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Coplanar waveguide

A coplanar waveguide (CPW) is a planar transmission line structure used in microwave and millimeter-wave engineering, consisting of a central signal conductor flanked by two coplanar ground planes separated by gaps, all fabricated on the same surface of a dielectric substrate.^[1] Introduced by C. P. Wen in 1969 as a surface strip transmission line suitable for nonreciprocal gyromagnetic device applications, it supports primarily a quasi-transverse electromagnetic (TEM) mode of propagation, where the electric field is predominantly transverse to the direction of propagation, enabling low-loss signal transmission at high frequencies.^[1]^[2] The basic structure of a CPW features a narrow center strip of width w, two symmetric gaps of width s on either side, and extended ground planes, with the characteristic impedance Z_0 determined by conformal mapping techniques involving complete elliptic integrals: Z_0 = \frac{30\pi}{\sqrt{\varepsilon_{\text{eff}}}} \frac{K(k')}{K(k)}, where \varepsilon_{\text{eff}} is the effective permittivity, k = \frac{w}{w + 2s}, k' = \sqrt{1 - k^2}, and K denotes the complete elliptic integral of the first kind.^[2] This configuration allows for air above the structure, reducing dispersion compared to microstrip lines, and the impedance can be tuned over a wide range (typically 20–100 Ω) by adjusting w and s.^[2] Variations include finite ground-plane CPW (FGCPW) for reduced radiation and shielded CPW for further loss minimization in enclosed environments.^[3] Key characteristics of CPWs include low dispersion up to millimeter-wave frequencies, support for both coplanar (quasi-TEM) and slotline (parallel-plate-like) modes, and field confinement primarily in the gaps and substrate, with minimal dependence on substrate thickness.^[2] Propagation losses arise from conductor resistance, dielectric absorption, and radiation at discontinuities, but these can be mitigated using air-bridges to suppress slotline mode excitation.^[2] The effective permittivity \varepsilon_{\text{eff}} typically ranges from 1 to the substrate's \varepsilon_r, influencing phase velocity.^[2] CPWs offer significant advantages over traditional transmission lines like microstrip or stripline, including the elimination of via holes for grounding, which simplifies fabrication in planar processes and enhances compatibility with semiconductor technologies such as gallium arsenide (GaAs) MMICs.^[2] They facilitate easy integration of lumped elements, active devices, and discontinuities directly on the top surface, reducing parasitic effects and enabling compact designs for high-frequency applications.^[2] Additionally, their flexibility in mm-wave regimes stems from photolithographic precision in defining slots, allowing greater design versatility than etched lines.^[2] However, potential drawbacks include higher radiation losses in open structures at very high frequencies and sensitivity to surface roughness.^[2] Notable applications of CPWs encompass microwave integrated circuits (MICs), hybrid-ring couplers, filters, antennas, and phase shifters in radar systems, wireless communications, and atomic physics experiments for microwave coupling.^[2]^[1] Since the 1980s, advancements in uniplanar CPW variants have expanded their use in monolithic integrated circuits, driven by demands for high-speed, low-cost RF front-ends.^[2]

Fundamentals

Definition and Principles

A coplanar waveguide (CPW) is a planar transmission line structure comprising a central signal conductor flanked by two ground planes, all situated on the same side of a dielectric substrate.^[1] This configuration supports the propagation of electromagnetic waves, approximating a transverse electromagnetic (TEM) mode, and is particularly suited for integrated microwave and millimeter-wave circuits.^[4] The core principle of operation in a CPW relies on quasi-TEM mode propagation, where the dominant mode has a zero cutoff frequency and the fields behave similarly to those in an ideal TEM line at lower frequencies.^[4] In this mode, electric fields are primarily confined between the signal conductor and the ground planes, with fringing fields extending across the slots, while magnetic fields form loops encircling the central conductor.^[4] This field distribution ensures efficient wave guidance along the structure with minimal dispersion in the quasi-static approximation.^[1] CPWs provide key advantages over other planar transmission lines, such as microstrip, including the ability to form shunt connections directly to the ground planes without vias and enhanced compatibility with monolithic integration processes.^[4] The uniplanar design facilitates simpler fabrication and denser circuit layouts by keeping all metallization on one substrate surface.^[4]

Historical Development

The coplanar waveguide (CPW) was invented in 1969 by Cheng P. Wen while working at RCA's David Sarnoff Research Center in Princeton, New Jersey. Wen developed the structure to address challenges in integrating nonreciprocal gyromagnetic devices, such as isolators and circulators, which required a transmission line configuration that allowed easy incorporation of magnetic materials without complex multilayer fabrication.^[5]^[6] Wen's seminal work was detailed in his 1969 paper titled "Coplanar Waveguide: A Surface Strip Transmission Line Suitable for Nonreciprocal Gyromagnetic Device Applications," published in the IEEE Transactions on Microwave Theory and Techniques. This publication introduced the basic geometry and analyzed its suitability for microwave applications, marking the first formal description of CPW as a planar transmission line with all conductors on the same substrate surface.^[5] During the 1970s and 1980s, CPW gained adoption in hybrid microwave integrated circuits (MICs) and early monolithic microwave integrated circuits (MMICs), driven by advancements in photolithographic fabrication techniques that enabled precise patterning of submicron features on semiconductors like GaAs. Key contributions included R. E. DeBrecht's 1973 application of CPW in high-power GaAs FET push-pull amplifiers and M. Houdart's 1976 exploration of CPW for broadband MICs, which highlighted its advantages in shunt and series connections without vias. By the late 1980s, researchers like G. Ghione and C. U. Naldi demonstrated CPW's utility in MMICs for improved impedance control and reduced coupling issues, facilitating its integration into compact, high-performance circuits.^[7] Post-1990s developments expanded CPW's role in advanced materials and high-frequency regimes, including integration with high-temperature superconducting films for low-loss applications, as explored in 1993 studies on high-Tc superconducting CPW circuits. This era also saw widespread use in millimeter-wave systems, with CPW enabling MMIC designs operating up to 100 GHz and beyond, supported by refined modeling techniques and enhanced fabrication processes.^[7] In the 2000s and 2010s, CPW found applications in high-speed digital circuits and photonic integrations. Into the 2020s, as of 2025, advancements have focused on flexible and conductor-backed CPW variants for 5G and emerging 6G communications, terahertz antennas, and quantum technologies, leveraging improved metamaterials and substrate materials for enhanced performance in wireless and sensing systems.^[8]^[9]

Physical Structure

Basic Geometry

A conventional coplanar waveguide (CPW) consists of a central strip conductor of width W, flanked on either side by gaps of width S, with semi-infinite ground planes extending outward, all fabricated on the top surface of a dielectric substrate of thickness H and relative permittivity \varepsilon_r.^[7]^[1] In a cross-sectional view, the structure features these coplanar metallic elements deposited on the substrate's upper face, with the region above typically exposed to air or vacuum, enabling an open electromagnetic field configuration; an optional continuous ground plane may be added to the substrate's bottom surface, though this distinguishes it from the ungrounded conventional form.^[7] The key geometric parameters are the center conductor width W and the gap width S, which primarily govern the confinement of the electromagnetic fields between the central strip and the adjacent ground planes, ensuring quasi-TEM mode propagation with fields distributed both in the substrate and the overlying air.^[7]^[1] Substrate materials are selected for their low-loss properties, such as alumina (\varepsilon_r \approx 9.8) or gallium arsenide (GaAs, \varepsilon_r \approx 12.9), supporting high-frequency operation while maintaining the open structure above the conductors.^[7] This geometry influences the overall wave propagation behavior by shaping the effective dielectric constant and mode confinement.^[7]

Variations

One prominent variation of the coplanar waveguide (CPW) is the grounded coplanar waveguide (GCPW), which incorporates a continuous ground plane on the underside of the substrate. This modification enhances electromagnetic shielding, reduces radiation losses by confining fields more effectively to the substrate, and provides improved mechanical stability along with better heat dissipation.^[7]^[10] Ground vias are often integrated along the edges to suppress unwanted parallel-plate modes, enabling broader bandwidth applications such as transitions and directional couplers.^[7] The finite ground coplanar waveguide (FGCPW) modifies the standard structure by limiting the extent of the ground planes on the top surface to a finite width, rather than extending them infinitely. This design minimizes parasitic discontinuities at junctions in integrated circuits, reduces field leakage into the substrate, and supports both CPW-like and microstrip-like modes for enhanced compactness.^[7] It is particularly advantageous in monolithic microwave integrated circuits where space constraints demand low parasitics, as seen in baluns achieving DC-to-12 GHz bandwidth.^[7] Other variations include the asymmetrical CPW, which features unequal gap widths between the central conductor and the ground planes to enable precise control over field distribution and impedance matching. This asymmetry allows tailored propagation characteristics without altering the overall coplanar layout, making it suitable for transitions requiring optimized field confinement.^[7] Similarly, the conductor-backed CPW adds a full metallic layer beneath the substrate, distinct from GCPW by its emphasis on structural reinforcement; it improves mechanical stability and reduces transmission losses through better mode control with lateral walls or photonic-bandgap elements.^[7]^[11] A related variant is the slotline, which evolves the CPW by emphasizing the gaps as the primary propagation path, effectively treating the slot itself as the transmission line bounded by ground planes. This structure facilitates mode conversion between slotline and CPW modes, supporting applications in filters and antennas where balanced-to-unbalanced transformations are needed, such as in baluns with low insertion loss around 1.5 dB at 6 GHz.^[7]

Electrical Characteristics

Characteristic Impedance

The characteristic impedance Z_0 of a coplanar waveguide (CPW) is defined as the ratio of the voltage to the current for the propagating transverse electromagnetic (TEM) mode along the line.^[1] This parameter is fundamental to matching impedances in microwave circuits and ensuring efficient power transfer without reflections. For an air-filled CPW, the quasi-static approximation yields the characteristic impedance using conformal mapping techniques, expressed as

Z_0 = \frac{30\pi}{\sqrt{\epsilon_\mathrm{eff}}} \frac{K(k')}{K(k)},

where K is the complete elliptic integral of the first kind, k = \frac{W}{W + 2S} with W as the center conductor width and S as the gap width to each ground plane, and k' = \sqrt{1 - k^2}.^[1] This formula originates from the analytical solution for the capacitance per unit length via Schwarz-Christoffel transformation in the complex plane.^[1] When the CPW is implemented on a dielectric substrate, the effective permittivity \epsilon_\mathrm{eff} must be accounted for, as the fringing electric fields occupy both the dielectric below the conductors and the air above, resulting in an effective medium between vacuum and the substrate material. A common approximation is \epsilon_\mathrm{eff} \approx \frac{1 + \epsilon_r}{2}, where \epsilon_r is the relative permittivity of the substrate, providing a simple yet accurate estimate for design purposes in many cases.^[12] The geometry significantly influences Z_0, with wider center conductors (W) relative to gaps (S) decreasing impedance by increasing capacitance, while narrower conductors or wider gaps increase it. Typical values for microwave applications range from 20 Ω to 100 Ω, allowing flexibility in circuit design for standard 50 Ω systems.^[13] Exact solutions rely on numerical evaluation of the elliptic integrals via conformal mapping, which remains the cornerstone analytical method despite advancements in simulation tools.^[1]

Propagation and Losses

Coplanar waveguides primarily support quasi-TEM propagation, in which the electromagnetic fields are predominantly transverse to the direction of propagation, approximating the characteristics of a pure transverse electromagnetic mode.^[7] The phase velocity v_p of this mode is given by v_p = \frac{c}{\sqrt{\epsilon_{eff}}}, where c is the speed of light in vacuum and \epsilon_{eff} is the effective dielectric constant of the structure, determined by the substrate permittivity and air above the line.^[7] At low frequencies, this propagation is nearly dispersionless, but slight dispersion arises at higher frequencies due to the excitation of higher-order modes, which alter the effective permittivity and phase velocity.^[7] Attenuation in coplanar waveguides arises from multiple mechanisms that degrade signal amplitude over distance. Conductor losses stem from the finite conductivity of the metal strips and the skin effect, which confines currents to the surface at high frequencies, increasing the effective resistance.^[7] Dielectric losses are due to the loss tangent \tan \delta of the substrate material, dissipating energy through molecular friction in the dielectric.^[7] Radiation losses occur in the open structure, particularly from discontinuities or leaky modes in the slots, but these are mitigated by the presence of ground planes that confine fields and suppress slotline modes.^[7]^[14] The conductor attenuation \alpha_c at low frequencies is approximated as \alpha_c \approx \frac{R_s}{Z_0 W}, where R_s = \sqrt{\frac{\omega \mu}{2 \sigma}} is the surface resistivity, Z_0 is the characteristic impedance, and W is the center conductor width; more precise models incorporate geometric factors like the complete elliptic integral ratio K(k')/K(k).^[7] Dielectric attenuation is \alpha_d \approx \frac{\pi}{\lambda_0} \sqrt{\varepsilon_{\rm eff}} \tan \delta, with \lambda_0 the free-space wavelength.^[7] The total attenuation constant is the sum \alpha = \alpha_c + \alpha_d + \alpha_r, where \alpha_r accounts for radiation.^[7]^[15] Losses exhibit strong frequency dependence, with conductor losses scaling as \sqrt{f} due to the skin effect and dielectric losses increasing linearly with frequency.^[7] Above 10 GHz, total attenuation rises significantly in open structures owing to the onset of substrate modes and enhanced radiation, leading to multimode propagation and energy leakage.^[16]^[17] To achieve ultra-low attenuation, mitigation strategies include selecting low-loss substrates such as high-resistivity silicon (>2500 \, \Omega \cdot \mathrm{cm}) to minimize dielectric dissipation and employing superconducting films like YBa_2Cu_3O_{7-\delta} for near-zero conductor resistance at cryogenic temperatures.^[7]

Design and Fabrication

Modeling and Calculation

Modeling of coplanar waveguides (CPWs) begins with analytical approaches that provide closed-form expressions for quasi-static parameters such as characteristic impedance and effective dielectric constant. Conformal mapping techniques transform the CPW geometry into simpler domains to compute capacitance per unit length, enabling the derivation of these parameters under the assumption of negligible frequency dispersion.^[7] These methods are particularly effective for uniform straight sections on homogeneous substrates, offering rapid design iterations with high accuracy at low frequencies.^[18] Spectral domain methods extend analytical modeling by incorporating frequency-dependent effects through Fourier transform-based solutions to integral equations for the electric field. This approach is well-suited for layered dielectrics and accounts for higher-order modes in quasi-TEM approximations, yielding parameters like propagation constant and attenuation.^[7] For instance, quasistatic spectral domain analysis has been applied to model gap discontinuities in CPWs, providing equivalent circuit elements for circuit-level simulations.^[19] Numerical techniques address the limitations of analytical models for complex geometries and full-wave effects. The Method of Moments (MoM) solves integral equations for current distributions on conductors, making it ideal for analyzing discontinuities such as bends and junctions in CPWs, where it computes scattering parameters efficiently in the frequency domain.^[20] The Finite Element Method (FEM) discretizes the 3D structure into tetrahedral meshes to solve Maxwell's equations, enabling accurate simulation of multilayer CPWs with arbitrary shapes and material anisotropies.^[21] For time-domain analysis, the Finite Difference Time Domain (FDTD) method grids the space and time-steps electromagnetic fields, capturing broadband transient responses in CPW transitions and revealing pulse distortion due to dispersion.^[20] Commercial software tools integrate these numerical methods for practical CPW design. Ansys HFSS employs FEM for full-wave simulations of CPW bends, T-junctions, and impedance transformers, optimizing structures for minimal return loss across microwave frequencies.^[22] Keysight ADS combines circuit and electromagnetic solvers, using MoM-based momentum simulations to model CPW components like filters, allowing co-simulation with active devices for system-level performance. Design optimization integrates characteristic impedance Z_0 formulas from conformal mapping with loss models from spectral methods to tailor CPW length and frequency response. For example, combining quasi-static Z_0 calculations with conductor and dielectric loss tangents enables minimization of insertion loss in broadband applications, adjusting slot widths and ground plane spacing iteratively.^[7] This approach ensures the structure meets specifications for effective dielectric constant and attenuation over the operational band. Validation of these models involves comparing simulated S-parameters with measurements from vector network analyzers. For CPW discontinuities, modeled scattering parameters from MoM or FEM show agreement within 1-2 dB of measured insertion loss up to 20 GHz, confirming accuracy for fabrication tolerances.^[23] In grounded CPW lines, HFSS simulations of return loss match experimental data with deviations under 0.5 dB, validating the inclusion of via effects and substrate losses.^[24]

Manufacturing Techniques

Coplanar waveguides are typically fabricated using photolithographic patterning techniques, where thin films of metals such as gold or copper are deposited onto substrates via evaporation or sputtering, followed by selective etching to define the center conductor and ground planes.^[7] This process ensures precise control over the geometry, with metal thicknesses often exceeding three times the skin depth—such as 1.5 μm for gold at Ka-band frequencies—to minimize conductor losses.^[7] For instance, in monolithic microwave integrated circuits (MMICs), sputtering of Cr-Au films followed by gold electroplating to 4 μm thickness is common on gallium arsenide substrates.^[7] Substrate preparation is critical for achieving low-loss performance, with high-resistivity silicon (resistivity >2500 Ω·cm), gallium arsenide, or alumina selected to minimize dielectric losses and substrate modes.^[25] High-resistivity silicon, for example, enables attenuation constants below 1 dB/mm in microwave and millimeter-wave bands when combined with insulating layers like SiO₂ or Si₃N₄ to ensure thin-film uniformity and suppress leakage currents.^[25] Alumina substrates, with a dielectric constant of 9.4–9.9 and thicknesses of 0.254–0.65 mm, are prepared by polishing and cleaning to maintain surface flatness, facilitating uniform metal adhesion during deposition.^[7] Integration challenges in coplanar waveguide fabrication include avoiding vias for shunt elements to preserve the planar structure, while incorporating through-substrate vias for series connections in grounded coplanar waveguides (GCPW) to ensure proper grounding and mode suppression.^[26] In GCPW designs, vias are etched reactively and metallized to connect top ground planes to a bottom ground layer, though this adds complexity compared to via-free transitions that rely on polymer substrates for broadband performance.^[26] Advanced fabrication methods address finer features, such as lift-off techniques that enable gaps below 10 μm by evaporating metal over a photoresist pattern and dissolving the resist to lift away excess material, ideal for high-impedance lines in compact circuits.^[27] For cryogenic applications, superconducting coplanar waveguides are produced using niobium or aluminum films deposited via sputtering—niobium at 100–200 nm on silicon substrates etched with inductively coupled plasma, or aluminum at 0.5 μm on sapphire for quarter-wavelength resonators with quality factors exceeding 10^6 at microwave frequencies.^[28]^[29] As of 2025, emerging techniques include extrusion printing for low-cost CPW fabrication on alumina substrates and tantalum films for superconducting resonators achieving even higher quality factors.^[30]^[31] Quality control of fabricated coplanar waveguides involves on-wafer measurements using vector network analyzers to verify characteristic impedance (Z_0) near 50 Ω and insertion loss, often with thru-reflect-line (TRL) calibration for accuracy up to 40 GHz.^[32] These tests detect deviations as small as 0.4% in impedance via time-domain reflectometry and confirm low attenuation, such as 0.14 dB at 20 GHz, ensuring compliance with design specifications.^[7]

Applications

Microwave Integrated Circuits

Coplanar waveguides (CPWs) serve as essential interconnects in monolithic microwave integrated circuits (MMICs) and hybrid circuits, facilitating the integration of active and passive components such as amplifiers, filters, and mixers due to their planar geometry and compatibility with semiconductor processes. This uniplanar structure allows for easy on-wafer probing and reduces the need for via holes, simplifying circuit layout and improving yield in high-frequency designs.^[33] In MMICs fabricated on materials like gallium arsenide or indium phosphide, CPWs provide low-parasitic connections that maintain signal integrity across broadband operations.^[34] CPW-based discontinuities enable the realization of key passive components, including open stubs that function as capacitors by providing shunt susceptance, and shorted stubs that act as inductors through series reactance.^[7] These elements are integral to lumped-element equivalents in distributed circuits, with open-circuit discontinuities modeled for their fringing capacitance effects.^[35] Interdigital filters, constructed using multiple coupled CPW sections, offer compact bandpass responses suitable for microwave front-ends, achieving sharp roll-offs with minimal size.^[36] At high frequencies, CPWs exhibit low dispersion, supporting operation up to 100 GHz with effective permittivity variations that enable broadband performance in 5G transceivers and radar systems.^[6] This characteristic stems from their quasi-TEM mode propagation, which minimizes frequency-dependent losses compared to other planar lines, as detailed in the propagation properties section.^[7] Elevated center-strip configurations further reduce conductor attenuation, enhancing efficiency in millimeter-wave applications.^[7] Transitions from CPW to microstrip or coaxial lines are commonly implemented using tapered lines to gradually match impedances or radial stubs to suppress unwanted modes, achieving low insertion losses such as 2.4 dB at 5.55 GHz.^[7] These structures ensure seamless integration with legacy systems, with radial stubs providing broadband matching over decades of frequency.^[37] Case studies highlight CPW's efficacy in advanced circuits, such as phased-array antennas where CPW-fed networks with ferroelectric phase shifters deliver 370° shifts at 31.34 GHz for beam steering in radar applications.^[7] In power dividers, CPW-based T-junctions and 3-dB hybrid couplers are used in MMIC designs for communication systems.^[7] These implementations underscore CPW's role in scalable, high-performance microwave architectures.^[38]

Nonreciprocal Gyromagnetic Devices

Coplanar waveguides (CPWs) were originally motivated for nonreciprocal gyromagnetic applications due to their ability to produce an inherently elliptical RF magnetic field polarization in the plane of the substrate, which aligns efficiently with the circularly polarized modes required to excite gyromagnetic resonances in magnetized ferrites.^[1] This coplanar field configuration simplifies the integration of ferrite materials without needing complex three-dimensional structures, enabling compact devices such as isolators and circulators that exhibit direction-dependent signal propagation.^[1] The operation of these devices relies on the interaction between the CPW's transverse magnetic fields and magnetized ferrite substrates, such as yttrium iron garnet (YIG), where the ferrite's tensor permeability—characterized by off-diagonal elements under an applied DC bias field—induces nonreciprocal phase shifts and attenuation for forward and reverse propagating waves.^[39] In the forward direction, the wave experiences low loss as the polarization matches the ferrite's low-loss mode, while in the reverse direction, it couples to a high-loss mode, resulting in strong attenuation.^[39] Representative examples include ferrite-loaded CPW isolators, where YIG substrates biased with an in-plane DC magnetic field achieve forward insertion losses below 2 dB and reverse isolation exceeding 20 dB, often up to 40 dB at center frequencies around 13-15 GHz.^[39] CPW-based gyrators, utilizing ferrite-coupled lines, provide nonreciprocal phase shifting for applications like circulators, with demonstrated bandwidths approaching 40% and isolation ratios supporting efficient signal routing in integrated systems.^[40] These devices integrate seamlessly with rectangular waveguide transitions, maintaining performance metrics such as 25-35% fractional bandwidth while preserving high isolation.^[41] Modern extensions employ lumped-element approximations of CPW structures loaded with varactors to realize tunable nonreciprocity, allowing voltage-controlled adjustment of phase and isolation without magnetic biasing, though retaining gyromagnetic principles in hybrid designs for enhanced bandwidth and miniaturization.^[42]

Solid-State Physics and Quantum Technologies

Coplanar waveguides (CPWs) serve as critical probes in solid-state physics for interfacing with superconducting qubits and fluxonium circuits, facilitating microwave readout at cryogenic temperatures. In these systems, CPWs enable the transmission and detection of microwave signals that interact dispersively with the qubit states, allowing non-destructive measurement of quantum information without collapsing the superposition. For instance, fluxonium qubits, which exhibit long coherence times due to their inductive shunting, are often coupled capacitively to CPW resonators for readout, where the resonator frequency shifts based on the qubit's flux state. In quantum computing applications, superconducting CPW resonators, typically designed as quarter-wavelength (λ/4) or half-wavelength (λ/2) structures, couple transmon or flux qubits to form the basis of circuit quantum electrodynamics (cQED) architectures. These resonators support high-fidelity qubit-qubit interactions mediated by virtual photon exchange, with internal quality factors exceeding 10^6 at frequencies around 5 GHz, enabling low-loss storage and manipulation of quantum states. Specific integrations include CPW-based setups for dispersive readout in cQED, where the qubit-resonator detuning allows high-speed state discrimination with fidelities above 99%. Additionally, CPW Penning traps utilize superconducting waveguides to generate precise microwave fields for ion manipulation, trapping single electrons or ions for quantum simulation and sensing.^[43]^[44]^[45] Key challenges in these applications include minimizing losses from two-level system (TLS) defects in amorphous dielectrics, which cause decoherence through resonant absorption of microwave photons at millikelvin temperatures. Solutions involve careful surface preparation and the use of high-purity substrates to reduce TLS density, alongside cryogenic compatibility achieved via niobium thin films sputtered in ultra-high vacuum, which maintain superconductivity below 9 K with minimal quasiparticle generation. Recent advances feature hybrid quantum systems where CPWs couple superconducting circuits to spin ensembles, such as nitrogen-vacancy centers in diamond, enabling quantum memories with coherence times extended to milliseconds through collective spin-photon interactions. As of 2025, CPWs are increasingly integrated in 6G quantum-enhanced communication prototypes for secure key distribution.^[43]

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[PDF] A Tunable Isolator Based on Coplanar High Impedance Wire
The proposed isolator features a coplanar waveguide (CPW) on a ferrite substrate (yttrium iron garnet [YIG]). Its operating frequency can be tuned either ...Missing: metrics | Show results with:metrics
[37]
[PDF] A Broadband CPW-FCL Gyrator
Jul 14, 2022 · Abstract—In this paper, a novel wideband gyrator based on a ferrite coupled line design approach and realized in coplanar waveguide ...
[38]
Theory and Design of Tunable Full-Mode and Half-Mode Ferrite ...
The full-mode isolator provides a maximum bandwidth of 45% and a peak isolator figure of merit (IFM) of over 65 dB at 7 GHz, whereas the half-mode design has a ...
[39]
Lumped modeling with circuit elements for nonreciprocal ...
Aug 6, 2025 · Superconducting tunable filter with constant bandwidth using coplanar waveguide resonators ... A generalized lumped-element equivalent circuit for ...
[40]
Engineering high-Q superconducting tantalum microwave coplanar ...
Dec 20, 2024 · Title:Engineering high-Q superconducting tantalum microwave coplanar waveguide resonators for compact coherent quantum circuits ; Subjects: ...
[41]
Flux qubits in a planar circuit quantum electrodynamics architecture
Jul 5, 2014 · Two qubits, independently biased and controlled, are coupled to a coplanar waveguide resonator. Dispersive qubit state readout reaches a maximum ...
[42]
Theory of the coplanar-waveguide Penning trap - IOPscience
Nov 18, 2011 · The introduced trap is also a coplanar-waveguide cavity, similar to those used in circuit quantum electrodynamics experiments with ...