A resonator is a device or system that exhibits resonance or resonant behavior. That is, it naturally oscillates with greater amplitude at some frequencies, called resonant frequencies, 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 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.
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:
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.
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.
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 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 oscillations in RF circuits. The self-resonance of inductors is used in a few circuits, such as the Tesla coil.
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.
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.
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 niobium cavities for improved performance compared to metallic (copper) cavities.
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.
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] 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, 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.
Automobiles
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.
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.
↑ 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", Review of Scientific Instruments, Rev. Sci Instrum, 76 (9) 095112, 76 (9): 095112–095112–8, Bibcode:2005RScI...76i5112B, doi:10.1063/1.2052027 .
An electronic oscillator is an electronic circuit that produces a periodic, oscillating or alternating current (AC) signal, usually a sine wave, square wave or a triangle wave, powered by a direct current (DC) source. Oscillators are found in many electronic devices, such as radio receivers, television sets, radio and television broadcast transmitters, computers, computer peripherals, cellphones, radar, and many other devices.
Microwave is a form of electromagnetic radiation with wavelengths ranging from about 30 centimeters to one millimeter corresponding to frequencies between 1000 MHz and 300 GHz respectively. Different sources define different frequency ranges as microwaves; the above broad definition includes UHF, SHF and EHF bands. A more common definition in radio-frequency engineering is the range between 1 and 100 GHz. In all cases, microwaves include the entire SHF band at minimum. Frequencies in the microwave range are often referred to by their IEEE radar band designations: S, C, X, Ku, K, or Ka band, or by similar NATO or EU designations.
A crystal oscillator is an electronic oscillator circuit that uses a piezoelectric crystal as a frequency-selective element. The oscillator 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 a quartz crystal, so oscillator circuits incorporating them became known as crystal oscillators. However, other piezoelectricity materials including polycrystalline ceramics are used in similar circuits.
Resonance is a phenomenon that occurs when an object or system is subjected to an external force or vibration that matches its natural frequency. When this happens, the object or system absorbs energy from the external force and starts vibrating with a larger amplitude. Resonance can occur in various systems, such as mechanical, electrical, or acoustic systems, and it is often desirable in certain applications, such as musical instruments or radio receivers. However, resonance can also be detrimental, leading to excessive vibrations or even structural failure in some cases.
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 lost in one radian of the cycle of oscillation. Q factor is alternatively defined as the ratio of a resonator's centre frequency to its bandwidth when subject to an oscillating driving force. These two definitions give numerically similar, but not identical, results. Higher Q indicates a lower rate of energy loss and 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.
A quartz crystal microbalance (QCM) measures a mass variation per unit area by measuring the change in frequency of a quartz crystal resonator. The resonance is disturbed by the addition or removal of a small mass due to oxide growth/decay or film deposition at the surface of the acoustic resonator. The QCM can be used under vacuum, in gas phase and more recently in liquid environments. It is useful for monitoring the rate of deposition in thin-film deposition systems under vacuum. In liquid, it is highly effective at determining the affinity of molecules to surfaces functionalized with recognition sites. Larger entities such as viruses or polymers are investigated as well. QCM has also been used to investigate interactions between biomolecules. Frequency measurements are easily made to high precision ; hence, it is easy to measure mass densities down to a level of below 1 μg/cm2. In addition to measuring the frequency, the dissipation factor is often measured to help analysis. The dissipation factor is the inverse quality factor of the resonance, Q−1 = w/fr ; it quantifies the damping in the system and is related to the sample's viscoelastic properties.
A gyrotron is a class of high-power linear-beam vacuum tubes that 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. The gyrotron was invented by Soviet scientists at NIRFI, based in Nizhny Novgorod, Russia.
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 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 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.
A parametric oscillator is a driven harmonic oscillator in which the oscillations are driven by varying some parameters of the system at some frequencies, typically different from the natural frequency of the oscillator. A simple example of a parametric oscillator is a child pumping a playground swing by periodically standing and squatting to increase the size of the swing's oscillations. The child's motions vary the moment of inertia of the swing as a pendulum. The "pump" motions of the child must be at twice the frequency of the swing's oscillations. Examples of parameters that may be varied are the oscillator's resonance frequency and damping .
In quantum computing, more specifically in superconducting quantum computing, flux qubits are micrometer sized loops of superconducting metal that is interrupted by a number of Josephson junctions. These devices function as quantum bits. The flux qubit was first proposed by Terry P. Orlando et al. at MIT in 1999 and fabricated shortly thereafter. During fabrication, the Josephson junction parameters are engineered so that a persistent current will flow continuously when an external magnetic flux is applied. Only an integer number of flux quanta are allowed to penetrate the superconducting ring, resulting in clockwise or counter-clockwise mesoscopic supercurrents 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 (macroscopic) 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.
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.
A microwave cavity or radio frequency cavity is a special type of resonator, consisting of a closed metal structure that confines electromagnetic fields in the microwave or RF 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.
Resonant inductive coupling or magnetic phase synchronous coupling is a phenomenon with inductive coupling in which the coupling becomes stronger when the "secondary" (load-bearing) side of the loosely coupled coil resonates. A resonant transformer of this type is often used in analog circuitry as a bandpass filter. Resonant inductive coupling is also used in wireless power systems for portable computers, phones, and vehicles.
A waveguide filter is an electronic filter constructed with waveguide technology. Waveguides are hollow metal conduits 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.
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.
Cavity optomechanics is a branch of physics which focuses on the interaction between light and mechanical objects on low-energy scales. It is a cross field of optics, quantum optics, solid-state physics and materials science. The motivation for research on cavity optomechanics comes from fundamental effects of quantum theory and gravity, as well as technological applications.
A loop-gap resonator (LGR) is an electromagnetic resonator that operates in the radio and microwave frequency ranges. The simplest LGRs are made from a conducting tube with a narrow slit cut along its length. The LGR dimensions are typically much smaller than the free-space wavelength of the electromagnetic fields at the resonant frequency. Therefore, relatively compact LGRs can be designed to operate at frequencies that are too low to be accessed using, for example, cavity resonators. These structures can have very sharp resonances making them useful for electron spin resonance (ESR) experiments, and precision measurements of electromagnetic material properties.
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