Calculation of CPW Resonator Properties Using the Quantum Technology File

This application note provides a comprehensive, step-by-step guide to designing and analyzing coplanar waveguide (CPW) resonators used in superconducting quantum systems, with a specific focus on qubit readout applications. Utilizing quantum design tools in Keysight’s Advanced Design System (ADS) and the Quantum Technology file, the note outlines how engineers and researchers can model, simulate, and extract critical properties of CPW-based transmission lines. These include characteristic impedance, effective dielectric constant, inductance, capacitance, and resonance frequency—parameters essential for building reliable and high-performing quantum devices.

CPW resonators are foundational components in superconducting qubit circuits. Their applications range from qubit readout and quantum buses to Purcell filters and interconnects. This guide focuses primarily on quarter-wavelength CPW resonators, which are favored for their frequency selectivity and compact design in cryogenic quantum computing environments. Starting from material stack setup—such as defining superconducting metals (e.g., aluminum) on low-loss substrates (e.g., silicon)—the application note walks through a structured simulation workflow that reflects real-world fabrication conditions.

At the heart of the design process is the Controlled Impedance Line Designer (CILD), a robust simulation tool included in ADS. CILD enables users to construct CPW geometries by assigning layer materials, modifying dimensions like trace width and gap spacing, and running simulations that calculate transmission line properties. By inputting design parameters and desired operating frequencies, engineers can obtain simulated results that guide their resonator layout decisions with a high degree of confidence.

A major contribution of this note is its emphasis on accurate calculation of per-unit-length inductance (L) and capacitance (C), which are crucial for estimating the total electrical behavior of the resonator. These parameters are then used to derive the physical length of the CPW structure needed to achieve a specific resonance frequency. The note also explains how to use the derived values to validate the expected performance of the resonator and ensure design alignment with theoretical expectations.

Importantly, the application note addresses a common pitfall: the misuse of lumped element formulas in the context of distributed CPW structures. It clarifies when lumped models are appropriate and how to properly derive equivalent lumped parameters from distributed transmission line simulations. Citing authoritative references like Pozar’s Microwave Engineering, the document bridges academic theory with practical simulation, making it useful to both novice and experienced engineers.

The CILD tool also includes optimization and statistical analysis features that help fine-tune designs for target impedances (e.g., 50 ohms) and account for real-world fabrication tolerances. These capabilities are especially important in superconducting quantum systems, where even minor geometric deviations can affect coherence times, signal fidelity, and crosstalk.

Engineers can apply this workflow not only to readout resonators but also to the design of feedlines and filters that form the signal backbone of scalable quantum processor architectures. The approach enables rapid design iteration, deeper insight into layout dependencies, and better alignment between simulation and physical outcomes.

In summary, this application note serves as a valuable resource for engineers and researchers using quantum design tools to build superconducting circuits. It streamlines the resonator design process, enhances simulation accuracy, and reduces design risk in quantum R&D. When combined with other Keysight QuantumPro resources, it equips innovators with the modeling capabilities they need to push the boundaries of quantum hardware design and accelerate development in this fast-evolving field.