Editing Resonator (section)

==Electromagnetics==
{{Electromagnetism|Network}}

===Resonant circuits===
{{main|electrical resonance}}

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 [[electrical resistance|resistance]] of the inductor windings.  Such [[resonant circuit]]s are also called [[RLC circuit]]s after the circuit symbols for the components.

A [[distributed-element model|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 [[filter (signal processing)|filtering]], is the [[helical resonator]].

An [[inductor]] consisting of a coil of wire, is self-resonant at a certain frequency due to the [[parasitic capacitance]] between its turns.  This is often an unwanted effect that can cause [[parasitic oscillation]]s in RF circuits.  The self-resonance of inductors is used in a few circuits, such as the [[Tesla coil]].

===Cavity resonators===
{{main|Microwave cavity}}
A ''cavity resonator'' is a hollow closed conductor such as a metal box or a cavity within a metal block, containing [[electromagnetic wave]]s (radio waves) reflecting back and forth between the cavity's walls.  When a source of radio waves at one of the cavity's [[resonant frequency|resonant frequencies]] is applied, the oppositely-moving waves form [[standing wave]]s, 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 factor]]s; that is their [[bandwidth (signal processing)|bandwidth]], the range of frequencies around the resonant frequency at which they will resonate, is very narrow.  Thus they can act as narrow [[bandpass filter]]s.   Cavity resonators are widely used as the frequency determining element in [[electronic oscillator|microwave oscillator]]s.  Their resonant frequency can be tuned by moving one of the walls of the cavity in or out, changing its size.

[[File:US Patent 2424267 Figs 1a, 1b, 1c.PNG|right|thumb|An illustration of the electric and magnetic field of one of the possible modes in a cavity resonator.]]

====Cavity magnetron====
{{main|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.

====Klystron====
{{main|klystron}}
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.

[[File:Aust.-Synchrotron,-RF-Cavities-of-Linac-(Bunchers),-14.06.2007.jpg|left<!--image on left to prevent a huge block of whitespace at the end-->|thumb|RF cavities in the [[Linear particle accelerator|linac]] of the [[Australian Synchrotron]] are used to accelerate and bunch beams of [[electron]]s; 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 [[radio frequency]] (RF) radiation. 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 radio frequency|superconducting niobium cavities]] for improved performance compared to metallic (copper) cavities.

===Loop-gap resonator===
{{main|loop-gap resonator}}
The [[loop-gap resonator]] (LGR) is made by cutting a narrow slit along the length of a conducting tube.  The slit has an effective capacitance and the bore of the resonator has an effective inductance.  Therefore, the LGR can be modeled as an RLC circuit and has a resonant frequency that is typically between 200 MHz and 2 GHz.  In the absence of radiation losses, the effective resistance of the LGR is determined by the resistivity and electromagnetic skin depth of the conductor used to make the resonator.

One key advantage of the LGR is that, at its resonant frequency, its dimensions are small compared to the free-space wavelength of the electromagnetic fields.  Therefore, it is possible to use LGRs to construct a compact and high-Q resonator that operates at relatively low frequencies where cavity resonators would be impractically large.

===Dielectric resonators===
{{main|Dielectric resonator}}
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.<ref name="pozar">{{cite book|first=David|last=Pozar|title=Microwave Engineering|edition=2|publisher=Wiley|location=New York|year=1998|isbn=9780470631553}}</ref>

===Transmission-line resonators===
[[Transmission line]]s 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.<ref name="pozar" />  A common form is the [[resonant stub]], a length of transmission line terminated in either a [[short circuit]] or open circuit, connected in series or parallel with a main transmission line. 

Planar transmission-line resonators are commonly employed for [[Coplanar waveguide|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 <ref>{{cite journal|author=D. Hafner |year=2014|title=Surface-resistance measurements using superconducting stripline resonators |journal=Rev. Sci. Instrum. |volume=85|issue=1|pages=014702 |doi=10.1063/1.4856475 |pmid=24517793|arxiv=1309.5331 |display-authors=etal|bibcode=2014RScI...85a4702H|s2cid=16234011}}</ref> and quantum information science.<ref>{{cite journal|author=L. Frunzio |year=2005|title=Fabrication and Characterization of Superconducting Circuit QED Devices for Quantum Computation |journal=IEEE Transactions on Applied Superconductivity |volume=15|issue=2|pages=860–863 |doi=10.1109/TASC.2005.850084 |arxiv = cond-mat/0411708 |display-authors=etal|bibcode=2005ITAS...15..860F|s2cid=12789596}}</ref><ref>{{cite journal|author=M. Göppl|year=2008|title=Coplanar waveguide resonators for circuit quantum electrodynamics|journal=[[Journal of Applied Physics|J. Appl. Phys.]]|volume=104|issue=11|pages=113904–113904–8|doi=10.1063/1.3010859|arxiv = 0807.4094 |bibcode = 2008JAP...104k3904G |s2cid=56398614|display-authors=etal}}</ref>

===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.