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A standing wave in a rectangular cavity resonator Two dim standing wave.gif
A standing wave in a rectangular cavity resonator

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 (including acoustic). 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.

Resonance phenomenon in which a vibrating system or external force drives another system to oscillate with greater amplitude at specific frequencies

In mechanical systems, resonance is a phenomenon that occurs when the frequency at which a force is periodically applied is equal or nearly equal to one of the natural frequencies of the system on which it acts. This causes the system to oscillate with larger amplitude than when the force is applied at other frequencies.

Oscillation repetitive variation of some measure about a central value

Oscillation is the repetitive variation, typically in time, of some measure about a central value or between two or more different states. The term vibration is precisely used to describe mechanical oscillation. Familiar examples of oscillation include a swinging pendulum and alternating current.

Frequency is the number of occurrences of a repeating event per unit of time. It is also referred to as temporal frequency, which emphasizes the contrast to spatial frequency and angular frequency. The period is the duration of time of one cycle in a repeating event, so the period is the reciprocal of the frequency. For example: if a newborn baby's heart beats at a frequency of 120 times a minute, its period—the time interval between beats—is half a second. Frequency is an important parameter used in science and engineering to specify the rate of oscillatory and vibratory phenomena, such as mechanical vibrations, audio signals (sound), radio waves, and light.


A cavity resonator is one in which waves exist in a hollow space inside the device. In electronics and radio, microwave cavities consisting of hollow metal boxes are used in microwave transmitters, receivers and test equipment to control frequency, in place of the tuned circuits which are used at lower frequencies. Acoustic cavity resonators, in which sound is produced by air vibrating in a cavity with one opening, are known as Helmholtz resonators.

Microwave cavity

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.

Helmholtz resonance

Helmholtz resonance or wind throb is the phenomenon of air resonance in a cavity, such as when one blows across the top of an empty bottle. The name comes from a device created in the 1850s by Hermann von Helmholtz, the Helmholtz resonator, which he used to identify the various frequencies or musical pitches present in music and other complex sounds.


A physical system can have as many resonant frequencies as it has degrees of freedom; each degree of freedom can vibrate as a harmonic oscillator. Systems with one degree of freedom, such as a mass on a spring, pendulums, balance wheels, and LC tuned circuits have one resonant frequency. Systems with two degrees of freedom, such as coupled pendulums and resonant transformers can have two resonant frequencies. A crystal lattice composed of N atoms bound together can have N resonant frequencies. As the number of coupled harmonic oscillators grows, the time it takes to transfer energy from one to the next becomes significant. The vibrations in them begin to travel through the coupled harmonic oscillators in waves, from one oscillator to the next.

In classical mechanics, a harmonic oscillator is a system that, when displaced from its equilibrium position, experiences a restoring force F proportional to the displacement x:

Pendulum weight suspended from a pivot

A pendulum is a weight suspended from a pivot so that it can swing freely. When a pendulum is displaced sideways from its resting, equilibrium position, it is subject to a restoring force due to gravity that will accelerate it back toward the equilibrium position. When released, the restoring force acting on the pendulum's mass causes it to oscillate about the equilibrium position, swinging back and forth. The time for one complete cycle, a left swing and a right swing, is called the period. The period depends on the length of the pendulum and also to a slight degree on the amplitude, the width of the pendulum's swing.

Balance wheel

A balance wheel, or balance, is the timekeeping device used in mechanical watches and some clocks, analogous to the pendulum in a pendulum clock. It is a weighted wheel that rotates back and forth, being returned toward its center position by a spiral torsion spring, the balance spring or hairspring. It is driven by the escapement, which transforms the rotating motion of the watch gear train into impulses delivered to the balance wheel. Each swing of the wheel allows the gear train to advance a set amount, moving the hands forward. The balance wheel and hairspring together form a harmonic oscillator, which due to resonance oscillates preferentially at a certain rate, its resonant frequency or 'beat', and resists oscillating at other rates. The combination of the mass of the balance wheel and the elasticity of the spring keep the time between each oscillation or ‘tick’ very constant, accounting for its nearly universal use as the timekeeper in mechanical watches to the present. From its invention in the 14th century until tuning fork and quartz movements became available in the 1960s, virtually every portable timekeeping device used some form of balance wheel.

The term resonator is most often used for a homogeneous object in which vibrations travel as waves, at an approximately constant velocity, bouncing back and forth between the sides of the resonator. The material of the resonator, through which the waves flow, can be viewed as being made of millions of coupled moving parts (such as atoms). Therefore, they can have millions of resonant frequencies, although only a few may be used in practical resonators. The oppositely moving waves interfere with each other, and at its resonant frequencies reinforce each other to create a pattern of standing waves in the resonator. If the distance between the sides is , the length of a round trip is . To cause resonance, the phase of a sinusoidal wave after a round trip must be equal to the initial phase so the waves self-reinforce. The condition for resonance in a resonator is that the round trip distance, , is equal to an integer number of wavelengths of the wave:

Standing wave wave that remains in a constant position

In physics, a standing wave, also known as a stationary wave, is a wave which oscillates in time but whose peak amplitude profile does not move in space. The peak amplitude of the wave oscillations at any point in space is constant with time, and the oscillations at different points throughout the wave are in phase. The locations at which the amplitude is minimum are called nodes, and the locations where the amplitude is maximum are called antinodes.

Phase (waves) position of a point in time (an instant) on a waveform cycle

Phase is the position of a point in time on a waveform cycle. A complete cycle is defined as the interval required for the waveform to return to its arbitrary initial value. The graph to the right shows how one cycle constitutes 360° of phase. The graph also shows how phase is sometimes expressed in radians, where one radian of phase equals approximately 57.3°.

If the velocity of a wave is , the frequency is so the resonant frequencies are:

So the resonant frequencies of resonators, called normal modes, are equally spaced multiples (harmonics) of a lowest frequency called the fundamental frequency. The above analysis assumes the medium inside the resonator is homogeneous, so the waves travel at a constant speed, and that the shape of the resonator is rectilinear. If the resonator is inhomogeneous or has a nonrectilinear shape, like a circular drumhead or a cylindrical microwave cavity, the resonant frequencies may not occur at equally spaced multiples of the fundamental frequency. They are then called overtones instead of harmonics. There may be several such series of resonant frequencies in a single resonator, corresponding to different modes of vibration.

Fundamental frequency Lowest frequency of a periodic waveform, such as sound

The fundamental frequency, often referred to simply as the fundamental, is defined as the lowest frequency of a periodic waveform. In music, the fundamental is the musical pitch of a note that is perceived as the lowest partial present. In terms of a superposition of sinusoids, the fundamental frequency is the lowest frequency sinusoidal in the sum. In some contexts, the fundamental is usually abbreviated as f0, indicating the lowest frequency counting from zero. In other contexts, it is more common to abbreviate it as f1, the first harmonic.

Since the fundamental is the lowest frequency and is also perceived as the loudest, the ear identifies it as the specific pitch of the musical tone [harmonic spectrum]....The individual partials are not heard separately but are blended together by the ear into a single tone.

Drum type of musical instrument of the percussion family

The drum is a member of the percussion group of musical instruments. In the Hornbostel-Sachs classification system, it is a membranophone. Drums consist of at least one membrane, called a drumhead or drum skin, that is stretched over a shell and struck, either directly with the player's hands, or with a percussion mallet, to produce sound. There is usually a resonance head on the underside of the drum, typically tuned to a slightly lower pitch than the top drumhead. Other techniques have been used to cause drums to make sound, such as the thumb roll. Drums are the world's oldest and most ubiquitous musical instruments, and the basic design has remained virtually unchanged for thousands of years.


An overtone is any frequency greater than the fundamental frequency of a sound. Using the model of Fourier analysis, the fundamental and the overtones together are called partials. Harmonics, or more precisely, harmonic partials, are partials whose frequencies are numerical integer multiples of the fundamental. These overlapping terms are variously used when discussing the acoustic behavior of musical instruments. The model of Fourier analysis provides for the inclusion of inharmonic partials, which are partials whose frequencies are not whole-number ratios of the fundamental.


Resonant circuits

An electrical circuit composed of discrete components can act as a resonator when both an inductor and capacitor are included. Oscillations are limited by the inclusion of resistance, either via a specific resistor component, or due to resistance of the inductor windings. Such resonant circuits are also called RLC circuits after the circuit symbols for the components.

Inductor passive two-terminal electrical component that stores energy in its magnetic field

An inductor, also called a coil, choke, or reactor, is a passive two-terminal electrical component that stores energy in a magnetic field when electric current flows through it. An inductor typically consists of an insulated wire wound into a coil around a core.

Capacitor electrical component used to store energy for a short period of time

A capacitor is a passive two-terminal electronic component that stores electrical energy in an electric field. The effect of a capacitor is known as capacitance. While some capacitance exists between any two electrical conductors in proximity in a circuit, a capacitor is a component designed to add capacitance to a circuit. The capacitor was originally known as a condenser or condensator. The original name is still widely used in many languages, but not commonly in English.

Resistor Passive electrical component providing electrical resistance

A resistor is a passive two-terminal electrical component that implements electrical resistance as a circuit element. In electronic circuits, resistors are used to reduce current flow, adjust signal levels, to divide voltages, bias active elements, and terminate transmission lines, among other uses. High-power resistors that can dissipate many watts of electrical power as heat, may be used as part of motor controls, in power distribution systems, or as test loads for generators. Fixed resistors have resistances that only change slightly with temperature, time or operating voltage. Variable resistors can be used to adjust circuit elements, or as sensing devices for heat, light, humidity, force, or chemical activity.

A distributed-parameter resonator has capacitance, inductance, and resistance that cannot be isolated into separate lumped capacitors, inductors, or resistors. An example of this, much used in filtering, is the helical resonator.

A single layer coil (or solenoid) that is used as a secondary or tertiary winding in a Tesla coil or magnifying transmitter is also a distributed resonator.

Cavity resonators

A cavity resonator is a hollow closed conductor such as a metal box or a cavity within a metal block, containing electromagnetic waves (radio waves) reflecting back and forth between the cavity's walls. When a source of radio waves at one of the cavity's resonant frequencies is applied, the oppositely-moving waves form standing waves, and the cavity stores electromagnetic energy.

Since the cavity's lowest resonant frequency, the fundamental frequency, is that at which the width of the cavity is equal to a half-wavelength (λ/2), cavity resonators are only used at microwave frequencies and above, where wavelengths are short enough that the cavity is conveniently small in size.

Due to the low resistance of their conductive walls, cavity resonators have very high Q factors; that is their bandwidth, the range of frequencies around the resonant frequency at which they will resonate, is very narrow. Thus they can act as narrow bandpass filters. Cavity resonators are widely used as the frequency determining element in microwave oscillators. Their resonant frequency can be tuned by moving one of the walls of the cavity in or out, changing its size.

An illustration of the electric and magnetic field of one of the possible modes in a cavity resonator. US Patent 2424267 Figs 1a, 1b, 1c.PNG
An illustration of the electric and magnetic field of one of the possible modes in a cavity resonator.

Cavity magnetron

The cavity magnetron is a vacuum tube with a filament in the center of an evacuated, lobed, circular cavity resonator. A perpendicular magnetic field is imposed by a permanent magnet. The magnetic field causes the electrons, attracted to the (relatively) positive outer part of the chamber, to spiral outward in a circular path rather than moving directly to this anode. Spaced about the rim of the chamber are cylindrical cavities. The cavities are open along their length and so they connect with the common cavity space. As electrons sweep past these openings they induce a resonant high frequency radio field in the cavity, which in turn causes the electrons to bunch into groups. A portion of this field is extracted with a short antenna that is connected to a waveguide (a metal tube usually of rectangular cross section). The waveguide directs the extracted RF energy to the load, which may be a cooking chamber in a microwave oven or a high gain antenna in the case of radar.


The klystron, tube waveguide, is a beam tube including at least two apertured cavity resonators. The beam of charged particles passes through the apertures of the resonators, often tunable wave reflection grids, in succession. A collector electrode is provided to intercept the beam after passing through the resonators. The first resonator causes bunching of the particles passing through it. The bunched particles travel in a field-free region where further bunching occurs, then the bunched particles enter the second resonator giving up their energy to excite it into oscillations. It is a particle accelerator that works in conjunction with a specifically tuned cavity by the configuration of the structures.

The reflex klystron is a klystron utilizing only a single apertured cavity resonator through which the beam of charged particles passes, first in one direction. A repeller electrode is provided to repel (or redirect) the beam after passage through the resonator back through the resonator in the other direction and in proper phase to reinforce the oscillations set up in the resonator.

RF cavities in the linac of the Australian Synchrotron are used to accelerate and bunch beams of electrons; the linac is the tube passing through the middle of the cavity. Aust.-Synchrotron,-RF-Cavities-of-Linac-(Bunchers),-14.06.2007.jpg
RF cavities in the linac of the Australian Synchrotron are used to accelerate and bunch beams of electrons; the linac is the tube passing through the middle of the cavity.

Application in particle accelerators

On the beamline of an accelerator system, there are specific sections that are cavity resonators for RF. The (charged) particles that are to be accelerated pass through these cavities in such a way that the microwave electric field transfers energy to the particles, thus increasing their kinetic energy and thus accelerating them. Several large accelerator facilities employ superconducting niobium cavities for improved performance compared to metallic (copper) cavities.

Dielectric resonators

If a piece of material with large dielectric constant is surrounded by a material with much lower dielectric constant, then this abrupt change in dielectric constant can cause confinement of an electromagnetic wave, which leads to a resonator that acts similarly to a cavity resonator. [1]

Transmission line resonators

Transmission lines are structures that allow broadband transmission of electromagnetic waves, e.g. at radio or microwave frequencies. Abrupt change of impedance (e.g. open or short) in a transmission line causes reflection of the transmitted signal. Two such reflectors on a transmission line evoke standing waves between them and thus act as a one-dimensional resonator, with the resonance frequencies determined by their distance and the effective dielectric constant of the transmission line. [1]

Planar transmission line resonators are commonly employed for coplanar, stripline, and microstrip transmission lines. Such planar transmission line resonators can be very compact in size and are widely used elements in microwave circuitry. In cryogenic solid-state research, superconducting transmission line resonators contribute to solid-state spectroscopy [2] and quantum information science. [3] [4]

Optical cavities

In a laser, light is amplified in a cavity resonator that is usually composed of two or more mirrors. Thus an optical cavity , also known as a resonator, is a cavity with walls that reflect electromagnetic waves (i.e. light). This allows standing wave modes to exist with little loss.


Mechanical resonators are used in electronic circuits to generate signals of a precise frequency. For example, piezoelectric resonators, commonly made from quartz, are used as frequency references. Common designs consist of electrodes attached to a piece of quartz, in the shape of a rectangular plate for high frequency applications, or in the shape of a tuning fork for low frequency applications. The high dimensional stability and low temperature coefficient of quartz helps keeps resonant frequency constant. In addition, the quartz's piezoelectric property converts the mechanical vibrations into an oscillating voltage, which is picked up by the attached electrodes. These crystal oscillators are used in quartz clocks and watches, to create the clock signal that runs computers, and to stabilize the output signal from radio transmitters. Mechanical resonators can also be used to induce a standing wave in other media. For example, a multiple degree of freedom system can be created by imposing a base excitation on a cantilever beam. In this case the standing wave is imposed on the beam. [5] This type of system can be used as a sensor to track changes in frequency or phase of the resonance of the fiber. One application is as a measurement device for dimensional metrology. [6]


The most familiar examples of acoustic resonators are in musical instruments. Every musical instrument has resonators. Some generate the sound directly, such as the wooden bars in a xylophone, the head of a drum, the strings in stringed instruments, and the pipes in an organ. Some modify the sound by enhancing particular frequencies, such as the sound box of a guitar or violin. Organ pipes, the bodies of woodwinds, and the sound boxes of stringed instruments are examples of acoustic cavity resonators.


A sport motorcycle, equipped with exhaust resonator, designed for performance Exhaust with Resonator.jpg
A sport motorcycle, equipped with exhaust resonator, designed for performance

The exhaust pipes in automobile exhaust systems are designed as acoustic resonators that work with the muffler to reduce noise, by making sound waves "cancel each other out". [7] The "exhaust note" is an important feature for some vehicle owners, so both the original manufacturers and the after-market suppliers use the resonator to enhance the sound. In "tuned exhaust" systems designed for performance, the resonance of the exhaust pipes can also be used to remove combustion products from the combustion chamber at a particular engine speed or range of speeds. [8]

Percussion instruments

In many keyboard percussion instruments, below the centre of each note is a tube, which is an acoustic cavity resonator. The length of the tube varies according to the pitch of the note, with higher notes having shorter resonators. The tube is open at the top end and closed at the bottom end, creating a column of air that resonates when the note is struck. This adds depth and volume to the note. In string instruments, the body of the instrument is a resonator. The tremolo effect of a vibraphone is achieved via a mechanism that opens and shuts the resonators.

Stringed instruments

A Dobro-style resonator guitar Steel guitar-KayEss.1.jpeg
A Dobro-style resonator guitar

String instruments such as the bluegrass banjo may also have resonators. Many five-string banjos have removable resonators, so players can use the instrument with a resonator in bluegrass style, or without it in folk music style. The term resonator, used by itself, may also refer to the resonator guitar.

The modern ten-string guitar, invented by Narciso Yepes, adds four sympathetic string resonators to the traditional classical guitar. By tuning these resonators in a very specific way (C, B♭, A♭, G♭) and making use of their strongest partials (corresponding to the octaves and fifths of the strings' fundamental tones), the bass strings of the guitar now resonate equally with any of the 12 tones of the chromatic octave. The guitar resonator is a device for driving guitar string harmonics by an electromagnetic field. This resonance effect is caused by a feedback loop and is applied to drive the fundamental tones, octaves, 5th, 3rd to an infinite sustain.

See also

References and notes

  1. 1 2 David Pozar, Microwave Engineering, 2nd edition, Wiley, New York, NY, 1998.
  2. D. Hafner; et al. (2014). "Surface-resistance measurements using superconducting stripline resonators". Rev. Sci. Instrum. 85: 014702. arXiv: 1309.5331 . Bibcode:2014RScI...85a4702H. doi:10.1063/1.4856475.
  3. L. Frunzio; et al. (2005). "Fabrication and Characterization of Superconducting Circuit QED Devices for Quantum Computation". IEEE Transactions on Applied Superconductivity. 15: 860. arXiv: cond-mat/0411708 . Bibcode:2005ITAS...15..860F. doi:10.1109/TASC.2005.850084.
  4. M. Göppl; et al. (2008). "Coplanar waveguide resonators for circuit quantum electrodynamics". J. Appl. Phys. AIP. 104: 113904. arXiv: 0807.4094 . Bibcode:2008JAP...104k3904G. doi:10.1063/1.3010859.
  5. M.B. Bauza; R.J Hocken; S.T Smith; S.C Woody (2005), The development of a virtual probe tip with application to high aspect ratio microscale features, Rev. Sci Instrum, 76 (9) 095112 .
  6. "Precision Engineering and Manufacturing Solutions - IST Precision". Archived from the original on 31 July 2016. Retrieved 7 May 2018.
  7. "How Mufflers Work". 19 February 2001. Archived from the original on 8 October 2005. Retrieved 7 May 2018.
  8. Advanced Automotive Technology, p. 84, Office of Technology Assessment, Diane Publishing, September 1995 ISBN   1428920021.

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Electronic oscillator electronic circuit that produces a repetitive, oscillating electronic signal, often a sine wave or a square wave

An electronic oscillator is an electronic circuit that produces a periodic, oscillating electronic signal, often a sine wave or a square wave. Oscillators convert direct current (DC) from a power supply to an alternating current (AC) signal. They are widely used in many electronic devices. Common examples of signals generated by oscillators include signals broadcast by radio and television transmitters, clock signals that regulate computers and quartz clocks, and the sounds produced by electronic beepers and video games.

Crystal oscillator electronic oscillator circuit

A crystal oscillator is an electronic oscillator circuit that uses the mechanical resonance of a vibrating crystal of piezoelectric material to create an electrical signal with a precise frequency. This frequency is often used to keep track of time, as in quartz wristwatches, to provide a stable clock signal for digital integrated circuits, and to stabilize frequencies for radio transmitters and receivers. The most common type of piezoelectric resonator used is the quartz crystal, so oscillator circuits incorporating them became known as crystal oscillators, but other piezoelectric materials including polycrystalline ceramics are used in similar circuits.

<i>Q</i> factor

In physics and engineering the quality factor or Q factor is a dimensionless parameter that describes how underdamped an oscillator or resonator is, and characterizes a resonator's bandwidth relative to its centre frequency. Higher Q indicates a lower rate of energy loss relative to the stored energy of the resonator; the oscillations die out more slowly. A pendulum suspended from a high-quality bearing, oscillating in air, has a high Q, while a pendulum immersed in oil has a low one. Resonators with high quality factors have low damping, so that they ring or vibrate longer.


A klystron is a specialized linear-beam vacuum tube, invented in 1937 by American electrical engineers Russell and Sigurd Varian, which is used as an amplifier for high radio frequencies, from UHF up into the microwave range. Low-power klystrons are used as oscillators in terrestrial microwave relay communications links, while high-power klystrons are used as output tubes in UHF television transmitters, satellite communication, radar transmitters, and to generate the drive power for modern particle accelerators.

Gunn diode diode

A Gunn diode, also known as a transferred electron device (TED), is a form of diode, a two-terminal passive semiconductor electronic component, with negative resistance, used in high-frequency electronics. It is based on the "Gunn effect" discovered in 1962 by physicist J. B. Gunn. Its largest use is in electronic oscillators to generate microwaves, in applications such as radar speed guns, microwave relay data link transmitters, and automatic door openers.


A gyrotron is a class of high-power linear-beam vacuum tubes which generates millimeter-wave electromagnetic waves by the cyclotron resonance of electrons in a strong magnetic field. Output frequencies range from about 20 to 527 GHz, covering wavelengths from microwave to the edge of the terahertz gap. Typical output powers range from tens of kilowatts to 1–2 megawatts. Gyrotrons can be designed for pulsed or continuous operation.

Stub (electronics) short electrical transmission line

In microwave and radio-frequency engineering, a stub or resonant stub is a length of transmission line or waveguide that is connected at one end only. The free end of the stub is either left open-circuit or short-circuited. Neglecting transmission line losses, the input impedance of the stub is purely reactive; either capacitive or inductive, depending on the electrical length of the stub, and on whether it is open or short circuit. Stubs may thus function as capacitors, inductors and resonant circuits at radio frequencies.

Backward-wave oscillator

A backward wave oscillator (BWO), also called carcinotron or backward wave tube, is a vacuum tube that is used to generate microwaves up to the terahertz range. Belonging to the traveling-wave tube family, it is an oscillator with a wide electronic tuning range.

A dielectric resonator is a piece of dielectric (nonconductive) material, usually ceramic, that is designed to function as a resonator for radio waves, generally in the microwave and millimeter wave bands. The microwaves are confined inside the resonator material by the abrupt change in permittivity at the surface, and bounce back and forth between the sides. At certain frequencies, the resonant frequencies, the microwaves form standing waves in the resonator, oscillating with large amplitudes. Dielectric resonators generally consist of a "puck" of ceramic that has a large dielectric constant and a low dissipation factor. The resonant frequency is determined by the overall physical dimensions of the resonator and the dielectric constant of the material.

Electrical resonance occurs in an electric circuit at a particular resonant frequency when the imaginary parts of impedances or admittances of circuit elements cancel each other

Electrical resonance occurs in an electric circuit at a particular resonant frequency when the impedances or admittances of circuit elements cancel each other. In some circuits, this happens when the impedance between the input and output of the circuit is almost zero and the transfer function is close to one.

Radio frequency (RF) and microwave filters represent a class of electronic filter, designed to operate on signals in the megahertz to gigahertz frequency ranges. This frequency range is the range used by most broadcast radio, television, wireless communication, and thus most RF and microwave devices will include some kind of filtering on the signals transmitted or received. Such filters are commonly used as building blocks for duplexers and diplexers to combine or separate multiple frequency bands.

Metamaterial antenna

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.

Cavity perturbation theory describes methods for derivation of perturbation formulae for performance changes of a cavity resonator. These performance changes are assumed to be caused by either introduction of a small foreign object into the cavity or a small deformation of its boundary.

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".

Coplanar waveguide

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.

Extended interaction oscillator

The extended interaction oscillator (EIO) is a linear-beam vacuum tube designed to convert direct current to RF power. The conversion mechanism is the space charge wave process whereby velocity modulation in an electron beam transforms to current or density modulation with distance.