# Coplanar waveguide

Last updated

Coplanar waveguide is a type of electrical planar transmission line which can be fabricated using printed circuit board technology, and is used to convey microwave-frequency signals. On a smaller scale, coplanar waveguide transmission lines are also built into monolithic microwave integrated circuits. Conventional coplanar waveguide (CPW) consists of a single conducting track printed onto a dielectric substrate, together with a pair of return conductors, one to either side of the track. All three conductors are on the same side of the substrate, and hence are coplanar. The return conductors are separated from the central track by a small gap, which has an unvarying width along the length of the line. Away from the cental conductor, the return conductors usually extend to an indefinite but large distance, so that each is notionally a semi-infinite plane.

Planar transmission lines are transmission lines with conductors, or in some cases dielectric (insulating) strips, that are flat, ribbon-shaped lines. They are used to interconnect components on printed circuits and integrated circuits working at microwave frequencies because the planar type fits in well with the manufacturing methods for these components. Transmission lines are more than simply interconnections. With simple interconnections, the propagation of the electromagnetic wave along the wire is fast enough to be considered instantaneous, and the voltages at each end of the wire can be considered identical. If the wire is longer than a large fraction of a wavelength, these assumptions are no longer true and transmission line theory must be used instead. With transmission lines, the geometry of the line is precisely controlled so that its electrical behaviour is highly predictable. At lower frequencies, these considerations are only necessary for the cables connecting different pieces of equipment, but at microwave frequencies the distance at which transmission line theory becomes necessary is measured in millimetres. Hence, transmission lines are needed within circuits.

A printed circuit board (PCB) mechanically supports and electrically connects electronic components or electrical components using conductive tracks, pads and other features etched from one or more sheet layers of copper laminated onto and/or between sheet layers of a non-conductive substrate. Components are generally soldered onto the PCB to both electrically connect and mechanically fasten them to it.

In radio-frequency engineering, a transmission line is a specialized cable or other structure designed to conduct alternating current of radio frequency, that is, currents with a frequency high enough that their wave nature must be taken into account. Transmission lines are used for purposes such as connecting radio transmitters and receivers with their antennas, distributing cable television signals, trunklines routing calls between telephone switching centres, computer network connections and high speed computer data buses.

## Contents

Conductor-backed coplanar waveguide (CBCPW) is a common variant which has a ground plane covering the entire back-face of the substrate. The ground-plane serves as a third return conductor.

In electrical engineering, a ground plane is an electrically conductive surface, usually connected to electrical ground. The term has two different meanings in separate areas of electrical engineering. In antenna theory, a ground plane is a conducting surface large in comparison to the wavelength, such as the Earth, which is connected to the transmitter's ground wire and serves as a reflecting surface for radio waves. In printed circuit boards, a ground plane is a large area of copper foil on the board which is connected to the power supply ground terminal and serves as a return path for current from different components on the board.

Coplanar waveguide was invented in 1969 by Cheng P. Wen, primarily as a means by which non-reciprocal components such as gyrators and isolators could be incorporated in planar transmission line circuits. [2]

In classical electromagnetism, reciprocity refers to a variety of related theorems involving the interchange of time-harmonic electric current densities (sources) and the resulting electromagnetic fields in Maxwell's equations for time-invariant linear media under certain constraints. Reciprocity is closely related to the concept of Hermitian operators from linear algebra, applied to electromagnetism.

A gyrator is a passive, linear, lossless, two-port electrical network element proposed in 1948 by Bernard D. H. Tellegen as a hypothetical fifth linear element after the resistor, capacitor, inductor and ideal transformer. Unlike the four conventional elements, the gyrator is non-reciprocal. Gyrators permit network realizations of two-(or-more)-port devices which cannot be realized with just the conventional four elements. In particular, gyrators make possible network realizations of isolators and circulators. Gyrators do not however change the range of one-port devices that can be realized. Although the gyrator was conceived as a fifth linear element, its adoption makes both the ideal transformer and either the capacitor or inductor redundant. Thus the number of necessary linear elements is in fact reduced to three. Circuits that function as gyrators can be built with transistors and op-amps using feedback.

An isolator is a two-port device that transmits microwave or radio frequency power in one direction only. It is used to shield equipment on its input side, from the effects of conditions on its output side; for example, to prevent a microwave source being detuned by a mismatched load.

The electromagnetic wave carried by a coplanar waveguide exists partly in the dielectric substrate, and partly in the air above it. In general, the dielectric constant of the substrate will be different (and greater) than that of the air, so that the wave is travelling in an inhomogeneous medium. In consequence CPW will not support a true TEM wave; at non-zero frequencies, both the E and H fields will have longitudinal components (a hybrid mode). However, these longitudinal components are usually small and the mode is better described as quasi-TEM. [3]

A dielectric is an electrical insulator that can be polarized by an applied electric field. When a dielectric is placed in an electric field, electric charges do not flow through the material as they do in an electrical conductor but only slightly shift from their average equilibrium positions causing dielectric polarization. Because of dielectric polarization, positive charges are displaced in the direction of the field and negative charges shift in the opposite direction. This creates an internal electric field that reduces the overall field within the dielectric itself. If a dielectric is composed of weakly bonded molecules, those molecules not only become polarized, but also reorient so that their symmetry axes align to the field.

An electric field surrounds an electric charge, and exerts force on other charges in the field, attracting or repelling them. Electric field is sometimes abbreviated as E-field. Mathematically the electric field is a vector field that associates to each point in space the force per unit of charge exerted on an infinitesimal positive test charge at rest at that point. The SI unit for electric field strength is volt per meter (V/m). Newtons per coulomb (N/C) is also used as a unit of electric field strengh. Electric fields are created by electric charges, or by time-varying magnetic fields. Electric fields are important in many areas of physics, and are exploited practically in electrical technology. On an atomic scale, the electric field is responsible for the attractive force between the atomic nucleus and electrons that holds atoms together, and the forces between atoms that cause chemical bonding. Electric fields and magnetic fields are both manifestations of the electromagnetic force, one of the four fundamental forces of nature.

A magnetic field is a vector field that describes the magnetic influence of electric charges in relative motion and magnetized materials. Magnetic fields are observed in a wide range of size scales, from subatomic particles to galaxies. In everyday life, the effects of magnetic fields are often seen in permanent magnets, which pull on magnetic materials and attract or repel other magnets. Magnetic fields surround and are created by magnetized material and by moving electric charges such as those used in electromagnets. Magnetic fields exert forces on nearby moving electrical charges and torques on nearby magnets. In addition, a magnetic field that varies with location exerts a force on magnetic materials. Both the strength and direction of a magnetic field vary with location. As such, it is an example of a vector field.

## Nonreciprocal devices

Nonreciprocal gyromagnetic devices depend on the microwave signal presenting a rotating (circularly polarized) magnetic field to a statically magnetized ferrite body. CPW is designed to produce just such a rotating magnetic field in the two slots between the central and side conductors.

A ferrite is a ceramic material made by mixing and firing large proportions of iron(III) oxide (Fe2O3, rust) blended with small proportions of one or more additional metallic elements, such as barium, manganese, nickel, and zinc. They are both electrically non-conductive, meaning that they are insulators, and ferrimagnetic, meaning they can easily be magnetized or attracted to a magnet. Ferrites can be divided into two families based on their resistance to being demagnetized (magnetic coercivity).

The dielectric substrate has no direct effect on the magnetic field of a microwave signal travelling along the CPW line. For the magnetic field, the CPW is then symmetrical in the plane of the metalization, between the substrate side and the air side. Consequently, currents flowing along parallel paths on opposite faces of each conductor (on the air-side and on the substrate-side) are subject to the same inductance, and the overall current tends to be divided equally between the two faces.

Conversely, the substrate does affect the electric field, so that the substrate side contributes a larger capacitance across the slots than does the air side. Electric charge can accumulate or be depleted more readily on the substrate face of the conductors than on the air face. As a result, at those points on the wave where the current reverses direction, charge will spill over the edges of the metalization between the air face and the substrate face. This secondary current over the edges gives rise to a longitudinal (parallel with the line), magnetic field in each of the slots, which is in quadrature with the vertical (normal to the substrate surface) magnetic field associated with the main current along the conductors.

If the dielectric constant of the substrate is much greater than unity, then the magnitude of the longitudinal magnetic field approaches that of the vertical field, so that the combined magnetic field in the slots approaches circular polarization. [2]

## Application in solid state physics

Coplanar waveguides play an important role in the field of solid state quantum computing, e.g. for the coupling of microwave photons to a superconducting qubit. In particular the research field of circuit quantum electrodynamics was initiated with coplanar waveguide resonators as crucial elements that allow for high field strength and thus strong coupling to a superconducting qubit by confining a microwave photon to a volume that is much smaller than the cube of the wavelength. To further enhance this coupling, superconducting coplanar waveguide resonators with extremely low losses were applied. [4] [5] (The quality factors of such superconducting coplanar resonators at low temperatures can exceed 106 even in the low-power limit. [6] ) Coplanar resonators can also be employed as quantum buses to couple multiple qubits to each other. [7] [8]

Another application of coplanar waveguides in solid state research is for studies involving magnetic resonance, e.g. for electron spin resonance spectroscopy [9] or for magnonics. [10]

Coplanar waveguide resonators have also been employed to characterize the material properties of (high-Tc) superconducting thin films. [11] [12]

## Related Research Articles

A resonator is a device or system that exhibits resonance or resonant behavior, that is, it naturally oscillates at some frequencies, called its resonant frequencies, with greater amplitude than at others. The oscillations in a resonator can be either electromagnetic or mechanical. Resonators are used to either generate waves of specific frequencies or to select specific frequencies from a signal. Musical instruments use acoustic resonators that produce sound waves of specific tones. Another example is quartz crystals used in electronic devices such as radio transmitters and quartz watches to produce oscillations of very precise frequency.

In quantum computing, a charge qubit is a qubit whose basis states are charge states. In superconducting quantum computing, a charge qubit is formed by a tiny superconducting island coupled by a Josephson junction to a superconducting reservoir. The state of the qubit is determined by the number of Cooper pairs which have tunneled across the junction. In contrast with the charge state of an atomic or molecular ion, the charge states of such an "island" involve a macroscopic number of conduction electrons of the island. The quantum superposition of charge states can be achieved by tuning the gate voltage U that controls the chemical potential of the island. The charge qubit is typically read-out by electrostatically coupling the island to an extremely sensitive electrometer such as the radio-frequency single-electron transistor.

Superconducting quantum computing is an implementation of a quantum computer in superconducting electronic circuits. Research in superconducting quantum computing is conducted by Google, Microsoft, IBM, Rigetti, and Intel. as of May 2016, up to nine fully controllable qubits are demonstrated in a 1D array, up to sixteen in a 2D architecture.

Microwave spectroscopy is the spectroscopy method that employs microwaves, i.e. electromagnetic radiation at GHz frequencies, for the study of matter.

Microstrip is a type of electrical transmission line which can be fabricated using printed circuit board technology, and is used to convey microwave-frequency signals. It consists of a conducting strip separated from a ground plane by a dielectric layer known as the substrate. Microwave components such as antennas, couplers, filters, power dividers etc. can be formed from microstrip, with the entire device existing as the pattern of metallization on the substrate. Microstrip is thus much less expensive than traditional waveguide technology, as well as being far lighter and more compact. Microstrip was developed by ITT laboratories as a competitor to stripline.

In quantum computing, and more specifically in superconducting quantum computing, flux qubits are micrometer sized loops of superconducting metal interrupted by a number of Josephson junctions, functioning as quantum bits. The junction parameters are engineered during fabrication so that a persistent current will flow continuously when an external magnetic flux is applied. As only an integer number of flux quanta are allowed to penetrate the superconducting ring, clockwise or counter-clockwise currents are developed in the loop to compensate a non-integer external flux bias. When the applied flux through the loop area is close to a half integer number of flux quanta, the two lowest energy eigenstates of the loop will be a quantum superposition of the clockwise and counter-clockwise currents. The two lowest energy eigenstates differ only by the relative quantum phase between the composing current-direction states. Higher energy eigenstates correspond to much larger persistent currents, that induce an additional flux quantum to the qubit loop, thus are well separated energetically from the lowest two eigenstates. This separation, known as the "qubit non linearity" criteria, allows operations with the two lowest eigenstates only, effectively creating a two level system. Usually, the two lowest eigenstates will serve as the computational basis for the logical qubit.

A split-ring resonator (SRR) is an artificially produced structure common to metamaterials. Their purpose is to produce the desired magnetic susceptibility in various types of metamaterials up to 200 terahertz. These media create the necessary strong magnetic coupling to an applied electromagnetic field, not otherwise available in conventional materials. For example, an effect such as negative permeability is produced with a periodic array of split ring resonators.

A dielectric resonator antenna (DRA) is a radio antenna mostly used at microwave frequencies and higher, that consists of a block of ceramic material of various shapes, the dielectric resonator, mounted on a metal surface, a ground plane. Radio waves are introduced into the inside of the resonator material from the transmitter circuit and bounce back and forth between the resonator walls, forming standing waves. The walls of the resonator are partially transparent to radio waves, allowing the radio power to radiate into space.

A quantum bus is a device which can be used to store or transfer information between independent qubits in a quantum computer, or combine two qubits into a superposition. It is the quantum analog of a classical bus.

A microwave cavity or radio frequency (RF) cavity is a special type of resonator, consisting of a closed metal structure that confines electromagnetic fields in the microwave region of the spectrum. The structure is either hollow or filled with dielectric material. The microwaves bounce back and forth between the walls of the cavity. At the cavity's resonant frequencies they reinforce to form standing waves in the cavity. Therefore, the cavity functions similarly to an organ pipe or sound box in a musical instrument, oscillating preferentially at a series of frequencies, its resonant frequencies. Thus it can act as a bandpass filter, allowing microwaves of a particular frequency to pass while blocking microwaves at nearby frequencies.

A terahertz metamaterial is a class of composite metamaterials designed to interact at terahertz (THz) frequencies. The terahertz frequency range used in materials research is usually defined as 0.1 to 10 THz.

Metamaterial antennas are a class of antennas which use metamaterials to increase performance of miniaturized antenna systems. Their purpose, as with any electromagnetic antenna, is to launch energy into free space. However, this class of antenna incorporates metamaterials, which are materials engineered with novel, often microscopic, structures to produce unusual physical properties. Antenna designs incorporating metamaterials can step-up the antenna's radiated power.

A tunable metamaterial is a metamaterial with a variable response to an incident electromagnetic wave. This includes remotely controlling how an incident electromagnetic wave interacts with a metamaterial. This means the capability to determine whether the EM wave is transmitted, reflected, or absorbed. In general, the lattice structure of the tunable metamaterial is adjustable in real time, making it possible to reconfigure a metamaterial device during operation. It encompasses developments beyond the bandwidth limitations in left-handed materials by constructing various types of metamaterials. The ongoing research in this domain includes electromagnetic materials that are very meta which mean good and has a band gap metamaterials (EBG), also known as photonic band gap (PBG), and negative refractive index material (NIM).

A waveguide filter is an electronic filter that is constructed with waveguide technology. Waveguides are hollow metal tubes inside which an electromagnetic wave may be transmitted. Filters are devices used to allow signals at some frequencies to pass, while others are rejected. Filters are a basic component of electronic engineering designs and have numerous applications. These include selection of signals and limitation of noise. Waveguide filters are most useful in the microwave band of frequencies, where they are a convenient size and have low loss. Examples of microwave filter use are found in satellite communications, telephone networks, and television broadcasting.

A nonlinear metamaterial is an artificially constructed material that can exhibit properties not found in nature. Its response to electromagnetic radiation can be characterized by its permittivity and material permeability. The product of the permittivity and permeability results in the refractive index. Unlike natural materials, nonlinear metamaterials can produce a negative refractive index. These can also produce a more pronounced nonlinear response than naturally occurring materials.

Circuit quantum electrodynamics provides a means of studying the fundamental interaction between light and matter. As in the field of cavity quantum electrodynamics, a single photon within a single mode cavity coherently couples to a quantum object (atom). In contrast to cavity QED, the photon is stored in a one-dimensional on-chip resonator and the quantum object is no natural atom but an artificial one. These artificial atoms usually are mesoscopic devices which exhibit an atom-like energy spectrum. The field of circuit QED is a prominent example for quantum information processing and a promising candidate for future quantum computation.

In quantum computing, and more specifically in superconducting quantum computing, a transmon is a type of superconducting charge qubit that was designed to have reduced sensitivity to charge noise. The transmon was developed by Robert J. Schoelkopf, Michel Devoret, Steven M. Girvin and their colleagues at Yale University in 2007. Its name is an abbreviation of the term transmission line shunted plasma oscillation qubit; one which consists of a Cooper-pair box "where the two superconductors are also capacitatively shunted in order to decrease the sensitivity to charge noise, while maintaining a sufficient anharmonicity for selective qubit control".

Air stripline is a form of electrical planar transmission line whereby a conductor in the form of a thin metal strip is suspended between two ground planes. The idea is to make the dielectric essentially air. Mechanical support of the line may be a thin substrate, periodical insulated supports, or the device connectors and other electrical items.

In quantum computing, a qubit is a unit of information analogous to a bit in classical computing, but it is affected by quantum mechanical properties such as superposition and entanglement which allow qubits to be in some ways more powerful than classical bits for some tasks. Qubits are used in quantum circuits and quantum algorithms composed of quantum logic gates to solve computational problems, where they are used for input/output and intermediate computations.

## References

1. Forman, Michael A. (2006). "Low-loss LIGA-fabricated coplanar waveguide and filter". 2006 Asia-Pacific Microwave Conference. pp. 1905–1907. doi:10.1109/APMC.2006.4429780. ISBN   978-4-902339-08-6.
2. Wen, Cheng P. (December 1969). "Coplanar Waveguide: A Surface Strip Transmission Line Suitable for Nonreciprocal Gyromagnetic Device Applications". IEEE Trans. Microw. Theory Tech. MTT-17: 1087–1090.
3. Rainee N. Simons, Coplanar Waveguide Circuits, Components, and Systems, pp. 1–2, Wiley, 2004 ISBN   9780471463931.
4. L. Frunzio; et al. (2005). "Fabrication and Characterization of Superconducting Circuit QED Devices for Quantum Computation". IEEE Transactions on Applied Superconductivity. 15 (2): 860–863. arXiv:. doi:10.1109/TASC.2005.850084.
5. M. Göppl; et al. (2008). "Coplanar waveguide resonators for circuit quantum electrodynamics". Journal of Applied Physics . 104 (11): 113904. arXiv:. Bibcode:2008JAP...104k3904G. doi:10.1063/1.3010859.
6. A. Megrant; et al. (2012). "Planar superconducting resonators with internal quality factors above one million". Appl. Phys. Lett. 100 (11): 113510. arXiv:. Bibcode:2012ApPhL.100k3510M. doi:10.1063/1.3693409.
7. M. A. Sillanpää; J. I. Park; R. W. Simmonds (2007-09-27). "Coherent quantum state storage and transfer between two phase qubits via a resonant cavity". Nature. 449 (7161): 438–42. arXiv:. Bibcode:2007Natur.449..438S. doi:10.1038/nature06124. PMID   17898762.
8. J. Majer; J. M. Chow; J. M. Gambetta; J. Koch; B. R. Johnson; J. A. Schreier; L. Frunzio; D. I. Schuster; A. A. Houck; A. Wallraff; A. Blais; M. H. Devoret; S. M. Girvin; R. J. Schoelkopf (2007-09-27). "Coupling superconducting qubits via a cavity bus". Nature. 449 (7161): 443–447. arXiv:. Bibcode:2007Natur.449..443M. doi:10.1038/nature06184. PMID   17898763.
9. Y. Wiemann; et al. (2015). "Observing electron spin resonance between 0.1 and 67 GHz at temperatures between 50 mK and 300 K using broadband metallic coplanar waveguides". Appl. Phys. Lett. 106 (19): 193505. arXiv:. Bibcode:2015ApPhL.106s3505W. doi:10.1063/1.4921231.
10. Kruglyak, V V; Demokritov, S O; Grundler, D (7 July 2010). "Magnonics". Journal of Physics D: Applied Physics. 43 (26): 264001. Bibcode:2010JPhD...43z4001K. doi:10.1088/0022-3727/43/26/264001.
11. W. Rauch; et al. (2015). "Microwave properties of YBa2Cu3O7−x thin films studied with coplanar transmission line resonators". J. Appl. Phys. 73 (4): 1866–1872. arXiv:. Bibcode:1993JAP....73.1866R. doi:10.1063/1.353173.
12. A. Porch; M.J. Lancaster; R.G. Humphreys (1995). "The coplanar resonator technique for determining the surface impedance of YBa2Cu3O7-delta thin films". IEEE Transactions on Microwave Theory and Techniques. 43 (2): 306–314. Bibcode:1995ITMTT..43..306P. doi:10.1109/22.348089.