50:
792:. Like an overdamped system, the output does not oscillate, and does not overshoot its steady-state output (i.e., it approaches a steady-state asymptote). Like an underdamped response, the output of such a system responds quickly to a unit step input. Critical damping results in the fastest response (approach to the final value) possible without overshoot. Real system specifications usually allow some overshoot for a faster initial response or require a slower initial response to provide a
761:) may oscillate only once or a few times before dying out. As the quality factor increases, the relative amount of damping decreases. A high-quality bell rings with a single pure tone for a very long time after being struck. A purely oscillatory system, such as a bell that rings forever, has an infinite quality factor. More generally, the output of a second-order
2680:
504:
2137:
240:
The definition of Q since its first use in 1914 has been generalized to apply to coils and condensers, resonant circuits, resonant devices, resonant transmission lines, cavity resonators, and has expanded beyond the electronics field to apply to dynamical systems in general: mechanical and acoustic
2427:
2558:
2304:
419:
1681:
1334:
because of its long ring-down time, where it can measure the velocities of blood flow. Meanwhile, a transducer with a low Q-factor has a short ring-down time and is suitable for organ imaging because it can receive a broad range of reflected echoes from bodily
344:
1969:
1777:
2889:
4532:
1995:
3023:
2667:
4612:
Tavakoli, Mehdi; Jalili, Yousef Seyed; Elahi, Seyed
Mohammad (2019-04-28). "Rayleigh-Wood anomaly approximation with FDTD simulation of plasmonic gold nanohole array for determination of optimum extraordinary optical transmission characteristics".
513:
expressible in simpler terms, involving only the coefficients of the second-order differential equation describing most resonant systems, electrical or mechanical. In electrical systems, the stored energy is the sum of energies stored in lossless
1873:
597:
144:
with greater amplitudes (at the resonant frequency) but have a smaller range of frequencies around that frequency for which they resonate; the range of frequencies for which the oscillator resonates is called the bandwidth. Thus, a
610:
at which the stored energy and power loss are measured. This definition is consistent with its usage in describing circuits with a single reactive element (capacitor or inductor), where it can be shown to be equal to the ratio of
1375:. Equivalently, it compares the frequency at which a system oscillates to the rate at which it dissipates its energy. More precisely, the frequency and period used should be based on the system's natural frequency, which at low
1174:
3150:
3451:
3301:
231:
was only because, at the time, all other letters of the alphabet were taken. The term was not intended as an abbreviation for "quality" or "quality factor", although these terms have grown to be associated with it.
3693:
will not evenly amplify the multiple frequencies an instrument produces. For this reason, string instruments often have bodies with complex shapes, so that they produce a wide range of frequencies fairly evenly.
4525:
3999:
3576:
707:
with different rates of decay. As the quality factor decreases the slower decay mode becomes stronger relative to the faster mode and dominates the system's response resulting in a slower system. A second-order
1022:
2315:
167:
The quality factor of oscillators varies substantially from system to system, depending on their construction. Systems for which damping is important (such as dampers keeping a door from slamming shut) have
4144:
Slyusar V. I. 60 Years of
Electrically Small Antennas Theory.//Proceedings of the 6-th International Conference on Antenna Theory and Techniques, 17–21 September 2007, Sevastopol, Ukraine. - Pp. 116 - 118.
182:. Clocks, lasers, and other resonating systems that need either strong resonance or high frequency stability have high quality factors. Tuning forks have quality factors around 1000. The quality factor of
2438:
1553:
1461:
499:{\displaystyle Q\mathrel {\stackrel {\text{def}}{=}} 2\pi \times {\frac {\text{energy stored}}{\text{energy dissipated per cycle}}}=2\pi f_{r}\times {\frac {\text{energy stored}}{\text{power loss}}}.}
2199:
1321:
1591:
3808:
2683:
A graph of a filter's gain magnitude, illustrating the concept of −3 dB at a voltage gain of 0.707 or half-power bandwidth. The frequency axis of this symbolic diagram can be linear or
263:
3641:
1884:
1692:
2132:{\displaystyle H(s)={\frac {\omega _{\mathrm {N} }^{2}}{s^{2}+\underbrace {\frac {\omega _{\mathrm {N} }}{Q}} _{2\zeta \omega _{\mathrm {N} }=2\alpha }s+\omega _{\mathrm {N} }^{2}}}\,}
2761:
4128:
946:
2930:
2569:
747:. Underdamped systems combine oscillation at a specific frequency with a decay of the amplitude of the signal. Underdamped systems with a low quality factor (a little above
1800:
3891:. While loss is normally considered a hindrance in the development of plasmonic devices, it is possible to leverage this property to present new enhanced functionalities.
551:
3206:
of an individual reactive component depends on the frequency at which it is evaluated, which is typically the resonant frequency of the circuit that it is used in. The
812:
of the closed-loop system; as the phase margin decreases, the approximate second-order closed-loop system is made more oscillatory (i.e., has a higher quality factor).
1082:
1046:
1261:
1224:
1204:
4591:
104:
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
4432:
4656:
Chen, Gang; Mahan, Gerald; Meroueh, Laureen; Huang, Yi; Tsurimaki, Yoichiro; Tong, Jonathan K.; Ni, George; Zeng, Lingping; Cooper, Thomas Alan (2017-12-31).
4726:
1089:
765:
with a very high quality factor responds to a step input by quickly rising above, oscillating around, and eventually converging to a steady-state value.
3073:
1349:
is approximately the ratio of the stored energy to the energy dissipated over one radian of the oscillation; or nearly equivalently, at high enough
3362:
3717:
for a brass instrument, giving it a muddy, breathy tone. Instruments made of stiffer plastic, brass, or wood have higher-Q. An excessively high
3220:
200:
There are many alternative quantities used by physicists and engineers to describe how damped an oscillator is. Important examples include: the
4078:
3993:
3512:
2422:{\displaystyle H(s)={\frac {{\frac {\omega _{\mathrm {N} }}{Q}}s}{s^{2}+{\frac {\omega _{\mathrm {N} }}{Q}}s+\omega _{\mathrm {N} }^{2}}}}
257:
becomes larger, meaning the resonator becomes less damped. One of these definitions is the frequency-to-bandwidth ratio of the resonator:
4575:
969:
4122:
4112:
2553:{\displaystyle H(s)={\frac {s^{2}+\omega _{\mathrm {N} }^{2}}{s^{2}+{\frac {\omega _{\mathrm {N} }}{Q}}s+\omega _{\mathrm {N} }^{2}}}}
4736:
4569:
4512:
4488:
4379:
4334:
4300:
4244:
4217:
4192:
3966:
3190:
is as in the series circuit. This is a common circumstance for resonators, where limiting the resistance of the inductor to improve
541:
More generally and in the context of reactive component specification (especially inductors), the frequency-dependent definition of
3167:
are all in parallel. The lower the parallel resistance, the more effect it will have in damping the circuit and thus the lower the
1505:
100:
when subject to an oscillating driving force. These two definitions give numerically similar, but not identical, results. Higher
4662:
2299:{\displaystyle H(s)={\frac {\omega _{\mathrm {N} }^{2}}{s^{2}+{\frac {\omega _{\mathrm {N} }}{Q}}s+\omega _{\mathrm {N} }^{2}}}}
3915:
1417:
187:
4781:
3852:
is equal to the ratio of the resonant frequency to the bandwidth of the cavity resonance. The average lifetime of a resonant
2917:
1676:{\displaystyle Q={\frac {1}{2\zeta }}={\frac {\omega _{\mathrm {N} }}{2\alpha }}={\frac {\tau \omega _{\mathrm {N} }}{2}},}
959:
is the pendulum's radian frequency of oscillation, and Γ is the frictional damping force on the pendulum per unit velocity.
4324:
1482:
691:. Such a system doesn't oscillate at all, but when displaced from its equilibrium steady-state output it returns to it by
205:
97:
4154:
1270:
4588:
642:
413:
is the ratio of the energy stored in the oscillating resonator to the energy dissipated per cycle by damping processes:
4019:
1974:
The energy of oscillation, or the power dissipation, decays twice as fast, that is, as the square of the amplitude, as
4801:
3709:
needs to be high enough to pick one frequency out of the broader-spectrum buzzing of the lips or reed. By contrast, a
368:(FWHM) i.e. the bandwidth over which the power of vibration is greater than half the power at the resonant frequency,
339:{\displaystyle Q\mathrel {\stackrel {\text{def}}{=}} {\frac {f_{r}}{\Delta f}}={\frac {\omega _{r}}{\Delta \omega }},}
3757:
96:
of the cycle of oscillation. Q factor is alternatively defined as the ratio of a resonator's centre frequency to its
1964:{\displaystyle \tau ={2Q \over \omega _{\mathrm {N} }}={1 \over \zeta \omega _{\mathrm {N} }}={\frac {1}{\alpha }}.}
1772:{\displaystyle \zeta ={\frac {1}{2Q}}={\alpha \over \omega _{\mathrm {N} }}={1 \over \tau \omega _{\mathrm {N} }}.}
1390:
factor is approximately the number of oscillations required for a freely oscillating system's energy to fall off to
365:
4037:
3604:
3888:
4421:
3910:
2884:{\displaystyle Q={\frac {2^{\frac {BW}{2}}}{2^{BW}-1}}={\frac {1}{2\sinh \left({\frac {1}{2}}\ln(2)BW\right)}},}
224:
43:
825:
156:; it would do a better job of filtering out signals from other stations that lie nearby on the spectrum. High-
4260:
4786:
1331:
1327:
713:
655:
behavior of simple damped oscillators. (For mathematical details about these systems and their behavior see
4355:
3018:{\displaystyle Q={\frac {1}{R}}{\sqrt {\frac {L}{C}}}={\frac {\omega _{0}L}{R}}={\frac {1}{\omega _{0}RC}}}
2662:{\displaystyle H(s)={\frac {s^{2}}{s^{2}+{\frac {\omega _{\mathrm {N} }}{Q}}s+\omega _{\mathrm {N} }^{2}}}}
4796:
161:
77:
3872:
of light that is much more intense than the laser's normal continuous output. This technique is known as
712:
with a very low quality factor has a nearly first-order step response; the system's output responds to a
3502:
of a resonator involving a series combination of a capacitor and an inductor can be determined from the
3041:
2696:
910:
92:
is. It is defined as the ratio of the initial energy stored in the resonator to the energy lost in one
1488:
The resonant frequency is often expressed in natural units (radians per second), rather than using the
4478:
4182:
3598:, where the damping force or drag force is proportional to velocity. The formula for the Q factor is:
1868:{\displaystyle \alpha ={\omega _{\mathrm {N} } \over 2Q}=\zeta \omega _{\mathrm {N} }={1 \over \tau }}
227:'s Engineering Department while evaluating the quality of coils (inductors). His choice of the symbol
4681:
4622:
3482:
3332:
398:
213:
209:
4658:"Losses in plasmonics: from mitigating energy dissipation to embracing loss-enabled functionalities"
2744:
value of 10 and a centre frequency of 100 kHz would have a 3 dB bandwidth of 10 kHz.
49:
4061:
3728:
656:
592:{\displaystyle Q(\omega )=\omega \times {\frac {\text{maximum energy stored}}{\text{power loss}}},}
153:
125:
53:
A damped oscillation. A low Q factor – about 5 here – means the oscillation dies out rapidly.
4791:
4671:
4638:
4069:
3935:
3900:
2700:
1485:, is the width of the range of frequencies for which the energy is at least half its peak value.
880:
4753:
883:(i.e., continuous-time filter with the flattest passband frequency response) has an underdamped
108:, while a pendulum immersed in oil has a low one. Resonators with high quality factors have low
3214:
of a resonant circuit using that inductor (including its series loss) and a perfect capacitor.
804:
systems, the dominant closed-loop response is often well-modeled by a second-order system. The
4732:
4699:
4565:
4559:
4484:
4385:
4375:
4330:
4296:
4240:
4234:
4213:
4188:
4118:
3989:
3962:
2165:
2157:
1986:
1579:
1575:
1567:
1474:
1357:
1051:
1031:
801:
788:
704:
692:
607:
383:
27:
Parameter describing the longevity of energy in a resonator relative to its resonant frequency
3983:
3956:
3731:
have a very high Q, as they are designed for picking out a very narrow range of frequencies.
1353:
values, 2π times the ratio of the total energy stored and the energy lost in a single cycle.
1233:
1209:
4689:
4630:
3702:
3052:
of the tuned circuit, respectively. The larger the series resistance, the lower the circuit
2169:
793:
700:
652:
527:
241:
resonators, material Q and quantum systems such as spectral lines and particle resonances.
1182:
4595:
4589:
Methods of
Experimental Physics – Lecture 5: Fourier Transforms and Differential Equations
4536:
4041:
4023:
3869:
3748:
3706:
762:
709:
4504:
3506:
values of the components, whether their losses come from series resistance or otherwise:
2176:
systems oscillate for many cycles. For example, high-quality bells have an approximately
2172:) into the system. A higher quality factor implies a lower attenuation rate, and so high-
4685:
4626:
1379:
values is somewhat higher than the oscillation frequency as measured by zero crossings.
3595:
612:
531:
194:
4775:
4722:
4642:
1563:
1404:
or 0.2%, of its original energy. This means the amplitude falls off to approximately
848:
201:
109:
3930:
3920:
805:
183:
1267:
scalar (m is azimuth index, p is radial index; in this application, skin depth is
1169:{\displaystyle Q_{\Omega }={\frac {R_{w}}{\delta }}{\frac {1-m^{2}}{v_{m,p}^{2}}}}
4290:
3868:
cavity is abruptly changed from a low value to a high one, the laser will emit a
3145:{\displaystyle Q=R{\sqrt {\frac {C}{L}}}={\frac {R}{\omega _{0}L}}=\omega _{0}RC}
3905:
3873:
3049:
2910:
1364:
852:
743:
534:
energies at some point in time; the lost energy is the work done by an external
149:
81:
62:
4634:
3884:
3045:
1264:
1227:
696:
687:
660:
616:
519:
85:
4703:
3725:
in an instrument may vary across frequencies, but this may not be desirable.
4389:
4012:
3690:
3591:
3446:{\displaystyle Q_{C}={\frac {-X_{C}}{R_{C}}}={\frac {1}{\omega _{0}CR_{C}}}}
2684:
2177:
2161:
1372:
1368:
717:
523:
515:
253:, which are not exactly equivalent. They become approximately equivalent as
141:
133:
129:
121:
89:
4147:
3296:{\displaystyle Q_{L}={\frac {X_{L}}{R_{L}}}={\frac {\omega _{0}L}{R_{L}}}}
4762:
4694:
4657:
3710:
2704:
963:
152:
in a radio receiver would be more difficult to tune, but would have more
17:
4034:
3925:
638:
58:
2679:
828:
with equal capacitors and equal resistors is critically damped (i.e.,
526:
per cycle. In mechanical systems, the stored energy is the sum of the
3853:
3740:
2748:
93:
3571:{\displaystyle Q={\frac {1}{{\frac {1}{Q_{L}}}+{\frac {1}{Q_{C}}}}}}
3356:
of a resonant circuit using that capacitor with a perfect inductor:
1411:
The width (bandwidth) of the resonance is given by (approximately):
4676:
4450:
4351:
2164:
of −α. That is, the attenuation parameter α represents the rate of
249:
In the context of resonators, there are two common definitions for
3865:
2678:
1496:
1017:{\textstyle Q_{D}\approx 30\left({\frac {L}{\lambda }}\right)^{2}}
535:
48:
4374:. Lang, Jeffrey (Jeffrey H.). Amsterdam: Elsevier. p. 647.
3352:
of a capacitor with a series loss resistance is the same as the
3178:
circuit where the main loss is the resistance of the inductor,
4754:
Calculating the cut-off frequencies when center frequency and
4599:
4540:
3171:. This is useful in filter design to determine the bandwidth.
4268:
The
Institute for Research in Electronics and Applied Physics
1548:{\displaystyle \omega _{\mathrm {N} }=2\pi f_{\mathrm {N} }.}
522:; the lost energy is the sum of the energies dissipated in
3713:
is made of flexible plastic, and therefore has a very low
2719:
The 2-sided bandwidth relative to a resonant frequency of
4114:
Encyclopedia of Laser
Physics and Technology, Vol. 1: A-M
3685:
of a musical instrument is critical; an excessively high
1456:{\displaystyle \Delta f={\frac {f_{\mathrm {N} }}{Q}},\,}
4372:
Foundations of analog & digital electronic circuits
1273:
972:
913:
4728:
Foundations of Analog and
Digital Electronic Circuits
4261:"Near THz Gyrotron: Theory, Design, and Applications"
3760:
3607:
3515:
3365:
3223:
3076:
2933:
2764:
2572:
2441:
2318:
2202:
2168:
of the oscillations (that is, of the output after an
1998:
1887:
1803:
1695:
1594:
1508:
1420:
1236:
1212:
1185:
1092:
1054:
1034:
554:
422:
266:
4561:
Networks and
Devices Using Planar Transmission Lines
4422:"Analog Dialogue Technical Journal - Analog Devices"
3658:
is the damping coefficient, defined by the equation
3210:
of an inductor with a series loss resistance is the
1330:, a transducer with a high Q-factor is suitable for
1316:{\textstyle \delta ={1}/{\sqrt {\pi f\sigma u_{o}}}}
4451:"Bandwidth in Octaves Versus Q in Bandpass Filters"
4236:
Circuit
Analysis with PSpice: A Simplified Approach
2747:In audio, bandwidth is often expressed in terms of
2156:(i.e., when the system is underdamped), it has two
1782:The envelope of oscillation decays proportional to
623:
4295:. Lippincott Williams & Wilkins. p. 331.
3985:Electronic circuits: fundamentals and applications
3802:
3635:
3570:
3445:
3295:
3144:
3017:
2883:
2661:
2552:
2421:
2298:
2131:
1963:
1867:
1771:
1675:
1547:
1455:
1356:It is a dimensionless parameter that compares the
1315:
1255:
1218:
1198:
1168:
1076:
1040:
1016:
940:
591:
498:
409:The other common nearly equivalent definition for
338:
4329:. Bristol: Institute of Physics Pub. p. 28.
3466:is the resonance frequency in radians per second,
3316:is the resonance frequency in radians per second,
4101:B. Jeffreys, Q.Jl R. astr. Soc. (1985) 26, 51–52
3194:and narrow the bandwidth is the desired result.
2180:for a long time after being struck by a hammer.
808:of the open-loop system sets the quality factor
3803:{\displaystyle Q={\frac {2\pi f_{o}\,E}{P}},\,}
120:The Q factor is a parameter that describes the
4013:Encyclopedia of Laser Physics and Technology:
3958:Analog Electronics: Analog Circuitry Explained
3856:in the cavity is proportional to the cavity's
2699:and, for electromechanical resonators such as
4292:Christensen's Physics of Diagnostic Radiology
3887:, where loss is linked to the damping of the
190:cavities used in accelerators, and some high-
162:oscillate with a smaller range of frequencies
8:
3636:{\displaystyle Q={\frac {\sqrt {Mk}}{D}},\,}
3586:For a single damped mass-spring system, the
851:(i.e., continuous-time filter with flattest
3590:factor represents the effect of simplified
1686:and the damping ratio can be expressed as:
4553:
4551:
4549:
4526:Frequency Response: Resonance, Bandwidth,
4401:
4399:
3494:is the series resistance of the capacitor.
3067:factor is the inverse of the series case:
4693:
4675:
4483:. Technical Publications. pp. 2–79.
4289:Curry, TS; Dowdey, JE; Murry, RC (1990).
3799:
3786:
3780:
3767:
3759:
3632:
3614:
3606:
3557:
3548:
3537:
3528:
3522:
3514:
3434:
3421:
3411:
3400:
3389:
3379:
3370:
3364:
3344:is the series resistance of the inductor.
3285:
3271:
3264:
3253:
3243:
3237:
3228:
3222:
3130:
3111:
3101:
3086:
3075:
3000:
2990:
2972:
2965:
2950:
2940:
2932:
2839:
2819:
2798:
2777:
2771:
2763:
2691:For an electrically resonant system, the
2650:
2644:
2643:
2621:
2620:
2614:
2605:
2594:
2588:
2571:
2541:
2535:
2534:
2512:
2511:
2505:
2496:
2484:
2478:
2477:
2464:
2457:
2440:
2410:
2404:
2403:
2381:
2380:
2374:
2365:
2344:
2343:
2337:
2334:
2317:
2287:
2281:
2280:
2258:
2257:
2251:
2242:
2231:
2225:
2224:
2218:
2201:
2128:
2119:
2113:
2112:
2084:
2083:
2072:
2056:
2055:
2048:
2038:
2027:
2021:
2020:
2014:
1997:
1948:
1935:
1934:
1921:
1909:
1908:
1894:
1886:
1855:
1845:
1844:
1817:
1816:
1810:
1802:
1756:
1755:
1742:
1730:
1729:
1720:
1702:
1694:
1657:
1656:
1646:
1626:
1625:
1619:
1601:
1593:
1535:
1534:
1514:
1513:
1507:
1452:
1437:
1436:
1430:
1419:
1305:
1290:
1285:
1280:
1272:
1241:
1235:
1211:
1190:
1184:
1158:
1147:
1136:
1123:
1112:
1106:
1097:
1091:
1062:
1053:
1033:
1008:
994:
977:
971:
933:
928:
920:
912:
576:
553:
483:
474:
451:
434:
429:
427:
426:
421:
317:
311:
292:
286:
278:
273:
271:
270:
265:
3824:is the stored energy in the cavity, and
2740:For example, an antenna tuned to have a
2182:
4187:. Technical Publications. p. 228.
4055:
4053:
4051:
4049:
4035:Time and Frequency from A to Z: Q to Ra
3947:
962:The design of a high-energy (near THz)
112:, so that they ring or vibrate longer.
4505:"Complete Response I - Constant Input"
4140:
4138:
3883:factor is of particular importance in
4472:
4470:
3848:is the power dissipated. The optical
966:considers both diffractive Q-factor,
695:, approaching the steady state value
390:is the angular half-power bandwidth.
7:
4176:
4174:
538:, per cycle, to maintain amplitude.
197:can reach as high as 10 and higher.
1985:For a two-pole lowpass filter, the
1024:as a function of resonator length (
941:{\textstyle Q={M\omega }/{\Gamma }}
4449:Dennis Bohn, Rane (January 2008).
3721:can make it harder to hit a note.
2645:
2622:
2536:
2513:
2479:
2405:
2382:
2345:
2282:
2259:
2226:
2114:
2085:
2057:
2022:
1936:
1910:
1846:
1818:
1757:
1731:
1658:
1627:
1536:
1515:
1438:
1421:
1382:Equivalently (for large values of
1098:
934:
826:Sallen–Key lowpass filter topology
661:linear time invariant (LTI) system
643:linear time invariant (LTI) system
324:
299:
25:
4615:Superlattices and Microstructures
4181:U.A.Bakshi, A. V. Bakshi (2006).
4060:Green, Estill I. (October 1955).
3182:, in series with the inductance,
2751:. Then the relationship between
1408:or 4% of its original amplitude.
716:input by slowly rising toward an
223:originated with K. S. Johnson of
4663:Advances in Optics and Photonics
4578:from the original on 2018-05-11.
4515:from the original on 2012-01-10.
4438:from the original on 2016-08-04.
4358:from the original on 2011-05-19.
4131:from the original on 2018-05-11.
4002:from the original on 2016-12-01.
2695:factor represents the effect of
4767:factor in radio tuning circuits
4564:. CRC Press. pp. 490–491.
4477:U.A.Bakshi; A.V.Bakshi (2008).
4160:from the original on 2017-08-28
4148:"ANTENNA THEORY AND TECHNIQUES"
4084:from the original on 2012-12-03
3916:List of piezoelectric materials
4408:Circuits, Signals, and Systems
3198:Individual reactive components
2918:tuned radio frequency receiver
2861:
2855:
2582:
2576:
2451:
2445:
2328:
2322:
2212:
2206:
2008:
2002:
705:decaying exponential functions
624:Individual reactive components
564:
558:
1:
2898:is the bandwidth in octaves.
80:parameter that describes how
3654:is the spring constant, and
356:is the resonant frequency, Δ
30:For other uses of the terms
4111:Paschotta, Rüdiger (2008).
3982:Tooley, Michael H. (2006).
3820:is the resonant frequency,
1206:is the cavity wall radius,
770:intermediate quality factor
457:energy dissipated per cycle
124:behavior of an underdamped
4818:
4635:10.1016/j.spmi.2019.04.035
4239:. CRC Press. p. 446.
4117:. Wiley-VCH. p. 580.
3988:. Newnes. pp. 77–78.
907:A pendulum's Q-factor is:
636:
366:full width at half maximum
212:and bandwidth measured in
29:
4558:Di Paolo, Franco (2000).
4350:Benjamin Crowell (2006).
4326:Novel Sensors and Sensing
4233:Sabah, Nassir H. (2017).
4208:James W. Nilsson (1989).
3889:surface plasmon resonance
3155:Consider a circuit where
1580:exponential time constant
1358:exponential time constant
386:resonant frequency, and Δ
4725:; Lang, Jeffrey (2005).
4370:Anant., Agarwal (2005).
4270:. University of Maryland
2186:Filter type (2nd order)
1077:{\displaystyle TE_{m,p}}
1041:{\displaystyle \lambda }
952:is the mass of the bob,
405:Stored energy definition
225:Western Electric Company
44:Q value (disambiguation)
2160:poles that each have a
1585:are related such that:
1341:Physical interpretation
1332:doppler ultrasonography
1328:medical ultrasonography
1256:{\displaystyle V_{m.p}}
1219:{\displaystyle \delta }
1048:), and ohmic Q-factor (
703:that is the sum of two
393:Under this definition,
4406:Siebert, William McC.
3961:. Newnes. p. 42.
3804:
3637:
3572:
3447:
3297:
3146:
3019:
2885:
2688:
2663:
2554:
2423:
2300:
2142:For this system, when
2133:
1965:
1869:
1773:
1677:
1549:
1457:
1317:
1257:
1220:
1200:
1170:
1078:
1042:
1018:
942:
651:factor determines the
593:
500:
340:
54:
4782:Electrical parameters
3955:Hickman, Ian (2013).
3805:
3638:
3573:
3448:
3298:
3147:
3020:
2886:
2711:Relationship between
2697:electrical resistance
2682:
2664:
2555:
2424:
2301:
2134:
1966:
1870:
1794:can be expressed as:
1774:
1678:
1550:
1458:
1345:Physically speaking,
1318:
1258:
1221:
1201:
1199:{\displaystyle R_{w}}
1171:
1079:
1043:
1019:
943:
855:) has an underdamped
594:
579:maximum energy stored
501:
397:is the reciprocal of
341:
164:and are more stable.
52:
4695:10.1364/AOP.9.000775
4323:Jackson, R. (2004).
3911:Chu–Harrington limit
3758:
3729:Helmholtz resonators
3605:
3513:
3483:capacitive reactance
3363:
3221:
3074:
2931:
2762:
2570:
2439:
2316:
2200:
2178:pure sinusoidal tone
1996:
1885:
1801:
1693:
1592:
1506:
1418:
1271:
1234:
1230:of the cavity wall,
1210:
1183:
1090:
1052:
1032:
970:
911:
552:
509:The factor 2π makes
420:
399:fractional bandwidth
264:
245:Bandwidth definition
4731:. Morgan Kaufmann.
4686:2017AdOP....9..775B
4627:2019SuMi..130..454T
4509:fourier.eng.hmc.edu
3472:is the capacitance,
3333:inductive reactance
2909:In an ideal series
2655:
2546:
2489:
2415:
2292:
2236:
2124:
2032:
1371:to its oscillation
1163:
725:high quality factor
657:harmonic oscillator
126:harmonic oscillator
4802:Engineering ratios
4594:2012-03-19 at the
4535:2014-12-06 at the
4352:"Light and Matter"
4070:American Scientist
4040:2008-05-04 at the
4022:2009-02-24 at the
3936:Dissipation factor
3901:Acoustic resonance
3800:
3677:Acoustical systems
3633:
3582:Mechanical systems
3568:
3443:
3322:is the inductance,
3293:
3142:
3015:
2881:
2689:
2675:Electrical systems
2659:
2639:
2550:
2530:
2473:
2419:
2399:
2296:
2276:
2220:
2189:Transfer function
2129:
2108:
2101:
2070:
2016:
1961:
1865:
1769:
1673:
1545:
1453:
1367:physical system's
1313:
1253:
1216:
1196:
1166:
1143:
1074:
1038:
1028:) and wavelength (
1014:
938:
881:Butterworth filter
796:against overshoot.
669:low quality factor
633:factor and damping
589:
496:
336:
206:relative bandwidth
188:superconducting RF
55:
4480:Electric Circuits
4210:Electric Circuits
3995:978-0-7506-6923-8
3794:
3673:is the velocity.
3627:
3623:
3566:
3563:
3543:
3441:
3406:
3291:
3259:
3121:
3096:
3095:
3013:
2985:
2960:
2959:
2948:
2876:
2847:
2814:
2790:
2755:and bandwidth is
2672:
2671:
2657:
2631:
2548:
2522:
2433:Notch (bandstop)
2417:
2391:
2354:
2294:
2268:
2166:exponential decay
2158:complex conjugate
2126:
2066:
2049:
2047:
1989:of the filter is
1987:transfer function
1956:
1943:
1916:
1863:
1832:
1764:
1737:
1715:
1668:
1641:
1614:
1568:natural frequency
1475:natural frequency
1447:
1311:
1164:
1121:
1002:
802:negative feedback
789:critically damped
768:A system with an
693:exponential decay
608:angular frequency
584:
583:
580:
491:
490:
487:
459:
458:
455:
439:
437:
331:
306:
283:
281:
16:(Redirected from
4809:
4742:
4708:
4707:
4697:
4679:
4653:
4647:
4646:
4609:
4603:
4586:
4580:
4579:
4555:
4544:
4523:
4517:
4516:
4501:
4495:
4494:
4474:
4465:
4464:
4462:
4461:
4446:
4440:
4439:
4437:
4426:
4418:
4412:
4411:
4403:
4394:
4393:
4367:
4361:
4359:
4347:
4341:
4340:
4320:
4314:
4313:
4311:
4309:
4286:
4280:
4279:
4277:
4275:
4265:
4257:
4251:
4250:
4230:
4224:
4223:
4205:
4199:
4198:
4184:Network Analysis
4178:
4169:
4168:
4166:
4165:
4159:
4152:
4142:
4133:
4132:
4108:
4102:
4099:
4093:
4092:
4090:
4089:
4083:
4066:
4062:"The Story of Q"
4057:
4044:
4032:
4026:
4010:
4004:
4003:
3979:
3973:
3972:
3952:
3847:
3845:
3844:
3839:
3836:
3809:
3807:
3806:
3801:
3795:
3790:
3785:
3784:
3768:
3703:brass instrument
3642:
3640:
3639:
3634:
3628:
3616:
3615:
3577:
3575:
3574:
3569:
3567:
3565:
3564:
3562:
3561:
3549:
3544:
3542:
3541:
3529:
3523:
3498:In general, the
3452:
3450:
3449:
3444:
3442:
3440:
3439:
3438:
3426:
3425:
3412:
3407:
3405:
3404:
3395:
3394:
3393:
3380:
3375:
3374:
3302:
3300:
3299:
3294:
3292:
3290:
3289:
3280:
3276:
3275:
3265:
3260:
3258:
3257:
3248:
3247:
3238:
3233:
3232:
3151:
3149:
3148:
3143:
3135:
3134:
3122:
3120:
3116:
3115:
3102:
3097:
3088:
3087:
3024:
3022:
3021:
3016:
3014:
3012:
3005:
3004:
2991:
2986:
2981:
2977:
2976:
2966:
2961:
2952:
2951:
2949:
2941:
2890:
2888:
2887:
2882:
2877:
2875:
2874:
2870:
2848:
2840:
2820:
2815:
2813:
2806:
2805:
2792:
2791:
2786:
2778:
2772:
2668:
2666:
2665:
2660:
2658:
2656:
2654:
2649:
2648:
2632:
2627:
2626:
2625:
2615:
2610:
2609:
2599:
2598:
2589:
2559:
2557:
2556:
2551:
2549:
2547:
2545:
2540:
2539:
2523:
2518:
2517:
2516:
2506:
2501:
2500:
2490:
2488:
2483:
2482:
2469:
2468:
2458:
2428:
2426:
2425:
2420:
2418:
2416:
2414:
2409:
2408:
2392:
2387:
2386:
2385:
2375:
2370:
2369:
2359:
2355:
2350:
2349:
2348:
2338:
2335:
2305:
2303:
2302:
2297:
2295:
2293:
2291:
2286:
2285:
2269:
2264:
2263:
2262:
2252:
2247:
2246:
2235:
2230:
2229:
2219:
2183:
2155:
2154:
2150:
2146: >
2138:
2136:
2135:
2130:
2127:
2125:
2123:
2118:
2117:
2100:
2090:
2089:
2088:
2071:
2062:
2061:
2060:
2050:
2043:
2042:
2031:
2026:
2025:
2015:
1970:
1968:
1967:
1962:
1957:
1949:
1944:
1942:
1941:
1940:
1939:
1922:
1917:
1915:
1914:
1913:
1903:
1895:
1874:
1872:
1871:
1866:
1864:
1856:
1851:
1850:
1849:
1833:
1831:
1823:
1822:
1821:
1811:
1793:
1778:
1776:
1775:
1770:
1765:
1763:
1762:
1761:
1760:
1743:
1738:
1736:
1735:
1734:
1721:
1716:
1714:
1703:
1682:
1680:
1679:
1674:
1669:
1664:
1663:
1662:
1661:
1647:
1642:
1640:
1632:
1631:
1630:
1620:
1615:
1613:
1602:
1584:
1576:attenuation rate
1554:
1552:
1551:
1546:
1541:
1540:
1539:
1520:
1519:
1518:
1462:
1460:
1459:
1454:
1448:
1443:
1442:
1441:
1431:
1403:
1402:
1398:
1363:for decay of an
1362:
1322:
1320:
1319:
1314:
1312:
1310:
1309:
1291:
1289:
1284:
1262:
1260:
1259:
1254:
1252:
1251:
1225:
1223:
1222:
1217:
1205:
1203:
1202:
1197:
1195:
1194:
1175:
1173:
1172:
1167:
1165:
1162:
1157:
1142:
1141:
1140:
1124:
1122:
1117:
1116:
1107:
1102:
1101:
1083:
1081:
1080:
1075:
1073:
1072:
1047:
1045:
1044:
1039:
1023:
1021:
1020:
1015:
1013:
1012:
1007:
1003:
995:
982:
981:
958:
947:
945:
944:
939:
937:
932:
927:
903:
902:
901:
900:
899:
892:
875:
874:
873:
872:
871:
864:
843:
842:
841:
837:
786:) is said to be
785:
784:
780:
760:
759:
755:
741:) is said to be
740:
739:
735:
731: >
701:impulse response
685:) is said to be
684:
683:
679:
675: <
598:
596:
595:
590:
585:
581:
578:
577:
505:
503:
502:
497:
492:
488:
485:
484:
479:
478:
460:
456:
453:
452:
441:
440:
438:
435:
433:
428:
345:
343:
342:
337:
332:
330:
322:
321:
312:
307:
305:
297:
296:
287:
285:
284:
282:
279:
277:
272:
181:
180:
176:
21:
4817:
4816:
4812:
4811:
4810:
4808:
4807:
4806:
4772:
4771:
4763:Explanation of
4758:factor is given
4750:
4745:
4739:
4721:
4717:
4715:Further reading
4712:
4711:
4655:
4654:
4650:
4611:
4610:
4606:
4596:Wayback Machine
4587:
4583:
4572:
4557:
4556:
4547:
4537:Wayback Machine
4524:
4520:
4503:
4502:
4498:
4491:
4476:
4475:
4468:
4459:
4457:
4448:
4447:
4443:
4435:
4424:
4420:
4419:
4415:
4405:
4404:
4397:
4382:
4369:
4368:
4364:
4349:
4348:
4344:
4337:
4322:
4321:
4317:
4307:
4305:
4303:
4288:
4287:
4283:
4273:
4271:
4263:
4259:
4258:
4254:
4247:
4232:
4231:
4227:
4220:
4207:
4206:
4202:
4195:
4180:
4179:
4172:
4163:
4161:
4157:
4150:
4146:
4143:
4136:
4125:
4110:
4109:
4105:
4100:
4096:
4087:
4085:
4081:
4064:
4059:
4058:
4047:
4042:Wayback Machine
4033:
4029:
4024:Wayback Machine
4011:
4007:
3996:
3981:
3980:
3976:
3969:
3954:
3953:
3949:
3944:
3897:
3840:
3837:
3832:
3831:
3829:
3818:
3776:
3769:
3756:
3755:
3749:resonant cavity
3737:
3735:Optical systems
3707:wind instrument
3679:
3664:
3603:
3602:
3584:
3553:
3533:
3527:
3511:
3510:
3492:
3479:
3465:
3430:
3417:
3416:
3396:
3385:
3381:
3366:
3361:
3360:
3342:
3329:
3315:
3281:
3267:
3266:
3249:
3239:
3224:
3219:
3218:
3200:
3126:
3107:
3106:
3072:
3071:
3059:For a parallel
2996:
2995:
2968:
2967:
2929:
2928:
2907:
2838:
2834:
2824:
2794:
2793:
2779:
2773:
2760:
2759:
2732:
2725:
2717:
2701:quartz crystals
2685:logarithmically
2677:
2616:
2601:
2600:
2590:
2568:
2567:
2507:
2492:
2491:
2460:
2459:
2437:
2436:
2376:
2361:
2360:
2339:
2336:
2314:
2313:
2253:
2238:
2237:
2198:
2197:
2152:
2148:
2147:
2079:
2051:
2034:
2033:
1994:
1993:
1930:
1926:
1904:
1896:
1883:
1882:
1840:
1824:
1812:
1799:
1798:
1791:
1751:
1747:
1725:
1707:
1691:
1690:
1652:
1648:
1633:
1621:
1606:
1590:
1589:
1582:
1573:
1530:
1509:
1504:
1503:
1494:
1472:
1432:
1416:
1415:
1400:
1396:
1395:
1360:
1343:
1338:
1301:
1269:
1268:
1237:
1232:
1231:
1208:
1207:
1186:
1181:
1180:
1132:
1125:
1108:
1093:
1088:
1087:
1058:
1050:
1049:
1030:
1029:
990:
989:
973:
968:
967:
953:
909:
908:
897:
895:
894:
890:
889:
884:
879:A second-order
869:
867:
866:
862:
861:
856:
847:A second-order
839:
835:
834:
829:
818:
782:
778:
777:
763:low-pass filter
757:
753:
752:
737:
733:
732:
710:low-pass filter
681:
677:
676:
645:
637:Main articles:
635:
550:
549:
470:
418:
417:
407:
380:
375: = 2π
373:
362:resonance width
354:
323:
313:
298:
288:
262:
261:
247:
238:
219:The concept of
178:
174:
173:
118:
47:
28:
23:
22:
15:
12:
11:
5:
4815:
4813:
4805:
4804:
4799:
4794:
4789:
4787:Linear filters
4784:
4774:
4773:
4770:
4769:
4760:
4749:
4748:External links
4746:
4744:
4743:
4737:
4723:Agarwal, Anant
4718:
4716:
4713:
4710:
4709:
4670:(4): 775–827.
4648:
4604:
4581:
4570:
4545:
4518:
4496:
4489:
4466:
4441:
4429:www.analog.com
4413:
4395:
4380:
4362:
4342:
4335:
4315:
4301:
4281:
4252:
4245:
4225:
4218:
4200:
4193:
4170:
4134:
4124:978-3527408283
4123:
4103:
4094:
4045:
4027:
4005:
3994:
3974:
3967:
3946:
3945:
3943:
3940:
3939:
3938:
3933:
3928:
3923:
3918:
3913:
3908:
3903:
3896:
3893:
3828: = −
3816:
3811:
3810:
3798:
3793:
3789:
3783:
3779:
3775:
3772:
3766:
3763:
3736:
3733:
3678:
3675:
3665: = −
3662:
3644:
3643:
3631:
3626:
3622:
3619:
3613:
3610:
3583:
3580:
3579:
3578:
3560:
3556:
3552:
3547:
3540:
3536:
3532:
3526:
3521:
3518:
3496:
3495:
3490:
3486:
3477:
3473:
3467:
3463:
3454:
3453:
3437:
3433:
3429:
3424:
3420:
3415:
3410:
3403:
3399:
3392:
3388:
3384:
3378:
3373:
3369:
3346:
3345:
3340:
3336:
3327:
3323:
3317:
3313:
3304:
3303:
3288:
3284:
3279:
3274:
3270:
3263:
3256:
3252:
3246:
3242:
3236:
3231:
3227:
3199:
3196:
3174:In a parallel
3153:
3152:
3141:
3138:
3133:
3129:
3125:
3119:
3114:
3110:
3105:
3100:
3094:
3091:
3085:
3082:
3079:
3026:
3025:
3011:
3008:
3003:
2999:
2994:
2989:
2984:
2980:
2975:
2971:
2964:
2958:
2955:
2947:
2944:
2939:
2936:
2906:
2900:
2892:
2891:
2880:
2873:
2869:
2866:
2863:
2860:
2857:
2854:
2851:
2846:
2843:
2837:
2833:
2830:
2827:
2823:
2818:
2812:
2809:
2804:
2801:
2797:
2789:
2785:
2782:
2776:
2770:
2767:
2730:
2723:
2716:
2709:
2676:
2673:
2670:
2669:
2653:
2647:
2642:
2638:
2635:
2630:
2624:
2619:
2613:
2608:
2604:
2597:
2593:
2587:
2584:
2581:
2578:
2575:
2565:
2561:
2560:
2544:
2538:
2533:
2529:
2526:
2521:
2515:
2510:
2504:
2499:
2495:
2487:
2481:
2476:
2472:
2467:
2463:
2456:
2453:
2450:
2447:
2444:
2434:
2430:
2429:
2413:
2407:
2402:
2398:
2395:
2390:
2384:
2379:
2373:
2368:
2364:
2358:
2353:
2347:
2342:
2333:
2330:
2327:
2324:
2321:
2311:
2307:
2306:
2290:
2284:
2279:
2275:
2272:
2267:
2261:
2256:
2250:
2245:
2241:
2234:
2228:
2223:
2217:
2214:
2211:
2208:
2205:
2195:
2191:
2190:
2187:
2140:
2139:
2122:
2116:
2111:
2107:
2104:
2099:
2096:
2093:
2087:
2082:
2078:
2075:
2069:
2065:
2059:
2054:
2046:
2041:
2037:
2030:
2024:
2019:
2013:
2010:
2007:
2004:
2001:
1972:
1971:
1960:
1955:
1952:
1947:
1938:
1933:
1929:
1925:
1920:
1912:
1907:
1902:
1899:
1893:
1890:
1876:
1875:
1862:
1859:
1854:
1848:
1843:
1839:
1836:
1830:
1827:
1820:
1815:
1809:
1806:
1790:, where α and
1780:
1779:
1768:
1759:
1754:
1750:
1746:
1741:
1733:
1728:
1724:
1719:
1713:
1710:
1706:
1701:
1698:
1684:
1683:
1672:
1667:
1660:
1655:
1651:
1645:
1639:
1636:
1629:
1624:
1618:
1612:
1609:
1605:
1600:
1597:
1571:
1556:
1555:
1544:
1538:
1533:
1529:
1526:
1523:
1517:
1512:
1492:
1470:
1464:
1463:
1451:
1446:
1440:
1435:
1429:
1426:
1423:
1342:
1339:
1337:
1336:
1324:
1308:
1304:
1300:
1297:
1294:
1288:
1283:
1279:
1276:
1250:
1247:
1244:
1240:
1215:
1193:
1189:
1178:
1177:
1161:
1156:
1153:
1150:
1146:
1139:
1135:
1131:
1128:
1120:
1115:
1111:
1105:
1100:
1096:
1071:
1068:
1065:
1061:
1057:
1037:
1011:
1006:
1001:
998:
993:
988:
985:
980:
976:
960:
936:
931:
926:
923:
919:
916:
905:
877:
845:
821:
817:
814:
798:
797:
766:
723:A system with
721:
697:asymptotically
667:A system with
634:
628:
613:reactive power
600:
599:
588:
575:
572:
569:
566:
563:
560:
557:
507:
506:
495:
482:
477:
473:
469:
466:
463:
450:
447:
444:
432:
425:
406:
403:
378:
371:
352:
347:
346:
335:
329:
326:
320:
316:
310:
304:
301:
295:
291:
276:
269:
246:
243:
237:
234:
136:having higher
117:
114:
67:quality factor
40:Quality factor
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
4814:
4803:
4800:
4798:
4797:Laser science
4795:
4793:
4790:
4788:
4785:
4783:
4780:
4779:
4777:
4768:
4766:
4761:
4759:
4757:
4752:
4751:
4747:
4740:
4738:1-55860-735-8
4734:
4730:
4729:
4724:
4720:
4719:
4714:
4705:
4701:
4696:
4691:
4687:
4683:
4678:
4673:
4669:
4665:
4664:
4659:
4652:
4649:
4644:
4640:
4636:
4632:
4628:
4624:
4620:
4616:
4608:
4605:
4601:
4597:
4593:
4590:
4585:
4582:
4577:
4573:
4571:9780849318351
4567:
4563:
4562:
4554:
4552:
4550:
4546:
4542:
4538:
4534:
4531:
4529:
4522:
4519:
4514:
4510:
4506:
4500:
4497:
4492:
4490:9788184314526
4486:
4482:
4481:
4473:
4471:
4467:
4456:
4452:
4445:
4442:
4434:
4430:
4423:
4417:
4414:
4409:
4402:
4400:
4396:
4391:
4387:
4383:
4381:9781558607354
4377:
4373:
4366:
4363:
4357:
4353:
4346:
4343:
4338:
4336:0-7503-0989-X
4332:
4328:
4327:
4319:
4316:
4304:
4302:9780812113105
4298:
4294:
4293:
4285:
4282:
4269:
4262:
4256:
4253:
4248:
4246:9781315402215
4242:
4238:
4237:
4229:
4226:
4221:
4219:0-201-17288-7
4215:
4211:
4204:
4201:
4196:
4194:9788189411237
4190:
4186:
4185:
4177:
4175:
4171:
4156:
4149:
4141:
4139:
4135:
4130:
4126:
4120:
4116:
4115:
4107:
4104:
4098:
4095:
4080:
4076:
4072:
4071:
4063:
4056:
4054:
4052:
4050:
4046:
4043:
4039:
4036:
4031:
4028:
4025:
4021:
4018:
4016:
4009:
4006:
4001:
3997:
3991:
3987:
3986:
3978:
3975:
3970:
3968:9781483162287
3964:
3960:
3959:
3951:
3948:
3941:
3937:
3934:
3932:
3929:
3927:
3924:
3922:
3919:
3917:
3914:
3912:
3909:
3907:
3904:
3902:
3899:
3898:
3894:
3892:
3890:
3886:
3882:
3878:
3876:
3871:
3867:
3863:
3859:
3855:
3851:
3843:
3835:
3827:
3823:
3819:
3796:
3791:
3787:
3781:
3777:
3773:
3770:
3764:
3761:
3754:
3753:
3752:
3750:
3746:
3742:
3734:
3732:
3730:
3726:
3724:
3720:
3716:
3712:
3708:
3704:
3700:
3695:
3692:
3688:
3684:
3676:
3674:
3672:
3668:
3661:
3657:
3653:
3650:is the mass,
3649:
3629:
3624:
3620:
3617:
3611:
3608:
3601:
3600:
3599:
3597:
3593:
3589:
3581:
3558:
3554:
3550:
3545:
3538:
3534:
3530:
3524:
3519:
3516:
3509:
3508:
3507:
3505:
3501:
3493:
3487:
3484:
3480:
3474:
3471:
3468:
3462:
3459:
3458:
3457:
3435:
3431:
3427:
3422:
3418:
3413:
3408:
3401:
3397:
3390:
3386:
3382:
3376:
3371:
3367:
3359:
3358:
3357:
3355:
3351:
3343:
3337:
3334:
3330:
3324:
3321:
3318:
3312:
3309:
3308:
3307:
3286:
3282:
3277:
3272:
3268:
3261:
3254:
3250:
3244:
3240:
3234:
3229:
3225:
3217:
3216:
3215:
3213:
3209:
3205:
3197:
3195:
3193:
3189:
3185:
3181:
3177:
3172:
3170:
3166:
3162:
3158:
3139:
3136:
3131:
3127:
3123:
3117:
3112:
3108:
3103:
3098:
3092:
3089:
3083:
3080:
3077:
3070:
3069:
3068:
3066:
3063:circuit, the
3062:
3057:
3055:
3051:
3047:
3043:
3039:
3035:
3031:
3009:
3006:
3001:
2997:
2992:
2987:
2982:
2978:
2973:
2969:
2962:
2956:
2953:
2945:
2942:
2937:
2934:
2927:
2926:
2925:
2923:
2919:
2915:
2913:
2904:
2901:
2899:
2897:
2878:
2871:
2867:
2864:
2858:
2852:
2849:
2844:
2841:
2835:
2831:
2828:
2825:
2821:
2816:
2810:
2807:
2802:
2799:
2795:
2787:
2783:
2780:
2774:
2768:
2765:
2758:
2757:
2756:
2754:
2750:
2745:
2743:
2738:
2736:
2729:
2722:
2715:and bandwidth
2714:
2710:
2708:
2706:
2703:, mechanical
2702:
2698:
2694:
2686:
2681:
2674:
2651:
2640:
2636:
2633:
2628:
2617:
2611:
2606:
2602:
2595:
2591:
2585:
2579:
2573:
2566:
2563:
2562:
2542:
2531:
2527:
2524:
2519:
2508:
2502:
2497:
2493:
2485:
2474:
2470:
2465:
2461:
2454:
2448:
2442:
2435:
2432:
2431:
2411:
2400:
2396:
2393:
2388:
2377:
2371:
2366:
2362:
2356:
2351:
2340:
2331:
2325:
2319:
2312:
2309:
2308:
2288:
2277:
2273:
2270:
2265:
2254:
2248:
2243:
2239:
2232:
2221:
2215:
2209:
2203:
2196:
2193:
2192:
2188:
2185:
2184:
2181:
2179:
2175:
2171:
2167:
2163:
2159:
2145:
2120:
2109:
2105:
2102:
2097:
2094:
2091:
2080:
2076:
2073:
2067:
2063:
2052:
2044:
2039:
2035:
2028:
2017:
2011:
2005:
1999:
1992:
1991:
1990:
1988:
1983:
1981:
1977:
1958:
1953:
1950:
1945:
1931:
1927:
1923:
1918:
1905:
1900:
1897:
1891:
1888:
1881:
1880:
1879:
1860:
1857:
1852:
1841:
1837:
1834:
1828:
1825:
1813:
1807:
1804:
1797:
1796:
1795:
1789:
1785:
1766:
1752:
1748:
1744:
1739:
1726:
1722:
1717:
1711:
1708:
1704:
1699:
1696:
1689:
1688:
1687:
1670:
1665:
1653:
1649:
1643:
1637:
1634:
1622:
1616:
1610:
1607:
1603:
1598:
1595:
1588:
1587:
1586:
1581:
1577:
1569:
1565:
1564:damping ratio
1561:
1542:
1531:
1527:
1524:
1521:
1510:
1502:
1501:
1500:
1498:
1491:
1486:
1484:
1480:
1476:
1469:
1449:
1444:
1433:
1427:
1424:
1414:
1413:
1412:
1409:
1407:
1393:
1389:
1385:
1380:
1378:
1374:
1370:
1366:
1359:
1354:
1352:
1348:
1340:
1333:
1329:
1325:
1306:
1302:
1298:
1295:
1292:
1286:
1281:
1277:
1274:
1266:
1248:
1245:
1242:
1238:
1229:
1213:
1191:
1187:
1159:
1154:
1151:
1148:
1144:
1137:
1133:
1129:
1126:
1118:
1113:
1109:
1103:
1094:
1086:
1085:
1069:
1066:
1063:
1059:
1055:
1035:
1027:
1009:
1004:
999:
996:
991:
986:
983:
978:
974:
965:
961:
957:
951:
929:
924:
921:
917:
914:
906:
887:
882:
878:
859:
854:
850:
849:Bessel filter
846:
832:
827:
824:A unity-gain
823:
822:
820:
816:Some examples
815:
813:
811:
807:
803:
795:
794:safety margin
791:
790:
776: =
775:
771:
767:
764:
750:
746:
745:
730:
726:
722:
719:
715:
711:
706:
702:
698:
694:
690:
689:
674:
670:
666:
665:
664:
662:
658:
654:
650:
644:
640:
632:
629:
627:
625:
622:
618:
614:
609:
605:
586:
573:
570:
567:
561:
555:
548:
547:
546:
544:
539:
537:
533:
529:
525:
521:
517:
512:
493:
486:energy stored
480:
475:
471:
467:
464:
461:
454:energy stored
448:
445:
442:
430:
423:
416:
415:
414:
412:
404:
402:
400:
396:
391:
389:
385:
381:
374:
367:
363:
359:
355:
333:
327:
318:
314:
308:
302:
293:
289:
274:
267:
260:
259:
258:
256:
252:
244:
242:
235:
233:
230:
226:
222:
217:
215:
211:
207:
203:
202:damping ratio
198:
196:
193:
189:
185:
184:atomic clocks
171:
165:
163:
159:
155:
151:
150:tuned circuit
148:
143:
139:
135:
131:
128:(resonator).
127:
123:
115:
113:
111:
107:
103:
99:
95:
91:
87:
83:
79:
78:dimensionless
75:
73:
68:
64:
60:
51:
45:
41:
37:
33:
19:
4764:
4755:
4727:
4667:
4661:
4651:
4618:
4614:
4607:
4584:
4560:
4527:
4521:
4508:
4499:
4479:
4458:. Retrieved
4455:www.rane.com
4454:
4444:
4428:
4416:
4410:. MIT Press.
4407:
4371:
4365:
4345:
4325:
4318:
4306:. Retrieved
4291:
4284:
4272:. Retrieved
4267:
4255:
4235:
4228:
4209:
4203:
4183:
4162:. Retrieved
4113:
4106:
4097:
4086:. Retrieved
4074:
4068:
4030:
4014:
4008:
3984:
3977:
3957:
3950:
3931:Q multiplier
3921:Phase margin
3880:
3874:
3864:factor of a
3861:
3857:
3849:
3841:
3833:
3825:
3821:
3814:
3812:
3751:is given by
3747:factor of a
3744:
3738:
3727:
3722:
3718:
3714:
3698:
3696:
3686:
3682:
3680:
3670:
3666:
3659:
3655:
3651:
3647:
3645:
3587:
3585:
3503:
3499:
3497:
3488:
3475:
3469:
3460:
3455:
3353:
3349:
3347:
3338:
3325:
3319:
3310:
3305:
3211:
3207:
3203:
3201:
3191:
3187:
3183:
3179:
3175:
3173:
3168:
3164:
3160:
3156:
3154:
3064:
3060:
3058:
3053:
3037:
3033:
3029:
3027:
2921:
2911:
2908:
2902:
2895:
2893:
2752:
2746:
2741:
2739:
2734:
2727:
2726: Hz is
2720:
2718:
2712:
2692:
2690:
2173:
2143:
2141:
1984:
1979:
1975:
1973:
1877:
1787:
1783:
1781:
1685:
1559:
1558:The factors
1557:
1489:
1487:
1478:
1467:
1465:
1410:
1405:
1391:
1387:
1383:
1381:
1376:
1355:
1350:
1346:
1344:
1025:
955:
949:
885:
857:
830:
819:
809:
806:phase margin
799:
787:
773:
769:
748:
742:
728:
724:
699:. It has an
686:
672:
668:
648:
646:
630:
620:
603:
601:
542:
540:
510:
508:
410:
408:
394:
392:
387:
376:
369:
361:
357:
350:
348:
254:
250:
248:
239:
228:
220:
218:
199:
191:
169:
166:
160:oscillators
157:
146:
137:
130:Sinusoidally
119:
105:
101:
71:
70:
66:
56:
39:
35:
31:
4621:: 454–471.
4077:: 584–594.
3906:Attenuation
3594:damping or
3050:capacitance
2924:factor is:
2916:, and in a
1394:, or about
1365:oscillating
853:group delay
744:underdamped
653:qualitative
154:selectivity
116:Explanation
82:underdamped
63:engineering
4776:Categories
4677:1802.01469
4460:2019-11-20
4308:22 January
4164:2017-09-02
4088:2012-11-21
3942:References
3885:plasmonics
3877:-switching
3046:inductance
3042:resistance
2920:(TRF) the
1265:eigenvalue
1228:skin depth
688:overdamped
617:real power
582:power loss
520:capacitors
489:power loss
236:Definition
134:resonators
86:oscillator
4792:Mechanics
4704:1943-8206
4643:150365680
4274:5 January
3860:. If the
3774:π
3691:resonator
3419:ω
3383:−
3269:ω
3128:ω
3109:ω
2998:ω
2970:ω
2853:
2832:
2808:−
2641:ω
2618:ω
2564:Highpass
2532:ω
2509:ω
2475:ω
2401:ω
2378:ω
2341:ω
2310:Bandpass
2278:ω
2255:ω
2222:ω
2162:real part
2110:ω
2098:α
2081:ω
2077:ζ
2068:⏟
2053:ω
2018:ω
1954:α
1932:ω
1928:ζ
1906:ω
1889:τ
1861:τ
1842:ω
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1814:ω
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1753:ω
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1727:ω
1723:α
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1654:ω
1650:τ
1638:α
1623:ω
1611:ζ
1528:π
1511:ω
1483:bandwidth
1422:Δ
1369:amplitude
1299:σ
1293:π
1275:δ
1214:δ
1130:−
1119:δ
1099:Ω
1036:λ
1000:λ
984:≈
935:Γ
925:ω
718:asymptote
574:×
571:ω
562:ω
545:is used:
528:potential
524:resistors
516:inductors
481:×
468:π
449:×
446:π
328:ω
325:Δ
315:ω
300:Δ
210:linewidth
122:resonance
98:bandwidth
90:resonator
4592:Archived
4576:Archived
4533:Archived
4513:Archived
4433:Archived
4390:60245509
4360:, Ch. 18
4356:Archived
4155:Archived
4129:Archived
4079:Archived
4038:Archived
4020:Archived
4000:Archived
3895:See also
3711:vuvuzela
3669:, where
3040:are the
2905:circuits
2705:friction
2194:Lowpass
1084:–modes)
964:gyrotron
948:, where
142:resonate
140:factors
36:Q factor
18:Q-factor
4682:Bibcode
4623:Bibcode
3926:Q meter
3866:laser's
3846:
3830:
3663:damping
3592:viscous
3481:is the
3456:where:
3331:is the
3306:where:
2914:circuit
2749:octaves
2687:scaled.
2170:impulse
2151:⁄
1578:α, and
1477:, and Δ
1473:is the
1399:⁄
1386:), the
1335:organs.
1263:is the
1226:is the
954:ω = 2π/
896:√
893:⁄
868:√
865:⁄
838:⁄
781:⁄
756:⁄
751:=
736:⁄
680:⁄
639:Damping
606:is the
532:kinetic
384:angular
382:is the
360:is the
214:octaves
177:⁄
132:driven
110:damping
59:physics
4735:
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4487:
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3992:
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3646:where
3028:where
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1466:where
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1179:where
602:where
349:where
195:lasers
94:radian
74:factor
65:, the
42:, see
38:, and
4672:arXiv
4639:S2CID
4436:(PDF)
4425:(PDF)
4264:(PDF)
4158:(PDF)
4151:(PDF)
4082:(PDF)
4065:(PDF)
3870:pulse
3701:of a
3689:in a
3485:, and
3335:, and
1499:, as
1497:hertz
536:force
172:near
145:high-
76:is a
4733:ISBN
4700:ISSN
4566:ISBN
4485:ISBN
4386:OCLC
4376:ISBN
4331:ISBN
4310:2023
4297:ISBN
4276:2021
4241:ISBN
4214:ISBN
4189:ISBN
4119:ISBN
3990:ISBN
3963:ISBN
3697:The
3681:The
3596:drag
3348:The
3202:The
3163:and
3048:and
3036:and
2829:sinh
1878:and
714:step
659:and
647:The
641:and
530:and
518:and
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4690:doi
4631:doi
4619:130
4600:PDF
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1978:or
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626:.)
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