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A resonator is a device or system that exhibits
resonance Resonance describes the phenomenon of increased amplitude that occurs when the frequency of an applied periodic force (or a Fourier component of it) is equal or close to a natural frequency of the system on which it acts. When an oscil ...
or resonant behavior. That is, it naturally
oscillates Oscillation is the repetitive or periodic variation, typically in time, of some measure about a central value (often a point of equilibrium) or between two or more different states. Familiar examples of oscillation include a swinging pendulum ...
with greater
amplitude The amplitude of a periodic variable is a measure of its change in a single period (such as time or spatial period). The amplitude of a non-periodic signal is its magnitude compared with a reference value. There are various definitions of am ...
at some frequencies, called
resonant frequencies Resonance describes the phenomenon of increased amplitude that occurs when the frequency of an applied periodic force (or a Fourier component of it) is equal or close to a natural frequency of the system on which it acts. When an oscillati ...
, than at other frequencies. 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. 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.


Explanation

A physical system can have as many
resonant frequencies Resonance describes the phenomenon of increased amplitude that occurs when the frequency of an applied periodic force (or a Fourier component of it) is equal or close to a natural frequency of the system on which it acts. When an oscillati ...
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,
pendulum 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 th ...
s, 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. 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 Resonance describes the phenomenon of increased amplitude that occurs when the frequency of an applied periodic force (or a Fourier component of it) is equal or close to a natural frequency of the system on which it acts. When an oscillati ...
reinforce each other to create a pattern of
standing wave In physics, a standing wave, also known as a stationary wave, is a wave that 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 respect ...
s in the resonator. If the distance between the sides is d\,, the length of a round trip is 2d\,. 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, 2d\,, is equal to an integer number of wavelengths \lambda\, of the wave: :2d = N\lambda,\qquad\qquad N \in \ If the velocity of a wave is c\,, the frequency is f = c / \lambda\, so the resonant frequencies are: :f = \frac\qquad\qquad N \in \ So the resonant frequencies of resonators, called normal modes, are equally spaced multiples ( harmonics) of a lowest frequency called the
fundamental frequency 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. I ...
. 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.


Electromagnetics


Resonant circuits

An electrical circuit composed of discrete components can act as a resonator when both an
inductor 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 c ...
and
capacitor A capacitor is a device that stores electrical energy in an electric field by virtue of accumulating electric charges on two close surfaces insulated from each other. It is a passive electronic component with two terminals. The effect of ...
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 circuit An RLC circuit is an electrical circuit consisting of a resistor (R), an inductor (L), and a capacitor (C), connected in series or in parallel. The name of the circuit is derived from the letters that are used to denote the constituent compon ...
s after the circuit symbols for the components. 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. An
inductor 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 c ...
consisting of a coil of wire, is self-resonant at a certain frequency due to the
parasitic capacitance Parasitic capacitance is an unavoidable and usually unwanted capacitance that exists between the parts of an electronic component or circuit simply because of their proximity to each other. When two electrical conductors at different voltages ...
between its turns. This is often an unwanted effect that can cause parasitic oscillations in RF circuits. The self-resonance of inductors is used in a few circuits, such as the Tesla coil.


Cavity resonators

A ''cavity resonator'' is a hollow closed conductor such as a metal box or a cavity within a metal block, containing
electromagnetic wave In physics, electromagnetic radiation (EMR) consists of waves of the electromagnetic (EM) field, which propagate through space and carry momentum and electromagnetic radiant energy. It includes radio waves, microwaves, infrared, (visible) ...
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 frequencies Resonance describes the phenomenon of increased amplitude that occurs when the frequency of an applied periodic force (or a Fourier component of it) is equal or close to a natural frequency of the system on which it acts. When an oscillati ...
is applied, the oppositely-moving waves form
standing wave In physics, a standing wave, also known as a stationary wave, is a wave that 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 respect ...
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 Microwave is a form of electromagnetic radiation with wavelengths ranging from about one meter to one millimeter corresponding to frequencies between 300 MHz and 300 GHz respectively. Different sources define different frequency ra ...
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 In physics and engineering, the quality factor or ''Q'' factor is a dimensionless parameter that describes how underdamped an oscillator or resonator is. It is defined as the ratio of the initial energy stored in the resonator to the energy ...
s; 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.


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

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.


Application in particle accelerators

On the beamline of an accelerator system, there are specific sections that are cavity resonators for
radio frequency Radio frequency (RF) is the oscillation rate of an alternating electric current or voltage or of a magnetic, electric or electromagnetic field or mechanical system in the frequency range from around to around . This is roughly between the up ...
(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 niobium cavities for improved performance compared to metallic (copper) cavities.


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

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.


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. A common form is the
resonant stub 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 (as is always the c ...
, a length of transmission line terminated in either a
short circuit A short circuit (sometimes abbreviated to short or s/c) is an electrical circuit that allows a current to travel along an unintended path with no or very low electrical impedance. This results in an excessive current flowing through the circu ...
or open circuit, connected in series or parallel with a main transmission line. 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 and quantum information science.


Optical cavities

In a
laser A laser is a device that emits light through a process of optical amplification based on the stimulated emission of electromagnetic radiation. The word "laser" is an acronym for "light amplification by stimulated emission of radiation". The ...
, 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 Light or visible light is electromagnetic radiation that can be perceived by the human eye. Visible light is usually defined as having wavelengths in the range of 400–700 nanometres (nm), corresponding to frequencies of 750–420 t ...
). This allows standing wave modes to exist with little loss.


Mechanical

Mechanical resonators are used in electronic circuits to generate signals of a precise
frequency Frequency is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as ''temporal frequency'' for clarity, and is distinct from ''angular frequency''. Frequency is measured in hertz (Hz) which is eq ...
. For example, piezoelectric resonators, commonly made from
quartz Quartz is a hard, crystalline mineral composed of silica ( silicon dioxide). The atoms are linked in a continuous framework of SiO4 silicon-oxygen tetrahedra, with each oxygen being shared between two tetrahedra, giving an overall chemical f ...
, 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 Voltage, also known as electric pressure, electric tension, or (electric) potential difference, is the difference in electric potential between two points. In a static electric field, it corresponds to the work needed per unit of charge to ...
, which is picked up by the attached electrodes. These crystal oscillators are used in
quartz clock Quartz clocks and quartz watches are timepieces that use an electronic oscillator regulated by a quartz crystal to keep time. This crystal oscillator creates a signal with very precise frequency, so that quartz clocks and watches are at leas ...
s 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 In physics, a standing wave, also known as a stationary wave, is a wave that 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 respect ...
is imposed on the beam. This type of system can be used as a sensor to track changes in
frequency Frequency is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as ''temporal frequency'' for clarity, and is distinct from ''angular frequency''. Frequency is measured in hertz (Hz) which is eq ...
or phase of the
resonance Resonance describes the phenomenon of increased amplitude that occurs when the frequency of an applied periodic force (or a Fourier component of it) is equal or close to a natural frequency of the system on which it acts. When an oscil ...
of the fiber. One application is as a measurement device for
dimensional metrology Dimensional metrology is the science of using physical measurement equipment to quantify the physical size, form, characteristics, and relational distance from any given feature. History of metrology Standardized measurements are essential to t ...
.


Acoustic

The most familiar examples of acoustic resonators are in
musical instrument A musical instrument is a device created or adapted to make musical sounds. In principle, any object that produces sound can be considered a musical instrument—it is through purpose that the object becomes a musical instrument. A person who pl ...
s. Every musical instrument has resonators. Some generate the sound directly, such as the wooden bars in a
xylophone The xylophone (; ) is a musical instrument in the percussion family that consists of wooden bars struck by mallets. Like the glockenspiel (which uses metal bars), the xylophone essentially consists of a set of tuned wooden keys arranged in ...
, the head of a drum, the strings in stringed instruments, and the pipes in an
organ Organ may refer to: Biology * Organ (biology), a part of an organism Musical instruments * Organ (music), a family of keyboard musical instruments characterized by sustained tone ** Electronic organ, an electronic keyboard instrument ** Hammond ...
. Some modify the sound by enhancing particular frequencies, such as the sound box of a
guitar The guitar is a fretted musical instrument that typically has six strings. It is usually held flat against the player's body and played by strumming or plucking the strings with the dominant hand, while simultaneously pressing selected string ...
or
violin The violin, sometimes known as a '' fiddle'', is a wooden chordophone ( string instrument) in the violin family. Most violins have a hollow wooden body. It is the smallest and thus highest-pitched instrument ( soprano) in the family in regu ...
. Organ pipes, the bodies of woodwinds, and the sound boxes of stringed instruments are examples of acoustic cavity resonators.


Automobiles

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". 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..


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

String instruments such as the bluegrass
banjo The banjo is a stringed instrument with a thin membrane stretched over a frame or cavity to form a resonator. The membrane is typically circular, and usually made of plastic, or occasionally animal skin. Early forms of the instrument were fashi ...
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 Folk music is a music genre that includes traditional folk music and the contemporary genre that evolved from the former during the 20th-century folk revival. Some types of folk music may be called world music. Traditional folk music has ...
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

*
Coupling coefficient of resonators The coupling coefficient of resonators is a dimensionless value that characterizes interaction of two resonators. Coupling coefficients are used in resonator filter theory. Resonators may be both electromagnetic and acoustic. Coupling coefficients t ...
* Crab cavity * Nuclear magnetic resonance *
Optical ring resonators An optical ring resonator is a set of waveguides in which at least one is a closed loop coupled to some sort of light input and output. (These can be, but are not limited to being, waveguides.) The concepts behind optical ring resonators are the ...
* Superconducting RF


References and notes


External links

*{{Commonscat-inline, Resonators Acoustics Electromagnetism Musical instrument parts and accessories Mechanical vibrations Resonance