uds = False # pyrefly: ignore[missing-attribute] # not in pyaedt 1.9 # Create temporary directory for project temp_dir = tempfile.TemporaryDirectory(suffix=".ansys_qpdk") project_path = Path(temp_dir.name) / "cpw_q2d.aedt" # Initialize Q2D q2d = Q2d( project=str(project_path), design="CPW_Impedance", non_graphical=False, new_desktop=True, version="2025.2", ) # PyAEDT logs through the desktop by default; reading it per message can drop the session. detach_desktop_logging(q2d) print(f"Q2D project created: {q2d.project_file}") print(f"Design name: {q2d.design_name}") ``` ```myst-ansi PyAEDT INFO: Python version 3.12.13 (main, Mar 3 2026, 14:59:34) [Clang 21.1.4 ]. ``` ```myst-ansi PyAEDT INFO: PyAEDT version 0.26.2. ``` ```myst-ansi PyAEDT INFO: Initializing new Desktop session. ``` ```myst-ansi PyAEDT INFO: AEDT version 2025.2. ``` ```myst-ansi PyAEDT INFO: New AEDT session is starting on gRPC port 57449. ``` ```myst-ansi PyAEDT INFO: Starting new AEDT gRPC session on port 57449. ``` ```myst-ansi PyAEDT INFO: Launching AEDT server with gRPC transport mode: TransportMode.UDS ``` ```myst-ansi PyAEDT INFO: Electronics Desktop started on gRPC port 57449 after 9.2 seconds. ``` ```myst-ansi PyAEDT INFO: AEDT installation Path /usr/ansys_inc/v252/AnsysEM ``` ```myst-ansi PyAEDT INFO: Connected to AEDT gRPC session on port 57449. ``` ```myst-ansi PyAEDT WARNING: Service Pack is not detected. PyAEDT is currently connecting in Insecure Mode. ``` ```myst-ansi PyAEDT WARNING: Please download and install latest Service Pack to use connect to AEDT in Secure Mode. ``` ```myst-ansi PyAEDT INFO: Project cpw_q2d has been created. ``` ```myst-ansi PyAEDT INFO: Added design 'CPW_Impedance' of type 2D Extractor. ``` ```myst-ansi PyAEDT INFO: AEDT objects correctly read ``` ```myst-ansi Q2D project created: /tmp/tmp70dmm41z.ansys_qpdk/cpw_q2d.aedt Design name: CPW_Impedance ``` ## Build CPW Cross-Section Geometry Read the CPW width and gap back from the gdsfactory cross-section with `get_cpw_dimensions()`, then build the CPW geometry (signal conductor, ground planes, substrate) with `create_2d_cpw()` on the `Substrate` and `M1` levels of the QPDK layer stack. ```ipython3 # Create the Q2D simulation q2d_sim = Q2D(q2d, material_properties=material_properties) # Create the 2D cross-section geometry xs_width, xs_gap = get_cpw_dimensions(cross_section) object_names = q2d_sim.create_2d_cpw( xs_width, xs_gap, LAYER_STACK, substrate_level="Substrate", conductor_level="M1", ground_width=30, ) print("Created Q2D geometry:") for role, name in object_names.items(): print(f" {role}: {name}") ``` ```myst-ansi PyAEDT INFO: Materials class has been initialized! Elapsed time: 0m 0sec ``` ```myst-ansi PyAEDT INFO: Adding new material to the Project Library: Nb ``` ```myst-ansi PyAEDT INFO: Material has been added in Desktop. ``` ```myst-ansi PyAEDT INFO: Adding new material to the Project Library: Si ``` ```myst-ansi PyAEDT INFO: Material has been added in Desktop. ``` ```myst-ansi PyAEDT INFO: Adding new material to the Project Library: AlOx/Al ``` ```myst-ansi PyAEDT INFO: Material has been added in Desktop. ``` ```myst-ansi PyAEDT INFO: Adding new material to the Project Library: In ``` ```myst-ansi PyAEDT INFO: Material has been added in Desktop. ``` ```myst-ansi PyAEDT INFO: Modeler2D class has been initialized! ``` ```myst-ansi PyAEDT INFO: Modeler class has been initialized! Elapsed time: 0m 0sec ``` ```myst-ansi PyAEDT INFO: Boundary SignalLine signal has been created. ``` ```myst-ansi PyAEDT INFO: Boundary ReferenceGround gnd has been created. ``` ```myst-ansi PyAEDT INFO: Mesh class has been initialized! Elapsed time: 0m 0sec ``` ```myst-ansi PyAEDT INFO: Mesh class has been initialized! Elapsed time: 0m 0sec ``` ```myst-ansi Created Q2D geometry: signal: signal gnd_left: gnd_left gnd_right: gnd_right substrate: substrate ``` ### Q2D Cross-Section Geometry Here is the 2D geometry of the CPW cross-section in Ansys 2D Extractor. ![Q2D geometry](_static/images/q2d_cpw_impedance_geom.jpg) ```ipython3 # Ensure Q2D model fits the screen fit_view(q2d) # Save screenshot img_dir = PATH.repo / "docs" / "_static" / "images" img_dir.mkdir(parents=True, exist_ok=True) q2d_img_path = img_dir / "q2d_cpw_impedance_geom.jpg" cast(PostProcessor3D, q2d.post).export_model_picture( full_name=str(q2d_img_path), show_axis=True, show_grid=False, show_ruler=True ) # Display in notebook display(Image(filename=str(q2d_img_path))) ``` ```myst-ansi PyAEDT INFO: Parsing /tmp/tmp70dmm41z.ansys_qpdk/cpw_q2d.aedt. ``` ```myst-ansi PyAEDT INFO: File /tmp/tmp70dmm41z.ansys_qpdk/cpw_q2d.aedt correctly loaded. Elapsed time: 0m 0sec ``` ```myst-ansi PyAEDT INFO: aedt file load time 0.002233743667602539 ``` ```myst-ansi PyAEDT INFO: PostProcessor class has been initialized! Elapsed time: 0m 0sec ``` ```myst-ansi PyAEDT INFO: Post class has been initialized! Elapsed time: 0m 0sec ``` ```myst-ansi ``` ## Configure Q2D Analysis Set up the solution with a frequency sweep from 1 GHz to 10 GHz to compute the characteristic impedance across the frequency range. ```ipython3 # Create setup setup = q2d.create_setup(name="Q2DSetup") # Add frequency sweep sweep = setup.add_sweep(name="FrequencySweep") sweep.props["RangeType"] = "LinearStep" sweep.props["RangeStart"] = f"{Q2D_CONFIG['sweep_start_ghz']}GHz" sweep.props["RangeStep"] = f"{Q2D_CONFIG['sweep_step_ghz']}GHz" sweep.props["RangeEnd"] = f"{Q2D_CONFIG['sweep_stop_ghz']}GHz" sweep.props["Type"] = "Interpolating" sweep.update() print("Q2D setup configured:") print( f" - Sweep range: {Q2D_CONFIG['sweep_start_ghz']} – {Q2D_CONFIG['sweep_stop_ghz']} GHz" ) print(f" - Step size: {Q2D_CONFIG['sweep_step_ghz']} GHz") ``` ```myst-ansi Q2D setup configured: - Sweep range: 1.0 – 10.0 GHz - Step size: 0.1 GHz ``` ## Run Simulation Execute the Q2D analysis. ```ipython3 print("Starting Q2D analysis...") print("(This may take a few minutes)") # Save project before analysis q2d.save_project() # Run the analysis start_time = time.time() success = q2d.analyze(cores=4) elapsed = time.time() - start_time if not success: raise RuntimeError("Q2D simulation failed. Check the AEDT log for details.") else: print(f"Analysis completed in {elapsed:.1f} seconds") ``` ```myst-ansi Starting Q2D analysis... (This may take a few minutes) PyAEDT INFO: Project cpw_q2d Saved correctly ``` ```myst-ansi PyAEDT INFO: Project cpw_q2d Saved correctly ``` ```myst-ansi PyAEDT INFO: Key Desktop/ActiveDSOConfigurations/2D Extractor correctly changed. ``` ```myst-ansi PyAEDT INFO: Solving all design setups. Analysis started... ``` ```myst-ansi PyAEDT INFO: Design setup None solved correctly in 0.0h 0.0m 8.0s ``` ```myst-ansi PyAEDT INFO: Key Desktop/ActiveDSOConfigurations/2D Extractor correctly changed. ``` ```myst-ansi Analysis completed in 8.4 seconds ``` ## Extract and Plot Impedance Extract the characteristic impedance $Z_0$ from Q2D and compare it with the analytical conformal-mapping estimate. The analytical value is shown as a horizontal dashed line. ```ipython3 # Extract Z0 from Q2D data = q2d.post.get_solution_data( expressions="Z0(signal,signal)", context="Original", setup_sweep_name="Q2DSetup : FrequencySweep", ) if isinstance(data, bool): raise TypeError(f"AEDT returned {data!r} instead of the Z0(signal,signal) data") frequencies_ghz = np.array(data.primary_sweep_values) _, z0_real = data.get_expression_data(formula="real") z0_q2d = np.array(z0_real) # --- Plot --- fig, ax = plt.subplots(figsize=(10, 5)) # Q2D result ax.plot(frequencies_ghz, z0_q2d, "b-", linewidth=2, label="Q2D (quasi-static)") # Analytical estimate as a horizontal line ax.axhline( y=float(z0_analytical), color="r", linestyle="--", linewidth=1.5, label=f"Analytical (conformal mapping): {z0_analytical:.2f} Ω", ) ax.set_xlabel("Frequency (GHz)") ax.set_ylabel("Characteristic Impedance $Z_0$ (Ω)") ax.set_title("CPW Characteristic Impedance: Q2D vs. Analytical Estimate") ax.legend() ax.grid(True) ax.set_xlim(Q2D_CONFIG["sweep_start_ghz"], Q2D_CONFIG["sweep_stop_ghz"]) plt.tight_layout() plt.show() # --- Numerical comparison --- z0_mean_q2d = np.mean(z0_q2d) relative_diff = (z0_mean_q2d - z0_analytical) / z0_analytical * 100 print("\n=== Impedance Comparison ===") print("-" * 45) print(f"Analytical Z₀ (conformal mapping): {z0_analytical:.2f} Ω") print(f"Q2D Z₀ (mean over frequency): {z0_mean_q2d:.2f} Ω") print(f"Relative difference: {relative_diff:+.2f}%") print("-" * 45) ``` ```myst-ansi PyAEDT WARNING: No report category provided. Automatically identified Matrix ``` ```myst-ansi PyAEDT INFO: Solution Correctly loaded. Elapsed time: 0m 0sec ``` ```myst-ansi PyAEDT INFO: Solution Correctly parsed. Elapsed time: 0m 0sec ``` ```myst-ansi ~/dev/quantum-rf-pdk/.venv/lib/python3.12/site-packages/ansys/aedt/core/visualization/post/solution_data.py:648: UserWarning: Method `data_real` is deprecated. Use :func:`get_expression_data` property instead. warnings.warn("Method `data_real` is deprecated. Use :func:`get_expression_data` property instead.") ``` ```myst-ansi
``` ```myst-ansi === Impedance Comparison === --------------------------------------------- Analytical Z₀ (conformal mapping): 49.31 Ω Q2D Z₀ (mean over frequency): 44.72 Ω Relative difference: -9.32% --------------------------------------------- ``` ## Cleanup Close the Q2D session and clean up temporary files. ```ipython3 # Save and close q2d.save_project() # q2d.release_desktop() # Uncomment to close the AEDT desktop session time.sleep(2) # Clean up temp directory temp_dir.cleanup() print("Q2D session closed and temporary files cleaned up") ``` ```myst-ansi PyAEDT INFO: Project cpw_q2d Saved correctly ``` ```myst-ansi Q2D session closed and temporary files cleaned up ``` ## Summary This notebook demonstrated: 1. **Cross-Section Definition**: Using QPDK’s `coplanar_waveguide` cross-section to define CPW geometry (10 µm width, 6 µm gap) 2. **Q2D Setup**: Initializing Ansys 2D Extractor via PyAEDT and building the cross-sectional geometry using `create_2d_cpw()` 3. **Impedance Extraction**: Running the Q2D quasi-static solver to compute $Z_0$ as a function of frequency from 1 to 10 GHz 4. **Analytical Validation**: Comparing the Q2D result with the conformal-mapping analytical estimate from [`cpw_parameters()`](https://gdsfactory.github.io/quantum-rf-pdk/models.html.md#qpdk.models.cpw_parameters) **Key Points for CPW Design:** - The Q2D solver gives frequency-dependent impedance including dispersion effects - The analytical conformal-mapping model provides a good quasi-static estimate - For superconducting CPWs (PEC conductors), the impedance is nearly frequency-independent in the low-GHz range - No backplate metallisation is used, matching typical superconducting fabrication **Next Steps:** - Vary CPW dimensions to study impedance sensitivity - Compare with HFSS 3D driven-modal simulations - Study the effect of conductor thickness on impedance ## References