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Microwave cavity

A microwave cavity or radio frequency (RF) cavity is a special type of resonator, consisting of a closed (or largely 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. f m n l = c 2 π μ r ϵ r ⋅ k m n l = c 2 π μ r ϵ r ( m π a ) 2 + ( n π b ) 2 + ( l π d ) 2 = c 2 μ r ϵ r ( m a ) 2 + ( n b ) 2 + ( l d ) 2 {displaystyle {egin{aligned}f_{mnl}&={frac {c}{2pi {sqrt {mu _{r}epsilon _{r}}}}}cdot k_{mnl}\&={frac {c}{2pi {sqrt {mu _{r}epsilon _{r}}}}}{sqrt {left({frac {mpi }{a}} ight)^{2}+left({frac {npi }{b}} ight)^{2}+left({frac {lpi }{d}} ight)^{2}}}\&={frac {c}{2{sqrt {mu _{r}epsilon _{r}}}}}{sqrt {left({frac {m}{a}} ight)^{2}+left({frac {n}{b}} ight)^{2}+left({frac {l}{d}} ight)^{2}}}end{aligned}}}     (1) Q c = ( k a d ) 3 b η 2 π 2 R s ⋅ 1 l 2 a 3 ( 2 b + d ) + ( 2 b + a ) d 3 {displaystyle Q_{c}={frac {(kad)^{3}beta }{2pi ^{2}R_{s}}}cdot {frac {1}{l^{2}a^{3}left(2b+d ight)+left(2b+a ight)d^{3}}},}     (3) Q d = 1 tan ⁡ δ {displaystyle Q_{d}={frac {1}{ an delta }},}     (4) Q = ( 1 Q c + 1 Q d ) − 1 {displaystyle Q=left({frac {1}{Q_{c}}}+{frac {1}{Q_{d}}} ight)^{-1},}     (2) L m n l = μ k m n l 2 V {displaystyle L_{mnl}=mu k_{mnl}^{2}V,}     (6) C m n l = ϵ k m n l 4 V {displaystyle C_{mnl}={frac {epsilon }{k_{mnl}^{4}V}},}     (7) f m n l = 1 2 π L m n l C m n l = 1 2 π 1 k m n l 2 μ ϵ {displaystyle {egin{aligned}f_{mnl}&={frac {1}{2pi {sqrt {L_{mnl}C_{mnl}}}}}\&={frac {1}{2pi {sqrt {{frac {1}{k_{mnl}^{2}}}mu epsilon }}}}end{aligned}}}     (5) A microwave cavity or radio frequency (RF) cavity is a special type of resonator, consisting of a closed (or largely closed) metal structure that confines electromagnetic fields in the microwave region of the spectrum. The structure is either hollow or filled with dielectric material. The microwaves bounce back and forth between the walls of the cavity. At the cavity's resonant frequencies they reinforce to form standing waves in the cavity. Therefore, the cavity functions similarly to an organ pipe or sound box in a musical instrument, oscillating preferentially at a series of frequencies, its resonant frequencies. Thus it can act as a bandpass filter, allowing microwaves of a particular frequency to pass while blocking microwaves at nearby frequencies. A microwave cavity acts similarly to a resonant circuit with extremely low loss at its frequency of operation, resulting in quality factors (Q factors) up to the order of 106, compared to 102 for circuits made with separate inductors and capacitors at the same frequency. They are used in place of resonant circuits at microwave frequencies, since at these frequencies discrete resonant circuits cannot be built because the values of inductance and capacitance needed are too low. They are used in oscillators and transmitters to create microwave signals, and as filters to separate a signal at a given frequency from other signals, in equipment such as radar equipment, microwave relay stations, satellite communications, and microwave ovens. RF cavities can also manipulate charged particles passing through them by application of acceleration voltage and are thus used in particle accelerators and microwave vacuum tubes such as klystrons and magnetrons. Most resonant cavities are made from closed (or short-circuited) sections of waveguide or high-permittivity dielectric material (see dielectric resonator). Electric and magnetic energy is stored in the cavity and the only losses are due to finite conductivity of cavity walls and dielectric losses of material filling the cavity. Every cavity has numerous resonant frequencies that correspond to electromagnetic field modes satisfying necessary boundary conditions on the walls of the cavity. Because of these boundary conditions that must be satisfied at resonance (tangential electric fields must be zero at cavity walls), it follows that cavity length must be an integer multiple of half-wavelength at resonance. Hence, a resonant cavity can be thought of as a waveguide equivalent of short circuited half-wavelength transmission line resonator. Q factor of a resonant cavity can be calculated using cavity perturbation theory and expressions for stored electric and magnetic energy. The electromagnetic fields in the cavity are excited via external coupling. An external power source is usually coupled to the cavity by a small aperture, a small wire probe or a loop. External coupling structure has an effect on cavity performance and needs to be considered in the overall analysis.

[ "Microwave", "Resonator", "Dielectric", "Cavity perturbation theory" ]
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