Talk:Q factor/Archive 1

FWHM vs 3dB

The article states:

the bandwidth is defined as the 3 dB change in level besides the center frequency.

The definition of the bandwidth BW as the "full width at half maximum" or FWHM is wrong.

Unless the definition depends on the slight difference between -3dB (1/1.995) and half maximum (1/2), this would seem to be the same thing. Anyone know for sure, here? -- DrBob 17:57, 27 Sep 2004 (UTC)

I might be able to help here... The reason we use FWHM and not 3dB for the Q factor of mechanical and optical resonators is that the angular frequencies for which a driven oscillator will store half the peak power is $\omega =\omega _{0}\left(1\mp {\frac {1}{2Q}}\right)$ so that conviniently: $\Delta \omega =\omega _{0}\left(1+{\frac {1}{2Q}}\right)-\omega _{0}\left(1-{\frac {1}{2Q}}\right)=\omega _{0}\cdot {\frac {1}{Q}}$. I would never have labelled that diagram as having bandwidth, it would always be FWHM (they are completely different and used in different situations). --152.78.72.172 (talk) 11:21, 7 August 2009 (UTC)

Strictly, the FWHM is full width at half-max, that is half power. In dB this is -3.01 dB, close enough to 3 dB down to not worry about it.

The definition "In optics..." appears strange to me. In mechanics the Q factor can be shown to be equal to 2 * Pi times the energy stored in the oscillator divided by the energy dissipated per cycle. I suspect this is the correct definition, applicable to optics, mechanics, and any other oscillating system.

24.245.15.183

I suspect you're absolutely correct about the definition applying to all oscillating systems. "Q-switching", though, is a very real phenomenon and used to great advantage in pulsed laser systems.

By the way, you can easily sign your "talk" posts by appending four tildes (~~~~) to the posting. When you "Save changes", this will be replaced by your username in a handy linked form and a timestamp of your edit.

Atlant 14:27, 10 August 2005 (UTC)

Q the cycles for energy to go to zero?

Alison Chaiken 00:00, 23 September 2005 (UTC): I've always thought of the quality factor as the number of cycles that it takes for energy to be dissipated from the system. Thus a Q of 1000 means that the excited oscillation will ring down to zero in 1000 cycles. I would think this article should mention this insight. I would add it except that I can remember if Q is the number of cycles to ring down to 1/2 the original energy or what exactly.

No, that's wrong. It never decays to zero. The article states correctly that it's the number of cycles required to decay to 1/535 of its original energy.--24.52.254.62 01:25, 21 October 2006 (UTC)

Alternative to 1/535 definition

I'd like to suggest a change to the definition of Q as the number of cycles for the response to decay to 1/535 of the original amplitude. Although this is certainly true, and used in the Crowell book, I've never seen it used elsewhere. The main problem is that as a definition for actually measuring Q (which is fun and instructive for students to do with a pendulum), it is practically useless. If you actually try to count the cycles, by the time the response decays to 1/535 it is so flat that the accuracy is lost. It also doesn't offer much insight into the mathematics.

The usual way of defining Q in engineering texts is that it is $2\pi \,$ times the number of cycles for the response to decay to $1/e=0.368\,$ which is one time constant of the exponential decay envelope. Although at first sight this looks more complicated, it shows that the Q is just the ratio of the exponential and sinusoidal time constants of the response: if the response is: $Ae^{\alpha t}cos{(\omega t+\phi )}\,$, then $Q=2\pi f/\alpha =\omega /\alpha \,$. And it is also a practical definition for measuring Q, since at 0.368 the response is still sloped enough to determine accurately when the amplitude falls below it.

I suggest changing the definition of Q to $2\pi \,$ times the number of cycles for the response to decay to $1/e=0.368\,$ of the original amplitude. --Chetvorno 21:02, 21 August 2007 (UTC)

I calculated $Q=f_{0}/B\,$, the definition of $Q\,$ over the bandwidth and your formula $Q=2\pi f/\alpha \,$ for a signal like $Ae^{\alpha t}cos{(\omega t+\phi )}\,$ and find out that there is always missing a factor of 2 between these formula. It has to be $Q={\frac {2\pi f}{2\alpha }}\,={\frac {\omega }{2\alpha }}$ like formula E.7 on this webpage http://ccrma.stanford.edu/~jos/filters/Quality_Factor_Q.html 77.10.132.145 (talk) 11:01, 5 December 2007 (UTC)

I noticed that Q is defined as number of cycles for the stored energy to decay to 1/535 of the original. I believe this is correct, but please note that stored energy is amplitude squared. So the amplitude will only decay to 1/23. Amplitude and energy seem to be confused in this discussion.Ken Wilsher 22:55, 5 February 2009 (UTC) —Preceding unsigned comment added by Kwilsher (talk • contribs)

Worth adding to this discussion that this https://ccrma.stanford.edu/~jos/fp/Decay_Time_Q_Periods.html page says this definition is an only approximation. In fact, 2pi(Energy stored)/(Energy dissipated in one cycle) is also an approximation https://ccrma.stanford.edu/~jos/fp/Q_Energy_Stored_over.html, though the main page gives it as the definition, so the "true" definition of Q isn't particularly clear (at least not to me!). It would be great if someone could give it as a function of an LTI system's matrix or eigenvalues or something like that. 174.252.36.13 (talk) 01:11, 9 December 2010 (UTC)

Reference for the Q-value equation in mechanical systems?

Where does the equation $Q={\frac {\sqrt {MK}}{R}}$ on mechanical systems derive from? I can't find a source and it's not cited. 130.233.189.53 14:07, 26 October 2007 (UTC)

Somehow it remained without attention until now, that the article suggests "In a parallel RLC circuit, Q is equal to the reciprocal of the above expression.", referring to the correct formula for Q in a RLC circuit as "the above expression". Which means that a parallel RLC circuit would have a Q-factor that grows with increasing R. Which, in turn, is an obvious nonsense. —Preceding unsigned comment added by 83.79.25.246 (talk) 19:58, 20 November 2007 (UTC)

Ooops, sorry. disregard the above. Of course, a parallel RLC circuit would prefer a higher R, ideally - no R at all (means open circuit istead of R), for an endless oscillation. —Preceding unsigned comment added by 83.78.43.62 (talk) 20:59, 20 November 2007 (UTC)

I think that in the Usefulness of 'Q' section, the Q factor for second order filters (Butterworth and Bessel) are derived from some equations and doesn't need to be cited. Probably someone with knowledge in these filters can show the derivations in this article. Hytar (talk) 15:08, 14 August 2008 (UTC)

Relationship to damping ratio

I'm not sure whether the equations relating $Q$ to $\zeta$ are marked "citation needed" because there is some doubt about their accuracy; or whether it's just there because it's good practice to reference these. When I first looked at them I was doubtful about them, but I think that was just because they were in a slightly unfamiliar form. I can't supply a citation as none of the texts I have to hand use the damping ratio as defined here. However, I can show that it follows straightforwardly from the definitions of $Q$ and $\zeta$ given in Wikipedia which hopefully is sufficient.

This article says $Q=1/2\zeta$ which we would like to verify. The damping ratio defines $\zeta$ in terms of the differential equation

${\frac {d^{2}x}{dt^{2}}}+2\zeta \omega _{0}{\frac {dx}{dt}}+\omega _{0}^{2}x=0.$

which has solutions of the form

$x=Ae^{-\zeta \omega _{0}t}\sin(\omega _{0}t+\delta ).$

This means the energy stored is

$E={\tfrac {1}{2}}m\omega _{0}^{2}A^{2}e^{-2\zeta \omega _{0}t},$

where m is the mass being oscillated (or, if you prefer, an arbitrary constant to make it dimensionally consistent — it cancels out later); and the power loss is

$-{\frac {dE}{dt}}=m\zeta \omega _{0}^{3}A^{2}e^{-2\zeta \omega _{0}t}.$

Using the definition of Q, this gives

$Q=\omega _{0}E/\left(-{\frac {dE}{dt}}\right)={\frac {1}{2\zeta }}$

as required. A bit more manipulation gives the more familar (to me, anyway) form

$\,Q=\pi f\tau$

where $f=\omega _{0}/2\pi$ is the frequency, and $\tau$, the time to decay to $1/e$. (I.e. $\tau =1/\zeta \omega _{0}$.)

Hope that helps. — ras52 (talk) 14:42, 30 December 2007 (UTC)

The equation for the Q-factor of a spring (in the Mechanical systems section) is similarly marked with a "citation needed". This one is even easier to see. The differential equation defining $\zeta$ was

${\frac {d^{2}x}{dt^{2}}}+2\zeta \omega _{0}{\frac {dx}{dt}}+\omega _{0}^{2}x=0.$

Multiplying through by $M$ gives the familar "F = ma" equation, and from the definition of $R$ in the article, obviously $R=2\zeta \omega _{0}M$. Then

$Q={\frac {1}{2\zeta }}={\frac {\omega _{0}M}{R}}={\sqrt {\frac {K}{M}}}{\frac {M}{R}}={\frac {\sqrt {KM}}{R}}.$

I think you're unlikely to find many references for these things as, at least in my experience, Q factors are not greatly used in mechanics. Looking through the indexes of three or four degree-level texts that I have to hand that mention this sort of mechanical oscillations, I can't find a single mention of Q factors.

I also notice that whilst these mechanical relations are marked with "citation needed", equally simple electrical relations are not. For example, the Q factor of RLC circuit is as obvious as the mechanical ones, but that is not marked "citation needed". Clearly citations would be desirable for all of these, but it is seems we're requiring a higher standard of referencing for mechanical examples than electrical examples. — ras52 (talk) 16:04, 30 December 2007 (UTC)

A possible reference for $Q=1/(2\zeta )$ would be W.T.Thomson, Theory of vibration with applications, and in the 3rd edition (London, 1988) it is on p75 equation (3.10-4). Fathead99 (talk) 16:38, 12 June 2008 (UTC)

Qualitiy factors of common systems

The three examples for the filters are marked with "citation needed".

A reference that points in the right way is Active Filter Design Techniqes by Texas Instruments. One may find tables with factors for the polynoms of the respective filter types' transfer functions and the definition of the Q factor based on these factors:

Q=sqrt(b_i) / a_i

Here's an example for a 2nd order butterworth filter:

The component values (R, L, C) of a practical circuit are chosen so that a = sqrt(2) and b = 1. Thus, the generalizes transfer function

A(s) = A₀ / (1+a*s+b*s²)

becomes

A(s) = A₀ / (1+sqrt(2)*s+1*s²)

Using the definition of Q for low-pass and high-pass filters, we obtain:

Q = sqrt(b) / a

Q = sqrt(1) / sqrt(2)

Q = 1 / sqrt(2)

Q = 0.707

Similar calculations will yield the Q factors for the other filter types based on the factors that may be found in the reference's tables.

I am aware that this is a hands-on approach based on some tables and definitions and not a really thorough derivation towards the requested citations, but it's a start showing that the numbers in the article are o.k. at least for 2nd order types of the filters named in the article. If anyone would like to give further information based on filter theory, it would certainly help the article. Also, further information for filters of a higher order than 2nd would be appreciated. --Zb-de (talk) 13:03, 5 January 2010 (UTC)

External links reverted as spam

The following weblinks have really to to with the Q factor and are no spam, like Dicklyon means.

Q factor to/from 'Bandwidth per octave' converter:

• http://www.sengpielaudio.com/calculator-bandwidth.htm

Q factor and center frequency - Find the cutoff frequencies of the bandwidth:

• http://www.sengpielaudio.com/calculator-cutoffFrequencies.htm
  

--Robert 19:42, 08 Oct 2008 (UTC)
Dick Lyon says: If an editor's only contribution is multiple ext. links to one site, I call it spam.

They may be perfectly good links, but if an anon user does nothing but post multiple links to a site, then that editor is a de-facto spammer, in my estimation. If someone who is not a spammer wants to review them, and decides to add them as external links, then that's more likely to be acceptable. Dicklyon (talk) 18:57, 8 October 2008 (UTC)

"Energy of steady-state vibrations" figure

The figure under "Physical interpretation of Q" shows that the bandwidth is determined by HALF of the PEAK ENERGY. As discussed earlier in this Talk page, the bandwidth is determined by half of the PEAK POWER (the square of energy). So the figure should be changed to be $E_{\text{max}}/{\sqrt {2}}$ or each $E_{\text{max}}$ should be changed to $P_{\text{max}}$. —TedPavlic | (talk) 14:51, 16 December 2008 (UTC)

You are incorrect here. Power is proportional to energy in a damped harmonic oscillation. You're thinking of amplitude, which is proportional to the square root of power or energy. Dicklyon (talk) 16:49, 16 December 2008 (UTC)

That's true. My mistake. P=E/t. I'm not sure that this will be clear to the average reader; "Half power" language is prolific in systems literature. —TedPavlic | (talk) 18:11, 16 December 2008 (UTC)

In this case, since the figure is about the steady state energy of a driven harmonic oscillator, the half-energy point is relevant. The power going into the system is not proportional to energy as the frequency changes. For a given frequency, the time at which the power being dissipated decreases to half is the same as the time at which the stored energy decreases to half, in a non-driven system. Dicklyon (talk) 01:28, 17 December 2008 (UTC)

Ok. So you're point is that the figure is not meant to depict the steady-state driven magnitude response, and so energy is the correct inner-product to use. Because the context of the section is a non-driven system that decays over time, the energy in the signal is finite, and so we use an energy signal. If it was driven, we'd have to use a power signal for the correct time normalization. I'll buy that explanation. Thanks. —TedPavlic | (talk) 14:08, 17 December 2008 (UTC)

It still appears like the section (and the figure, actually) are handling the driven case. The section talks about filtering and such. Perhaps the figure caption needs a change of wording... —TedPavlic | (talk) 14:10, 17 December 2008 (UTC)

You misunderstood me, and yes it depicts that driven case. I'm not sure what conflict you see in that. Dicklyon (talk) 14:12, 17 December 2008 (UTC)

The energy in a periodic signal is infinite. The output will be periodic if the input is periodic, and so the output will have infinite energy. However, both the input and output will have finite power. So (I think?) the figure only makes sense in terms of power. —TedPavlic | (talk) 15:25, 17 December 2008 (UTC)

The energy referred to is the energy in the system, the sum of its potential and kinetic energies, not the integrated power. Dicklyon (talk) 16:13, 17 December 2008 (UTC)

Error with attenuation constant?

There seems to be an error. The article lists one definition of the Q factor as the angular frequency divided by double the attenuation coefficient. That would give Q dimensions of length per time when in fact Q is dimensionless. The attenuation coefficient is a spatial decay measure not a temporal decay measure. I believe what was meant is that Q = angular frequency over decay rate. I will change it. Please explain to me how I am in error before changing it back. —Preceding unsigned comment added by 129.63.129.170 (talk) 20:11, 13 January 2009 (UTC)

Perhaps you are wrong in assuming the units you did for alpha? What source are you relying on for alpha and lambda? For now, let's leave it as it was; we should be able to quickly come to an agreement here. Dicklyon (talk) 05:52, 14 January 2009 (UTC)

According to the attenuation article, as used in ultrasound, $\alpha$ is typically measured in dB/(MHz·cm) — i.e. its dimensions are [time · length^-1], dB being dimensionless. That would give $Q=\omega _{0}/2\alpha$ units of [length · time^-2], not [length · time^-1] as the anonymous editor states. However, it strikes me as far more likely that a different definition of the attenuation coefficient, $\alpha$, is being used. It's hardly novel to find the same term being used in different branches of physics with slightly different meanings. Really, we should see Siebert's Circuits, Signals, and Systems says as that is the reference given for the equation. I rather expect that we'll find that he defines $\alpha$ so that the damped harmonic equation reads

${\frac {d^{2}x}{dt^{2}}}+2\alpha {\frac {dx}{dt}}+\omega _{0}^{2}x=0.$

That would a very common form of the equation, right down to using $2\alpha$ as the coefficient of the first derivative, although I don't recall having seen that $\alpha$ referred to as the attenuation. (I can't easily look it up as all my books are packed up in boxes while I have a new floor laid.) — ras52 (talk) 10:51, 14 January 2009 (UTC)

Note that the Attenuation coefficient article (which is linked from the ultrasound paragraph in the attenuation page, which is more of a disambig page anyway) gives $\alpha$ in essentially the same units as are given here (in the Q factor article). However, it refers to the "linear attenuation coefficient." The point here is that different contexts are going to have different domains of interest, but in all cases there's some sort of decay (that may be in one or more dimensions) that behaves in roughly the same way. When dealing with Q factor, we are implicitly using the linear case. —TedPavlic (talk) 14:46, 14 January 2009 (UTC)

The $\alpha$ given here is the real part of a complex pole of a second-order system. That is, it is the coefficient of oscillatory damping. The second-order complex poles will produce oscillations like...

$e^{-\alpha t}\sin(\omega t)\,$

Here, $\alpha$ is a temporal rate of decay only because the domain of interest is time. In other contexts where the systems are functions of space, $\alpha$ will represent the exponential decay rate of spatial oscillations. So I'm not quite sure what the problem is here. Certainly on the Q factor page time is going to be the most relevant domain of interest (at least for example sake), and so it's reasonable that $\alpha$ be described as a temporal rate. Typically it is only used as a spatial rate of decay when space is the domain of interest.—TedPavlic (talk) 14:40, 14 January 2009 (UTC)

Also note that $\alpha$ is frequently given in units of Nepers because it represents an exponential decay. —TedPavlic (talk) 14:40, 14 January 2009 (UTC)

Problem in "Usefulness of the Q factor"

Quote: "Likewise, a high-quality bell rings with a single pure tone endlessly after being struck."

If it rings (out in the air), then it dissipates power, and thus will not ring forever. —Preceding unsigned comment added by 129.240.84.144 (talk) 09:30, 1 April 2009 (UTC)

Who said anything about the bell ringing in the air? For one, it's a limiting example. However, technically speaking, "ringing" need not involve the transmission of sound through a medium. Power need not be dissipated for a bell to "ring." A pendulum need not swing through the air in order to swing. Finally, it's obvious that "endlessly" makes no sense for any passive system (i.e., when thinking of the universe as closed, then ANY system). The statement is an rhetorical ideal used to communicate a point. —TedPavlic (talk) 03:12, 29 May 2009 (UTC)

Can This Be Less Esoteric?

While it is true that Q describes how underdamped an osc is, that is far from the meaning of Q. I think the meaning of Q has more to do with not loosing energy. Can we make the lead article assessable by (and meaningful to) laymen? John (talk) 01:26, 29 May 2009 (UTC)

The opening paragraph, as it is, seems to already match your request.

In physics and engineering the quality factor or Q factor describes how under-damped an oscillator is. Higher Q indicates a lower rate of energy loss relative to the stored energy of the oscillator; 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. Oscillators with high quality factors have low damping so that they ring longer.

Can you suggest how it might be changed? It already discusses energy loss/storage and "ringiness." —TedPavlic (talk) 03:08, 29 May 2009 (UTC)

Suggesting an improvement is somewhat harder than complaining, I am still in the complaining stage. Ill keep thinking... I am having trouble convincing myself Q describes an oscillator vice a resonator. Describing it in terms of how underdamped it is is not too satisfying either, few laymen will relate to that. John (talk) 20:46, 1 June 2009 (UTC)

Can you explain your objections a little bit more? Perhaps give an example. A resonator is just a specialized oscillator. Perhaps you're having trouble picturing how a Q factor could be used when the device is, say, active because the energy in the system is not simply the energy from the input. Is that the problem? A couple of comments...

• In an active device, the energy being added to the system is being used to control the dissipation of the input energy. That is, it can work to dissipate the input energy quickly, or it can work to prevent the loss of that input energy. Input energy that is lost might get "re-supplied" by the external source, which means that you'll have a higher energy "stored" to energy "lost" ratio. We're just using an active device to supply extra power rather than polishing surfaces to remove the friction that causes the loss; however, it's basically the same idea.
• Stepping back to the math, any system that can be described by a second-order linear ordinary differential equation (ODE) has a Q factor. If it helps, think of Q as a mathematical construct that has a special physical meaning in certain contexts. However, I don't think you have to stretch the physical interpretation much to apply it to any general second-order linear ODE. If you perturb the ODE off of its equilibrium, it follows a certain trajectory back to it. That trajectory might be slow and oscillatory, or it might be fast and monotonic. Either way, without the initial perturbation, the movement wouldn't occur. The Q factor describes how quickly the input influence is damped out. It's possible that it will be sustained forever. In a perfect world, that would occur with lossless components. Because it's not a perfect world, we can use an active device to give us the behavior of lossless components. Sure, energy is being added from another source, but the net effect is that the energy from the input is "sustained" forever.
• From a black box perspective, an active device that implements the same differential equation as a passive device may as well be the passive device. All we really care about is input–output relationship. If it helps to think of it as a passive device (some resonance well or RLC circuit or mass–spring system or whatever), then that's fine, but it's not necessary.
• Finally, consider:
  • A bell that has some fancy inertial units (e.g., motors) mounted on its sides that can induce additional oscillations in the bell. If we like, we can set the motors up to make sure induced oscillations from a strike of the bell never die out. The extra energy will be coming from remote (external power supplies powering the actuators), but the net effect will be that the bell rings forever. Is that not an infinite Q factor?
  • A cart with a motor-driven wheels and a control system that ensures that the motor back-EMF stays constant. Assuming that a quick shove on the cart can overpower the control, the cart will roll forever despite friction trying to slow it down. We've implemented ice with an external power supply (motor batteries). Sure, the system isn't truly frictionless, but what do we care? It behaves frictionless, and that's all that really matters. We're SUSTAINING the input kinetic energy by RE-supplying it when it gets lost to friction. That makes it have a high Q.

So maybe the best definition of Q factor would refer to "input energy sustained" rather than lost and stored. Does that make sense? —TedPavlic (talk) 13:02, 2 June 2009 (UTC)

Seems to me energy and its loss, and sustain doesn't capture enough of the notion of Q. There is also a selectivity feature that is not apparent in the doorbell-with-motor view. Your notes sure help focus the question. I am not sure this captures the essence of Q. Still thinking (kinda slow, huh?) John (talk) 20:22, 2 June 2009 (UTC)

Remember that energy, when discussing Q factor, is meant in a signal processing sense. That is, it's a more general property than the "energy" you see in physical systems. It's referring to the energy in the signal (say, at the output of a bell). Hence, you need not worry about physical energy lost and gained when batteries are included. Instead, you think about how much energy is tied up in an output (especially after an impulse). —TedPavlic (talk) 18:18, 3 June 2009 (UTC)

Ted, Not sure its relevant, but I think energy is just metadata for signal processing resonance. A passive, real inductive & capacitive electrical resonant circuit ringing with finite Q looses real energy to real heat and its amplitude decays over time. An appropriately connected amplifier (active element) can replace that energy and make up for the heat loss and keep it ringing. In a software emulation of that, nothing real gets really warmer. But that’s not the thread I thought I was pulling on. I was thinking about addressing some kind of selectivity notion: that a resonant system with high enough Q does not ring as much as a lower Q system if the excitation is too far off frequency. John (talk) 20:25, 6 June 2009 (UTC)

The energy referred to in Q factor is the energy discussed on Energy (signal processing). Using that mathematical definition of the energy of a time signal, "Q factor" applies to all systems – passive, active, and abstract. If you would like to give some qualitative comparison of Q factor that more obviously applies to a wide range of systems (which may or may not be physical), then that's probably a good thing. —TedPavlic (talk) 14:11, 7 June 2009 (UTC)

I strongly agree that this article, especially its introduction, should be much less esoteric and more accessible to laypersons. What would be wrong with leading off the article with something like: "The Q Factor is a measure of the relationship between stored energy and rate of energy dissipation in certain electrical components, devices, etc, thus indicating their efficiency. It is a measure of the quality of an electric circuit; the ratio of the reactance to the resistance. For a capacitor, inductor or tuned circuit, the Q factor, or Q, is a figure of merit. The higher the Q, the lower the loss and the more efficient the component." --Westwind273 (talk) 16:57, 8 March 2011 (UTC)

While I applaud your goal of making the article clearer to laypeople, I feel your suggested lead doesn't do that. Your proposed text only covers the use of Q in electronic components, and also doesn't mention that it has anything to do with resonance or oscillation. The concept of Q is broader than its use in electronics; it is used in connection with all types of resonators. I think introducing it in the context of mechanical vibration gives laypeople a clearer picture of what it's all about. --Chetvorno^TALK

Thank you for the critique of my suggestion. It has helped me understand the topic better in general. Although a purist would probably say that the mechanical definition is the most true basic explanation of Q, it seems to me that my electrical explanation is much closer to the practical knowledge that a layperson would be seeking. Note that English language dictionaries usually focus on Q in its electrical context. At the very least, it seems like the sentences I wrote should be somewhere in the introduction. I would argue that Q's meaning of "efficiency" is more central to its real world application, than Q's meaning of "oscillation". I would compare this Q factor article with the use of the Q factor term in the Wikipedia article on Equivalent Series Resistance. Put differently, let's say a layperson was looking over an inductor datasheet and saw "Q" for the first time. Would the current article be instructive to them in understanding this concept? I think not. It seems that there is a kind of battle for the soul of Wikipedia here: Is Wikipedia meant to be instructive to the population at large? Or is Wikipedia a place where academics come together to record the purest definition of terms in their field of specialty? --Westwind273 (talk) 11:14, 9 March 2011 (UTC)

This is how I have come to understand Q-factor. And this is accessable to a layman. Think of a playground for cildren and a swing. You put your little child in the swing and start pushing. She will swing with a frequency solely dependant on the length of the swing's chains. (OK and gravity.) You could tie the shaft of a rake to the swing and by putting in some energy make it swing at a higher or lower frequency. Now put the fattest man on earth in the swing and repeat the above. You will need to put in more enery to deviate from the resonance frequency. That is due to a higher Q-factor. Am I right or am I right? ;-) — Preceding unsigned comment added by 81.227.219.164 (talk) 21:00, 5 May 2018 (UTC)

Parallel RLC Q factor

Looking at the recent edit history, some editors do not fully understand Q factor in a parallel RLC circuit. It used to be correct here. The wikibooks circuit theory page has it correct, Q=R*sqrt(C/L): http://en.wikibooks.org/wiki/Circuit_Theory/RLC_Circuits . I am going to update the article page now. The intuitive justification (for editors who disagree) is that as R goes to infinity, Q must go to infinity as well because it because an ideal LC resonator with no resistor. As C increases, the peak voltage across the resistor for a given starting energy will decrease, so resistor power dissipation decreases, thus Q increases. As L increases, peak voltage increases, thus increasing resitor power dissipation, decreasing Q. Mattski (talk) 08:26, 24 February 2010 (UTC)

I'm glad someone is looking into this! I noticed the recent edits also and I was suspicious. I had this on my list to try to find reliable sources, but had not yet gotten around to it. Do you have any reference citations that could be used? Especially for equations and such, it is nice to have a place to double check things. Someone recently changed a constant in list of moments of inertia, and I had to sit there and spend 10 minutes re-work the integral from scratch, just to convince myself the old version was right and the new one was wrong! (I need to find references for that article too...) CosineKitty (talk) 18:33, 24 February 2010 (UTC)

Most books seem to just talk about the series case and skip the parallel, but I'll see if I can find a good source. Are posted lecture notes a good source, or should I go for academic paper/textbook? Mattski (talk) 23:13, 1 March 2010 (UTC)

X=?

In the last paragraph of the RLC section, the sentence "In this case the X and R are interchanged." occurs and yet X has had no previous mention. 62.49.27.35 (talk) —Preceding undated comment added 14:52, 20 April 2010 (UTC).

The guy who added that on Feb. 22 doesn't seem to be around, but you can probably figure out a fix from this version: [1]. Dicklyon (talk) 06:37, 22 April 2010 (UTC)

Removed the offending sentence. I don't see that it adds anything.Tunborough (talk) 13:23, 22 November 2011 (UTC)

Complex impedances

I don't see any justification for the equations in this section. The complex impedance is frequency dependent, but Q is not. In particular, the phase angle is zero at resonance, so tan $\phi$ would be zero at resonance, whereas Q would not be zero. I suggest this section should be removed, but I'm reluctant to do this much damage alone. Tunborough (talk) 13:05, 22 November 2011 (UTC)

I found a source for what I hope is the correct calculation: http://www.qsl.net/va3iul/Impedance_Matching/Impedance_Matching.pdf I will go about implementing it now.siNkarma86—Expert Sectioneer of Wikipedia
^{86 = 19+9+14 + karma = 19+9+14 + talk} 05:34, 26 November 2011 (UTC)

Here is another good document which can be used for later: http://www.edn.com/contents/images/159688.pdf siNkarma86—Expert Sectioneer of Wikipedia
^{86 = 19+9+14 + karma = 19+9+14 + talk} 03:44, 3 January 2012 (UTC)

The section referred to has been renamed to Q factor#Individual reactive components; I repaired an internal section link just now, and added a comment about why Q is frequency dependent. Dicklyon (talk) 04:10, 3 January 2012 (UTC)

Originated

"The concept of Q factor originated in electronic engineering, as a measure of the 'quality' desired in a good tuned circuit or other resonator. [edit]"

Please, please! Anyone have a reference for the above claim?? It's very important to me.

i.e. not originated WRT mechanical oscillators?

Wikiecorrect (talk) 19:51, 4 March 2012 (UTC)

p.s. my name is cleyet. Search and answer off the talk page in addition to adding the reference on the Wiki page -- thanks!

I have given a reference to this - as requested. There is another article on the history, also by Bertha, Lady Jeffreys in either Wireless Word or Physics World (or Physics Bulletin) round about the same time. - Brian Cowan. — Preceding unsigned comment added by 80.229.155.170 (talk) 21:43, 5 June 2012 (UTC)

Apparent discrepancy between fundamental and reactive based definitions

In this section of the article I believe that the first equation is wrong, because the current used in the energy stored is the peak current, and the energy used in the power dissipated is the rms current whereas the text says they are both rms. If the same current is used for both the worrying factor of 1/2 disappears. The following discussion which explains it in terms of total stored energy is incorrect, because the energy stored in the capacitor and the energy stored in the inductor are the same energy, not separate energies that can be added together, the energy swaps place 4 times a cycle, from the capacitor to the inductor, back to the capacitor and then back to the inductor again, maintaining the same total energy all the time. When the voltage is highest on the capacitor there is no current in the inductor, and vice versa. The total energy can be calcuated at any point in the cycle and is half the capacitance times the peak voltage squared (or the capacitance times the the RMS voltage squared), or half the inductance times the peak current squared (or the inductance times the rms current squared), or proportions of each added together, but they always give the same total (at the resonant frequency). 192.93.164.28 (talk) 10:29, 7 March 2012 (UTC)

You are right, the equation is wrong for the reason you say. Constant314 (talk) 02:47, 8 June 2012 (UTC)

I think the section has a point. On average, the inductor stores 1/2L<I^2> energy (where <I^2> is the time average of the squared current, i.e. the RMS current squared), and -- on resonance -- resonators store one half their energy in the inductor and one half in the capacitor (when time averaged), so the total energy stored is 2(1/2L<I^2>)=L<I^2>. Likewise, the time averaged power dissipated in the resistor is R<I^2>, so the quality is w(energy stored)/(power dissipate)=wL<I^2>/R/<I^2> = wL/R = 1/R(L/C)^(1/2). However, when you just have the inductor, you're off by a factor of 2. Dlenmn (talk) 18:55, 8 April 2012 (UTC)

Parse errors?

There is suddenly a lot of red text about parse errors on the page. I think something is wrong there? CodeCat (talk) 15:52, 7 September 2012 (UTC)

It must be a temporary error on Wikipedia servers. It appears that the formulas work just fine under the edit preview. Go to (http://en.wikipedia.org/w/index.php?title=Q_factor&action=submit) and hit "Show preview" to see what I mean.siNkarma86—Expert Sectioneer of Wikipedia
^{86 = 19+9+14 + karma = 19+9+14 + talk} 19:56, 7 September 2012 (UTC)

Q factor for individual reactive components

First posting for Wikipedia, so I apologize in advance if I have not posted according to all guidelines. In studying the Q factor for individual reactive components, I have discovered an possible inconsistency with the definition

$Q_{C}={\frac {X_{C}}{R_{C}}}={\frac {1}{\omega CR_{C}}}$,

because the capacitive reactance $X_{C}$ is defined (properly, I believe) in the provided link as:

$X_{C}=-{\frac {1}{\omega C}}=-{\frac {1}{2\pi fC}}$

This would imply a more suitable definition for the Q factor should include a negative sign (recognizing that $Q$ is non-negative):

$Q_{C}=-{\frac {X_{C}}{R_{C}}}={\frac {1}{\omega CR_{C}}}$

or perhaps a more generic equation that could be applied to the inductive case as well:

$Q_{C}={\frac {|X_{C}|}{R_{C}}}={\frac {1}{\omega CR_{C}}}$.

The trouble is that many of the references I have studied and checked seem to agree with the current Q factor equation in Wikipedia:

$Q_{C}={\frac {X_{C}}{R_{C}}}={\frac {1}{\omega CR_{C}}}$.

Since $X_{C}<0$ (agreed?), can anyone shed light on this possible inconsistency? Thanks.Stribs17 (talk) 19:23, 30 November 2012 (UTC)

Sign ambiguity of this sort is very common in many fields. In this case, there's a general inconsistency in how to treat the sign of capacitive reactance (see Talk:Electrical reactance for lots of discussion about it). It can be negative, so that it measures the same direction as inductive reactance, or positive, so it's measuring the opposite direction. When people write the ratio, they conveniently ignore whichever sign convention they might otherwise use. It would be good to fix it; I like your absolute value idea. Dicklyon (talk) 20:10, 30 November 2012 (UTC)

Depending on your definition, $X_{C}$ and $X_{L}$ can be seen as imaginary: $X_{C}=1/j\omega C=-j/\omega C$, so the absolute value is definitely in order. Q is inherently real and positive. Go for it.Tunborough (talk) 16:50, 1 December 2012 (UTC)

Attenuation Coefficient

In the section "Physical Interpretation of Q" the main article states: "The factors Q, Damping Ratio ζ, and Attenuation α are related such that..."
...and then proceeds with different formulas relating the variables Q, ζ and α .

I have a problem with the link to the Attenuation article because this article does not explain what the Alpha α variable is and this article does not contain even one formula with this variable α.

Thus, the better article to link in its place is the Attenuation Coefficient article, because it better defines the variable Alpha α.
Alternatively, see the Attenuation Constant article, which also rigorously defines Alpha α in another exponential formula.

The way the article is written now, it is not easy to discover that the Attenuation Coefficient or Attenuation Constant Alpha α is related to the Exponential Decay Constant λ.

This relation is important to be able to answer "time of decay" questions. For example such as the one below:

Q: "It takes N cycles for the amplitude of a sine wave to decay to 50% of its original amplitude. What is its Q Factor ?"

In engineering texts, the Q Factor is usually defined as 2π times the number of cycles for the response to decay to 1/e = 0.368, which is 1 time constant of the exponential decay envelope.

The Attenuation Coefficient ( which is the same as the Exponential Decay Constant ) provides the clearest conceptual link to other exponential decay functions in such problems.

Verpies (talk) —Preceding undated comment added 13:32, 22 January 2014 (UTC)

"Attenuation rate" is a good name for it, since it's a rate constant (nepers per second). But the articles you linked, attenuation coefficient and attenuation constant both use spatial definitions (nepers per meter), not temporal. If you can find something more appropriate to link (like the lambda in Exponential decay), or create something, that would be better than those. Adding a formula with $\exp(-\alpha t)$ is a good idea. Dicklyon (talk) 15:36, 22 January 2014 (UTC)

I will look for a temporal definition of Alpha.

Verpies (talk) 00:47, 23 January 2014 (UTC)

It's in Exponential decay. It doesn't really matter that they call it lambda there, as it's the same thing. I usually call it sigma, personally. Dicklyon (talk) 08:04, 23 January 2014 (UTC)

Actually, alpha is the decay rate for amplitude, not energy; it is in nepers per second, since nepers are defined as natural log of ratio of field quantities, not powers or energies. The energy decay rate is 2alpha per second, which is probably worth clarifying with a formula with $\exp(-2\alpha t)$. Dicklyon (talk) 16:19, 22 January 2014 (UTC)

Indeed the distinction between field decay rates and energy decay rates is an important one.

Verpies (talk) 00:47, 23 January 2014 (UTC)

A resonant system with Q = 5, plotting the oscillation and the decaying (from 1) amplitude and energy, with key times and factors marked. For any other Q value, the graph would be the same except for a different number of cycles of oscillation under the curve.

For your consideration: I made this figure. Use it if you think it's helpful. Dicklyon (talk) 00:46, 24 January 2014 (UTC)

Q factor definition in the context of individual reactive components

In the context of individual reactive passive components (e.g. inductors & capacitors), I'm familiar with the following definition:

$Q(f)\ {\stackrel {\mathrm {def} }{=}}\ {\frac {X(f)}{R(f)}}.$

The aforementioned definition is presented, in some form, in section Individual reactive components of the article, however, the section Definition of the quality factor has no mentioning of it. Instead, the following definition is presented:

$Q(\omega )=\omega \times {\frac {\text{Maximum Energy Stored}}{\text{Power Loss}}},\,$

a definition which is practically the same as the other energy-based definition in the section, and furthermore, includes a reference to James W. Nilsson's Electric Circuits 1989 edition. I've went through a recent (much newer) edition of the book, and found no energy-based definition of any kind for Q - whether for resonator circuits or individual components. I therefore tagged the reference as "Failed verification", and additionally, I wonder what is the point of this definition, which is practically the same as the previous one in the article. It seems to me that one of them is superfluous.

--Sagie (talk) 14:15, 6 February 2015 (UTC)

It seems that the only difference between that formula and the preceding one is the substitution of ω for 2πf which I would allow as trivial mathematical substitution. However, it also doesn't add any new information so I would not object to its removal. I do, however believe that the energy based definition should be the first definition because it applies to all situations and simple elements are never simple in reality. All inductors have capacitance.Constant314 (talk) 20:27, 7 February 2015 (UTC)

The substitution of ω for 2πf is a minor difference. The main, and major, difference between the two formulae, which is surprisingly subtle, is the explicit indication that the Q factor definition for the individual components is frequency-dependent. Another issue is that this definition isn't equivalent to the definition in section Individual reactive components of the article ($Q(f)\ {\stackrel {\mathrm {def} }{=}}\ {\frac {X(f)}{R(f)}}$).

I'm not sure what makes you say that "energy based definition ... applies to all situations". The frequency-to-bandwidth ratio definition is just as applicable for any system for which one would like to express a Q factor. Anyhow, the bottom line is that in my experience, the frequency-to-bandwidth ratio definition is the most prevalent definition in textbooks, as well as the one which is mostly used in technical documentation and specifications of filters and other systems, hence its placement as the first defintion.

--Sagie (talk) 21:59, 11 February 2015 (UTC)

I found it interesting that in the article one can read the phrase "In the context of resonators, there are two common definitions for Q, which aren't necessarily equivalent.". In my opinion, this statement has something missing in it, as it seems that the physical meaning is the same in both definitions. Why are they not equivalent (I know that it might not be an argument that would stick with everybody from all fields, but... I'm just trying to help)? You mean NUMERICALLY equivalent? I believe such could be the case, but that does give me the feeling that one of the definitions is not tied to its physical origin (it is just a technical detail), while the other is... Let us say you have a wierd emission spectrum in front of you (so it is not necessary to have a simetric emission in relation to the value at which such system has a maximum intensity in the range of the frequencies you are looking at - which to me seems to be a general consideration), with frequency $f$ being its maximum value - when the hypothesis of no interference from the detection apparatus in the spectrum is valid - and with $\Delta f$ being the half-power bandwidth (which is not a general definition, but could be easily superseeded by variance or such things - but as this doesn't seem to add much substance to the discussion, the half-power bandwidth definition serves well). Wouldn't, from the point of view of an experimenter, it seem to him that the quality factor should just be $Q = f/ \Delta f$? Without knowing how the energy loss works in the system (which means the experimentalist is not yet sure on how he could improve his quality factor), I think the only honest way of looking at it is this. The number doesn't matter as long as the same physical definition is always used. And then you express it in ways that are mathematically more general than the simplest definition, but its meaning is still intact. Notice that the definition has to be frequency dependent, as loss mechanisms change when you go from microwaves to the optical domain, just to give some physical example, and I'm sure more general grounds would have such property... And that is fine(!), as, in reality, the person making the measurement of such parameter normally is not interested in the loss mechanism that is happening right when he measures the mentioned parameter. This person wants to characterize something in a reliable and verifiable manner. So that is, in my opinion, why you felt that "It seems to me that one of them is superfluous."... Because it seems to be the indeed case, even if I don't think one should remove the (minor) reason for the difference between both definitions, but state it, while removing some of the discussion regarding the differences between the definitions. I'd also love to ask you one question: has the quality factor any relation with the uncertainty principle? Maybe that is completely out of the scope of this discussion... so I don't mind not being answered. — Preceding unsigned comment added by 143.107.229.249 (talk) 19:06, 25 March 2015 (UTC)

Could you elaborate on "the explicit indication that the Q factor definition for the individual components is frequency-dependent". Are you saying that the Q of individual components is frequency dependent and that the formula does not explicitly show that or that the Q of individual components is not frequency dependent and that the formula suggests that it is? The Q of frequency dependent elements (inductors and capacitors) is frequency dependent. Constant314 (talk) 20:08, 14 February 2015 (UTC)

I did not express my concerns well. I’ll try again. My complaint is with Q = X(f)/R(f), which is fine with a mathematically ideal component (for example: a pure inductor and resistance with no capacitance). I hope I can explain this without a circuit and equations. I work with inductors and resonating them. I have a useful impedance meter that measures the real and imaginary parts of the impedance at the specific frequency I select. It can report the measurements in a variety of ways: real and imaginary, Z and θ, Z and Q, Land Q, L and R_series, L and R_shunt. It is a good meter and it makes accurate measurements and it does the correct math, but it is dumb in the sense that it only uses measurements taken at one frequency. Then, I resonate the inductor with a parallel NP0 capacitor of very low ESR. I adjust the capacitance until it resonates at the same frequency that I measured the parameters of the inductor. The tuned Q is always lower. The reason is that the inductor has inter-turn capacitance. The meter assumes that the component is a pure inductance and series resistance and it computes Q as X(f)/R(f). But the shunt capacitance makes X(f) larger than ωL and that causes the meter to report a higher Q and a higher inductance. The real Q of the tuned circuit is ωL/R_series. So, I guess I am saying, in the case of an inductor, that Q = X(f)/R(f) is an approximation of the real Q which is ωL /R_series. The approximate Q is usually higher than the real Q and that results in disappointing circuit performance. But maybe that is out of scope. Constant314 (talk) 20:24, 14 February 2015 (UTC)

I haven't really delved into your whole story with your impedance meter, but it seems you don't fully understand what you write. Some pointers:

1. Notice in the article that the definition for the individual components has "$Q(\omega )=...$" (i.e. Q is explicitly dependent on ω), whereas the filter/system definitions are "$Q\ {\stackrel {\mathrm {def} }{=}}\ ...$" (no explicit dependence).
2. Resonance frequency is a characteristic of a system, not of an external forcing oscillation applied to it. In the presence of an external force, a system (in its steady state) will oscillate at the forced frequency, not at its resonance frequency.
3. Any passive system or component (ideal or not) with two leads can be described as a frequency dependent, apparent impedance between these leads. You can measure its apparent impedance (at some frequency), in the exact same manner whether it's a plain single resistor or a complex network (in parallel, serial, or a combination) of resistors, capacitors, inductors, crystals, etc. If you define X to be the imaginary part of the apparent impedance, and R as the real part, then you have no problem to calculate and present Q(f) = X(f)/R(f), regardless of what component or system you are measuring. Note that an ideal inductor or capacitor have zero resistance, and as a result have infinite Q.

--Sagie (talk) 15:47, 27 February 2015 (UTC)

Anonymous communications systems is not an appropriate topic for this article

This topic is not logically part of Q factor as defined in the lede. It perhaps should have its own article. I've copied here so that it can be moved elswhere

Anonymous communications systems

In the field of anonymous communications, ${\textstyle q}$ factor is a combinatorial metric that encompasses both anonymity and performance. If either anonymity and/or performance fall below an arbitrarily set threshold at any point during an observation (whether by an attacker of the network operator) event is captured. Boolean values for both anonymity ($v_{a}$) and performance ($v_{b}$), based on the thresholds are:

$v_{a}\equiv a>\theta _{a}$

and

$v_{b}\equiv b>\theta _{b}$

The q-factor is calculated as simply the conjunction of $v_{a}$ and $v_{b}$.

$q=v_{b}\cdot v_{b}$

A value of 0 of ${\textstyle q}$ indicates that some network management intervention is required, otherwise if ${\textstyle q}$ = 0 the network can continue to operate as it is. Approaches to intervention may including the re-direction of users to a sparsely used channel with the aim to improve anonymity (the overall anonymity set, `plausible denial-ability') or divert users away to another channel to provide a better balance of resource allocation (e.g., bandwidth).

Constant314 (talk) 19:54, 14 October 2015 (UTC)

References

A suggested new order for the presentation and inappropriate illustration picture

I suggest that instead of starting from a filter point of view, the Quality factor should be introduced for components or resonators as the ratio of reactive power to loss power (or stored energy compared to energy loss for a cycle). I see three main reasons for doing that:

- modern components datasheets always involve Q-factor measurements because all modern energy storage and converter technologies involve the use of high-Q components.

- the quality factor of a serial resonator can then be derived from the components: 1/Q=1/QL+1/QC.

- the same definition can be applied to any resonator structure even in cases were an equivalent RLC circuit is not defined.

I also have a problem with the illustrated example that represents a band pass filter which is not at all well defined through the single idea of Quality factor.--Henri BONDAR (talk) 15:32, 18 February 2016 (UTC)

You will get quite a bit of opposition to that. There are many objects and systems that have a Q but do not have components such as a bell or an optical cavity.Constant314 (talk) 19:50, 18 February 2016 (UTC)

Sorry for my perhaps unclear explanation. I totally agree with you, but I didn't suggest to introduce the Q-factor through the only idea of a defined L or C component but through the idea of the ratio of reactive to resistive power. This idea is much more general than dumping consideration of a resonator (but can be applied to it as a special sub-case). So I suggest to use instead of "In physics and engineering the quality factor or Q factor is a dimensionless parameter that describes how under-damped an oscillator or resonator is" a sentence such as "Quality factor is a measure of relative loss compared to energy storage in a cycle, applied to components it can be used to measure the performance of a component designed to store electrical energy, applied to resonators it enables to compute the dumping of the oscillations with time, applied to filters it enables to compute the bandwidth" or something similar. Besides the picture used is a band-pass filter response and it doesn't look like a resonance curb at all! As you know band-pass filters are characterized by upper and lower cutoff frequencies. The idea of Q-factor combined with the central frequency can be applied to it but for narrow bandwidth response (large Q-factors). It is usually not not used for large bandwidth situations because the central frequency can be defined in various ways and doesn't have any special meaning in such cases. In most cases Q-factor is applied to situations where an equivalent LC circuit can be defined such as piezoelectric resonators, dielectric resonators, microwave cavity and so on. — Preceding unsigned comment added by Henri BONDAR (talk • contribs) 14:31, 19 February 2016 (UTC)

I generally agree that the ratio of energy stored to energy dissipated is a more fundamental definition than the ratio of center frequency to bandwidth, but the energy definition involves calculous whereas the frequency definition involves arithmetic. Wikipedia articles are not academic articles and so they typically start off with the most popular definitions instead on the most fundamental definitions. Fortunately, the more fundamental definitions are given further down in the article. Constant314 (talk) 20:07, 19 February 2016 (UTC)

Probably the filter point of view was the most popular fifty years ago but it is no more. I was very surprised to see it as an introduction for this subject that pervades now the whole physics (to say you the truth I had to switch to another link for a didactic job on electromagnetism I am working on). I think you will have large difficulties to maintain that idea of largest popularity especially when the alternate and more general explanation is also much more easy to grasp. --Henri BONDAR (talk) 08:50, 21 February 2016 (UTC)

What about the idea of using also a more appropriate picture ? --Henri BONDAR (talk) 08:52, 21 February 2016 (UTC)

l agree with Henri that the introductory graph is poor and should be replaced, but I oppose most of the other proposed changes. As Constant314 says, Wikipedia is a general encyclopedia, and technical concepts should be introduced in a way that makes them easiest to understand. I wouldn't object to the lead sentence Henri suggested defining the Q as rate of energy loss compared to energy storage; as mentioned that is the more fundamental def. But I think defining it as the ratio of reactive to resistive power, or starting with defining the Q of individual inductor or capacitor components, is way too abstract an approach for the introduction. --Chetvorno

I’m OK with the ratio of energy stored to energy dissipated. To be sure, I checked the IEEE dictionary. They give “Two pi times the maximum energy stored to the energy dissipated per cycle at a given frequency.” It further says an approximant equivalent definition which may be applied to other structures is the ratio of the resonant frequency to 3dB bandwidth. Constant314 (talk) 15:48, 21 February 2016 (UTC)

One possibility could be to separate more clearly the filter point of view (starting from a basic second order LC filter and related picture and getting into more details such as transfer functions) form the component side (with also more details for instance on measuring techniques). Q-factors are a growing concern for power converters and coupled resonant circuits (for wireless power transfer). In such cases the important quantity is kQ (sometimes called coupling index), when the coupling index is large the distance between the two modes (analog to a bandwidth) can be explained as a function of k only (and not Q, so the filter interpretation is not used in WPT).

They were also a lot of new inputs recently for components Q-factors, for instance resonance is no more used to measure Q-factors, many technology are available but the most widely used is the auto-balanced bridge technique that uses a virtual ground technique to measure very accurately U and I and then extract Z and compute Q=X/R with a good accuracy even for very large Q-factors (>500).

For a first introductory sentence, I personally prefer the definition based on the ratio reactive to dissipative power but I agree that some readers may not be familiar with the reactive power concept, most presentations start with the energy ratio (and unfortunately the two pi factor). Besides a word can be added to introduce the loss angle (with a link to dielectric loss) and the dissipation factor (if not already done).--Henri BONDAR (talk) 16:07, 23 February 2016 (UTC)

After a two years work devoted to resonant circuits related to power applications, I still continue to think that it will be more general to start this page with component Q-factors. Then you may introduce the bandwidth of resonant circuits and filters as a consequence of the quality factors of elementary components (lumped element models). You could start with a second order resonant circuit as most resonances and anti-resonances in many different domains of physics can be modeled accurately around the resonance frequencies using such circuits. An appropriate picture should also be used. According to me, the generalization to band-pass filters should arrive in the last part of the article.

Please check the web for alternative dictionary and encyclopedia definitions and you will see that this page is nearly the only one to proceed in a reverse manner, starting by a specific case (the band-pass filter) and later on coming to the wider definitions (Quality of components, description of resonances). Henri BONDAR (talk) 16:07, 13 January 2019 (UTC)

I strongly oppose this idea, introducing Q factors of components in the article before Q factors of resonators. I'm sorry, Henri, but I don't see how anyone could possibly think that is a better way of introducing the concept of Q to general readers. The Q factor of a harmonic oscillator (resonator) like a tuned circuit or bell has a clear intuitive interpretation that is easy to understand: as the degree of damping of the oscillator, and a second intuitive interpretation as the narrowness of the bandwidth. The Q factor of an individual component like a capacitor or inductor has no intuitive interpretation, it is just an obscure parameter. Second, as Constant314 said, there are many harmonic oscillators, both electrical and mechanical, that don't consist of two separate energy storage components like a tuned circuit: what about a microwave cavity, quartz crystal, laser cavity, or any acoustic resonator, a bell, tuning fork, organ pipe, piano string? This article is not just about tuned circuits. I looked up the chapters introducing Q factor in electronics and physics textbooks [2], [3], [4], [5], [6], [7], [8] and NONE of them explain it that way. --Chetvorno^TALK 17:18, 14 January 2019 (UTC)

I agree with Chet, though I do have some sympathy for the idea of more prominence to the definition "ratio of reactive power to loss power". For components, this never made a lot of sense to me, since it depends on frequency, so without knowing the resonant frequency, which is affected by other components, the frequency to use would be unknown or arbitrary. For a resonator, "ratio of reactive power to loss power" makes more sense, whether it's made of electrical components, mechanical, cavity, or whatever. If Henri can show specific texts whose approach he likes, that might help us tune up the presentation. Dicklyon (talk) 04:04, 15 January 2019 (UTC)

And I see had something to do with that awful graphic. I have a copy in my local wiki pix folder, which means I edited it at least, but I see I don't claim it on my user page, so someone else probably did it first. Hard to tell from the history on commons. Anyway, I'd support changing it to a more typical resonance shape, even though the Q concept is also applied to bandpass filters of more flat-topped shapes, which I think was the point there. Dicklyon (talk) 04:12, 15 January 2019 (UTC)

This is not a very important point I agree, maybe it is because I am essentially working with components, materials (piezo-electric materials are characterized by their intrinsic Q-factors for instance) and resonator models. I will respect the consensus but I still think that bandwidth considerations as well as damping are consequences and not the underlying core aspect. Indeed changing the picture to fit a classical second order serial resonance will be great first step. Considering the reactive to loss power ratio, as I did in my courses for engineers should be great to, but agreed with Chet that reactive power is not enough spread in litterature to be used here. Henri BONDAR (talk) 07:08, 15 January 2019 (UTC)

Maybe with this figure as starting point someone can make a replacement? Dicklyon (talk) 07:31, 15 January 2019 (UTC)

Indeed, beside the original picture can be used later on as an illustration of the specific case of a band-pass filter (that need more parameters for a complete characterization such as the order of the amplitude decrease on both side of the two cutting frequencies). Another picture showing typical energy relaxation in resonators is welcomed.

Don't get me wrong, I am OK to use these examples as an introduction to the field, but in the development of the article, I suggest that an energy related definition should come first (as in most of other dictionaries and encyclopedias), then material Q-factors (or loss angles), then components Quality and finally more complex behaviors such a band-pass filters.

Concerning the frequency dependent argument; in all non-dimensional analysis, the Q-factors appear on equal footing with other reactance ratios (such as load factor, over-voltage, efficiency....) that are all potentially frequency dependent. Indeed the behavior of more complex circuit (including band-pass filters) is more difficult to describe and allows different points of view (sometime every component comes with it associated Q, often only coils Q are considered (as capacitor Q are much larger) and in rare cases only a single Q for the whole equivalent circuit can be used with a reduced meaning. Henri BONDAR (talk) 09:56, 15 January 2019 (UTC)

One typical example is to consider two coupled resonant circuits that were used as band-pass filter in the beginning of electronics and nowadays for Wireless Power Transfer. The behavior is well described using the coupling index k(Q₁Q₂)^1/2. The response is close to the ideal band-pass filter only for symetrical Q-factors and a coupling index equal to 1. However in practice most HF amplifiers were tuned with a coupling index of sqrt(2) for the coupling resonant transformers. For WPT systems, in order to obtain large efficiencies, the coupling index is usually much larger than 1. Using a single Q to describe the whole response of a filter is very reductive in most practical cases. Henri BONDAR (talk) 11:31, 15 January 2019 (UTC)

Example of Q-factor applied to materials can be found here: http://piezo-kinetics.com/wp-content/uploads/2017/04/pki-specs-2016-1.pdf all manufacturers have similar datasheets for their materials. For dielectric materials, dissipation factor or loss angle is often used but the principle is the same (ratio of stored energy to corresponding loss). Similar considerations are used for ferrite materials however because losses are both frequency and amplitude dependent, they are presented in a slightly different manner (functions of both frequency and field amplitude levels). Henri BONDAR (talk) 13:33, 15 January 2019 (UTC)

Surprisingly, I am much more comfortable with the dissipation factor page: https://en.wikipedia.org/wiki/Dissipation_factor where resistive to reactive power ratio is introduced in the widest possible sense. As admittedly DF=1/Q, how do you explain a so large discrepancy between the two articles? Don't you think they should share a similar content? Henri BONDAR (talk) 18:37, 15 January 2019 (UTC)

Suggested addition to the article

I like Dicklyon's graph above, Universal Resonance Curve.svg, as a replacement for the existing bad graph in the article, although it would be good to label the coordinate axes and indicate the bandwidth explicitly. Here's another graph that might be a good addition; it shows how the resonance curve gets more peaked as Q increases. It would be easy to change the damping factor ζ values in the diagram to Q values. --Chetvorno^TALK 19:23, 16 January 2019 (UTC)

Perfect for me, if Q-factor values are used instead of damping factor. Henri BONDAR (talk) 19:44, 16 January 2019 (UTC)

@Henri BONDAR: @Dicklyon: Here are my (humble) opinions on the issues above:

• I agree that the Q = reactive power / loss power definition should be given more prominence, and I'm convinced by Henri's arguments that it is the most general definition, and I wouldn't mind the article saying that. But I don't think it should be the lead definition in the introduction; that should remain the damping definition which is most intuitive.
• Since nobody is going to know what "reactive power" is, I think the power definition should be expressed in the more understandable form Q = 2π(stored energy / energy loss per period), or stored energy / energy loss per radian if we want to eliminate the 2π.
• I think that in the Definitions section all 3 definitions should be given:

Damping: Q = π(resonant frequency f₀ / attenuation α) = π(time constant τ / oscillation period T₀) ...take your pick.

Bandwidth: Q = resonant frequency / bandwidth

Energy: Q = stored energy / energy loss per radian

• I think the definitions of component Q factors should be introduced in a separate section, to avoid confusing readers.

--Chetvorno^TALK 03:11, 17 January 2019 (UTC)

OK the most important is that every aspects are present, the introduction order is a matter of endless debate I am afraid. Do you mind if we add a material characterization section, with reference to piezoelectric, dielectric and ferrite materials, although in the last case the Q-factors are infrequently used because of the strong level dependence of the losses in their usual working domains? Henri BONDAR (talk) 04:31, 17 January 2019 (UTC)

The following links are examples among thousands of Q-factors used for material characterization in three different domains:

Recent article from Caltech.edu concerning dielectric ceramics: https://authors.library.caltech.edu/82778/1/s41598-017-14333-9.pdf

From journal of electronic material (2015) concerning ferrites: https://link.springer.com/article/10.1007/s11664-015-3978-z

Measuring Properties of Piezoelectric Ceramics from Sparkler manufacturer: http://www.sparklerceramics.com/pdf/sp-011-05.pdf

Henri BONDAR (talk) 12:25, 17 January 2019 (UTC)

Yes, add a section or two. Consider also the existence of Dielectric loss which duplicates a lot of Dissipation factor. Is it possible that we want to have separate articles on material Q and resonator Q? Or go the other way and merge these other articles? Or make this article a "summary style" article dispatching to other more specialized articles? I don't know. Lots of perspectives. Dicklyon (talk) 04:57, 18 January 2019 (UTC)

Good ideas, more possibilities and difficult choice. Google search for "Q factor" leads to 1.880.000 Occurrences, "Q factor" + material: 848.000, "Q factor" + component: 713.000, "Q factor" + resonator: 269.000, "Q-factor" + band-pass: 230.000. A "summary article" introducing the general concept and its various implementations is my preference. Beside I don't consider the Wikipedia article rating as "weak importance" is appropriate. Henri BONDAR (talk) 11:52, 18 January 2019 (UTC)

The general reader’s most common contact with Q, is how long the bell rings. While this is discussed, I’d like to suggest that the first figure show to decaying sinewaves of the same frequency and initial amplitude but one with a rapid decay labeled “low Q” and one with a slow decay labeled “high Q.” An interesting characteristic of a second order resonator (one L and one C) is that if a particular resonator requires n cycles to decay a certain fraction of its initial value (such as 1/2, 1/e or 1/10) then all second order resonators of the same Q will require n cycles to decay that fraction, without regard to the actual frequency of resonance. I don’t remember the relationship, but it emphasizes the unit-less nature of Q. Constant314 (talk) 21:41, 18 January 2019 (UTC)

The relationship you are thinking of is Q = π(time constant τ / oscillation period T). Or in other words, Q is equal to the number of cycles required to decay to 1/e = 0.368, multiplied by pi. That is an important equation because as you say it makes every decaying sinusoid with the same Q look the same, when normalized for frequency and amplitude. That definition, or the equivalent π(resonant frequency f₀ / attenuation α) should be included in the Definitions section. I like your idea of showing the graphs of low Q and high Q; in fact I think it could be elaborated by showing a series of graphs of increasing specific Q factors: 2, 5, 10, 20, 50, say, to illustrate the increasing persistence of the oscillations. A person can actually estimate the Q factor of a system from its oscilloscope trace if he is familiar with what they look like. --Chetvorno^TALK 00:24, 19 January 2019 (UTC)

A proposed “modern” introduction to Quality Factors

Quality factor or its abbreviation Q-factor is a concept that pervades every domain of physics were energy is stored/restored dynamically with associated measurable losses. Large Quality factor means large energy storage for small associated losses. The concept is used to characterize materials as well as components and devices. Q-factors are dimensionless quantities defined in mechanics, acoustics, electronics… as the ratio of energy stored/retrieved for a given amount of losses. Although general definitions based on energy or power ratios are available, they are various usages according to application domains. The reverse quantity is named Dissipation Factor and is defined as the amount of losses involved for a given storage amount.

You may then structure the content accordingly, perhaps using an historical introduction centered on the old idea of bandwidth and decay, but you should not forget to introduce materials Q-factors and to keep a general coherence with the DF page. Keep in mind that modern students and engineers know Q-factors as direct throughputs of Impedance Analysers, Vector Network Analysers and LCR meters without involving any reference to bandwidth or decay of resonators and any direct link with filters performance. I would also like to use the reactive power concept as done in the DF page as it leads to extremely simple formula and interpretation (when you get used with it). Henri BONDAR (talk) 08:07, 16 January 2019 (UTC)

Might work. Please note MOS:CAPS; don't capitalize Quality, Dissipation Factor, and such. I'm more used to damping factor; is dissipation factor common in some fields? Dicklyon (talk) 16:39, 16 January 2019 (UTC)

And I'd still want to emphasize the most common application to resonant systems, where the frequency is not arbitrary. Dicklyon (talk) 16:41, 16 January 2019 (UTC)

Dissipation factor/Q-factor are like reactance/admittance; alternately used according to situations. An advantage to the use of the dissipation factor is that, like loss angles, they directly add, whereas for the Q-factors the algebra is more complex. One domain where there is a clear preference for dissipation factor is the capacitor, this is probably to avoid confusions with the letter Q for the electric charge.

On my side I see Q-factors everywhere and not only to describe resonators, although I agree that it has, at least, an historical importance and is very usefull to describe "clean" resonances and anti-resonances. Modern laboratory equipment's measure Q-factors accurately using a method called "auto-balancing bridge", and Q factors measurements are detailed in service manuals without referring to the notions of resonance, bandwidth or damping. Most modern components datasheet come with associated Q-factor measurements (single value or curves). I am pretty sure that Q-factor for materials and components are much more common in recent literature than Q-factors for resonators and filters. Worse than that, the use of the Q-factor as introduced in the article is receding in article dealing with SAW filters (bandpass filters) where the standard is to use bandwidth and insertion loss values. See for instance: https://areeweb.polito.it/didattica/corsiddc/ETLCEnTO/Studmat/SAW08/SAWfilterReport-TomaszTrzcinski.pdf where Q-factor is not mentioned at all.

Finally I don't understand your reluctance to use frequency dependent quantities; what about impedance curves or transmittance curves if you want an example of a dimensionless frequency dependent quantity? Henri BONDAR (talk) 19:11, 16 January 2019 (UTC)

Q is the ratio of energy stored/retrieved for a given amount of losses per cycle. I think we need to keep the per cycle in the description. Constant314 (talk) 20:39, 17 January 2019 (UTC)

The reluctance to use frequency-dependent Q quantities stems from long familiarity with Q being just a number, not a function. Both are valid, but in my field(s), I never see Q as function of frequency, nor Q depending on an arbitrary frequency. Dicklyon (talk) 03:26, 18 January 2019 (UTC)

In the Journal of Electronic Material article you linked, for instance, the abstract says "the Q factor ... could be as high as 118.19." But this is for a material, not a resonance, so at what frequency? Later it says "a higher Q factor at frequency of 13.56 MHz could be obtained". When you read the first pages of the paper, they're not totally clear, but reading between the lines it sounds like this is the frequency that's used in their NFC application, so it's not as arbitrary or unknown as it came across in the index. Seems like a weird use. Dicklyon (talk) 03:40, 18 January 2019 (UTC)

13.553 MHz is the lowest unconditional ISM band frequency. Constant314 (talk) 03:49, 18 January 2019 (UTC)

Let's try to be clearer, for "clean" resonance or antiresonance, i.e. for resonances that are not bothered by near overtones or harmonics; the whole impedance/admittance/transfer function curves are well described by only two numbers: a central frequency and a Q-factor (or several Q-factors if several coils are involved in the equivalent lumped element circuit). For components and materials the Q factor is indeed defined and currently measured as a function of frequency (and sometimes of amplitudes levels) so that, if you use the component at a given frequency (amplitude level), for instance in a resonant circuit, you can easily compute losses if you have the appropriate datasheet Q-curves. For many components and materials only orders of magnitude are indicated and single digit Q values are provided for a reference frequency. See for instance SMD coils manufacturers datasheets: https://www.murata.com/~/media/webrenewal/support/library/catalog/products/inductor/chip/o05e.ashx p200 and above, where both single values and Q curves are provided for every component.

Note that in some cases the Q-factor frequency behavior is quite simple, for instance for a mono-layer flat air coils, for frequencies well below the self resonance, the Q is proportional to the square root of frequency (due to skin effect). Note also that, in the specific well-behaved cases that you like, measuring accurately large Q-factors values is not possible too. For instance measuring the anti-resonnance Q of a quartz crystal in its fundamental mode is not even possible as the impedance of the device is in the Giga to Tera Ohm range around that specific frequency.

The main question is: what do you want to do here, duplicate the knowledge of the years 1920 or make a page in agreement with modern developments? To address Chet concern about non expert readers, why not starting with a wide definition based on energy considerations and then developing in an historical order, starting the description with the perfect resonator, band-pass and dammping concerns and the appropriate pictures you have suggested and then progressively introducing components with impedance ratios and finally materials with reactive power ratios that are, I am sorry to insist, the every day business of any modern design engineer. Henri BONDAR (talk) 06:44, 18 January 2019 (UTC)

I agree that the Q factors of electrical components and materials should be in the article, I just think they should be in a separate section after the more widely used concept of Q factor of a resonator is explained. Similarly the intro should first introduce Q of a resonator, then Q of components and materials. Henri's proposed introduction at top is a common error often found in Wikipedia technical articles: editors generalize the lead to cover broader areas and marginal cases, and abstract it to the point that it is incomprehensible to ordinary readers. This article is not an engineering textbook, it is a general encyclopedia article, and "it is particularly important for the lead section to be understandable to a broad readership" (WP:EXPLAINLEAD). The above vague, amorphous introduction does not even mention rate of change with time, loss rate.

While the Q factor of materials is of importance to some specialists: materials scientists, microwave engineers, and acoustic design engineers, the concept of the Q of an oscillating system is a much more basic idea used throughout mechanical engineering, electrical engineering, physics, control systems theory, structural engineering, acoustics, quantum mechanics, molecular chemistry, particle physics, laser optics and signal processing and is taught in every secondary school physics course.

I feel the introduction should first define and introduce the Q of a resonator as it does now (which is by far the most common way it is introduced [9], [10], [11], [12], [13], [14], [15]), then in the 2nd or 3rd paragraph could introduce the more general concept of Q factor as a ratio of "stored energy / loss rate" that can be applied to individual components and materials. --Chetvorno^TALK 23:42, 18 January 2019 (UTC)

There is a large amount of WP:NPOV here (including mine probably), from a reduced number of participants (other opinions welcomed). I agree that, for the common reader, the engineer point of view is not always easy to grasp at first sight, however I cannot leave the sentence: "The above vague, amorphous introduction does not even mention rate of change with time, loss rate " unanswered. As already explained, the time decay of oscillators is a consequence of the presence of losses not its core aspect. ' It is exactly like if nuclear reactions were being defined though their half-life time constant instead of the underlying instability of the nucleus. Will you agree to see dissipation factor or dielectric loss (see the pages) defined through the time constant of the discharge of the capacitor? ' Henri BONDAR (talk) 05:52, 19 January 2019 (UTC)

I spent the last four years characterizing high-Q piezoelectric resonators, more accurately the fundamental thickness mode for non energy trapped devices (devices where oscillation occurs in the whole volume instead of very small areas oscillating surrounded by evanescent fields for energy trapped devices), I may explain, if you like, why two or three point measurements (3dB, 6dB or whatever) are scarcely used in practice and replaced by multi-point measurements and least square fitting procedures. The point is, I cannot be suspected to deny the importance of Q-factors in resonator analysis. Besides I have absolutely no problem with the dissipation factor and dielectric loss pages. Henri BONDAR (talk) 15:43, 19 January 2019 (UTC)

Both the above sections are WP:TLDR, even the opening of this one which fails to succintly state its case. The bottom line for me at the moment Henri, is that I am nowhere in that wall of text seeing you support your approach with reliable sources that so treat Q. That is our yardstick on Wikipedia—what is the normal way for sources to explain Q. Until that happens, there can be no question of a major revision to the article. SpinningSpark 20:14, 19 January 2019 (UTC)

Agreed, way too long and its my fault, but what about the internal coherence between dissipation factor and Q factor that are two sides of the same thing? Henri BONDAR (talk) 21:45, 19 January 2019 (UTC)

Peak energy or total energy?

Introduction of the article: "It is defined as the ratio of the peak energy stored in the resonator in a cycle of oscillation to the energy lost per radian of the cycle.[1] " and later in the article: "Physically speaking, Q is 2π times the ratio of the total energy stored and the energy lost in a single cycle, or equivalently, the ratio of the stored energy to the energy dissipated over one radian of the oscillation.[12]"

The second explanation is much more clear. Also "peak energy" would suggest that only the energy of the highest amplitude cycle, or even he peak of such a cycle is only considered.

If someone knows what was really meant, please edit to clarify. — Preceding unsigned comment added by 88.219.179.67 (talk) 08:25, 4 December 2020 (UTC)

Because Q is a property of linear circuits, these definitions are equivalent. Q is equal to 2π times the ratio of stored energy at the beginning of a cycle to the energy loss during the cycle, for any cycle in the waveform. --Chetvorno^TALK 10:03, 4 December 2020 (UTC)

Just elaborating, it is the total peak energy over the cycle. In the usual case where the energy is being dissipated, the peak energy occurs at the beginning of the cycle. You can start the cycle at any point so long as you use the total energy in all the energy storing components. In a simple parallel LC circuit, that means the energy in the capacitor plus the energy in the inductor. In an underdamped situation (i.e. there is ringing), at some point in the cycle of the simple LC, all the energy will be in the capacitor and at some other point all the energy will bein the inductor. You can start the cycle at either of those points or you can use an arbitrary point in the cycle just so long as you use all the energy. In a more complicated resonant circuit, there may be no point at which all the energy is in a single component. Constant314 (talk) 21:29, 4 December 2020 (UTC)

That ref [12] definition that measures energy loss over a whole cycle is much less accurate at low Q than the one based on a radian is; I'd delete it. In terms of ratios of rate of energy loss to rate of oscillation, to get it right down to low Q you need to use the exponential decay time constant $\tau$ or rate $\alpha$, not the total loss over a radian or a cycle; and for the rate of oscillation, you need to use the "natural frequency" $\omega _{N}$, which is a bit higher than the "oscillation frequency", esp. at low Q (near 0.5) where the oscillation frequency goes to zero. See my book; $\zeta =1/(\omega _{N}\tau )=\alpha /\omega _{N}$; $Q=1/(2\zeta )=\omega _{N}\tau /2=\omega _{N}/(2\alpha ))$ Dicklyon (talk) 00:47, 5 December 2020 (UTC)

I've always taken 2π times the ratio of the total energy stored and the energy lost in a single cycle as the definition and that everything else uses Q in an approximate way. Constant314 (talk) 01:01, 5 December 2020 (UTC)

Not so. And ah, crap, I see it was I who added that ref in 2007. Dicklyon (talk) 01:19, 5 December 2020 (UTC)

Consider Q = 2π; would all the energy be lost in one cycle? No, the energy is never all lost. Dicklyon (talk) 01:31, 5 December 2020 (UTC)

I see that. It would imply that the minimum Q based on energy per cycle was 2π but you do see instance of Q < 2π. Constant314 (talk) 02:10, 5 December 2020 (UTC)

I think the original definition from this edit might be right, if be "number of oscillations" one means at natural frequency (so it could even apply to critically damped and overdamped systems). Dicklyon (talk) 01:34, 5 December 2020 (UTC)

You have made me pull out my old notes. I see that I do have $Q=\omega _{N}/(2\alpha ))$ but it only applies to a simple harmonic oscilator, that is when there are only two energy storage devices like and L and a C, or a spring and a mass. But when there are more elements, the meaning of $\alpha$ is vague, maybe undefined even, but the definition based on energy stored and dissipated still works. I guess that only applies if there are cycles. Constant314 (talk) 01:36, 5 December 2020 (UTC)

I think Q is well defined only for second-order physical systems. For more general filters, different parts of the system can have different rates of energy loss, and the initial energies in those parts, as well as the cycle rate, depend on initial conditions. This is where the various approximate definitions come in, like center frequency divided by 3 dB bandwidth. Dicklyon (talk) 18:46, 5 December 2020 (UTC)

Yeah, each pole has its own Q. I think the Q's are relatively independent only when the critical frequencies are well separated. Most elementary applications are to harmonic oscillators with a single resonant frequency, so I would suggest that systems with multiple poles be treated in a separate section. I have no objection to the radian definition, but most elementary readers don't know what a radian is so it would be nice to keep the cycle definition as an approximate one. Also, why are the energy and power definitions in a section titled "Coils and condensers"? I believe they apply to any harmonic oscillator. --Chetvorno^TALK 22:47, 5 December 2020 (UTC)

By the way, another definition in the article which is useless in practice is:

"Q factor is approximately the number of oscillations required for a freely oscillating system's energy to fall off to e^−2π, or about ​1⁄535 or 0.2%, of its original energy. This means the amplitude falls off to approximately e^−π or 4% of its original amplitude."

Yes, this is found in a number of textbooks. But by the time the amplitude has fallen to 4% the waveform is far into its exponential tail, so unless the amplitude (voltage) measurements are extremely precise, any count of the number oscillations is going to be inaccurate enough to be useless. A better definition is that Q is π times the number of oscillations required for the amplitude response to fall to $1/e=$ 36.8%. --Chetvorno^TALK 22:47, 5 December 2020 (UTC)

Back before network analyzers were cheap, I used the effect to measure Q of LC resonators in a factory test setup.Constant314 (talk) 00:03, 6 December 2020 (UTC)

Chet, your proposed alternate definition is good if Q is high, but it limits out sooner unless you're pretty good at counting fractional oscillation cycles. It's easier to conceptualize the 4% amplitude, perhaps. Or say it's the number of half cycles to fall to 21% amplitude as a compromise. I have no idea which if any of these ideas are in books. Dicklyon (talk) 01:55, 6 December 2020 (UTC)

In your factory test you actually counted the number of cycles to reach 4% amplitude? Wow. How many significant figures for Q do you think you ended up with? --Chetvorno^TALK 19:41, 6 December 2020 (UTC)

The threshold doesn't have to be 4%. It scales. We drove the resonators up to a fixed amplitude and then cut off the drive and then counted the cycles that exceeded a simple threshold as they decayed. Just a comparator and a couple of 4-bit counters. The nice thing about it was that it is independent of the actual resonant frequency. The same fixture could be used over a 3:1 frequency range.Constant314 (talk) 20:17, 6 December 2020 (UTC)

Yeah you can use any threshold if you have a calculator, I'm just saying that the 4% threshold in the article's procedure is 3.2 time constants out. But you're right, it isn't that much more inaccurate than my method. If you can measure amplitude to 1% of the initial value (the limit of old-school oscilloscopes) and fractions of a cycle perfectly, the error in Q with a 4% threshold is about 9%, while with a 36.8% threshold is 3%. --Chetvorno^TALK 20:40, 6 December 2020 (UTC)

This was circa 1975. I think we used a threshold of about 37%.Constant314 (talk) 21:14, 6 December 2020 (UTC)

@Spinningspark: The lead definition is not awful, but it was inserted in front of a ref that it didn't come from, in this edit. I took out the ref, as I didn't see anything useful in it, and called for a citation. Dicklyon (talk) 02:32, 6 December 2020 (UTC)

I found and added an eBook ref for that def. It discusses both peak energy (for the case of an inductor alone) and stored energy in a resonator (constant throughout the cycle it says, neglecting the dissipation). Dicklyon (talk) 02:45, 6 December 2020 (UTC)

Why is bandwidth here?

I came here from a reddit post: https://www.reddit.com/r/explainlikeimfive/comments/d8j17p/eli5_what_is_q_factor_measuring/

OP says "I feel like I may need a PhD to start understanding what's being described there." and this DEFINITELY not should be the case for such a simple topic.

So sorry to say, but I think the article is very badly structured. While the text speaks ONLY about oszillation and damping, there is suddenly a picture of something with a bandwidth next to it. I think that the physical interpretation: "Physically speaking, Q is 2π times the ratio of the total energy stored divided by the energy lost in a single cycle or equivalently the ratio of the stored energy to the energy dissipated over one radian of the oscillation." should be one of the first sentences on the page.

(edit: Okay, it kinda is, but I think that the current explanation about "undampedness" could live with the added precission of "ratio of the total energy stored divided by the energy lost in a single cycle". Not my main point anyway)

On a meta level, I think that the article was written be an engineer. I studied physics, and I have no idea why the whole bandwidth stuff suddenly appears. An oszillator has ONE frequency after all? Unfortunately it will be probably frowned upon if I just delete half of the article for not being relevant, so please someone rewrite it. My suggestion would be to remove the whole bandwidth thing and the low/high passes, or at least put it on the bottom of the article as an extra part.

(Sorry new here, no idea where to put it, so I put it on top)

Hakunamatator (talk) 08:56, 24 September 2019 (UTC)

This is a fundamental property of all harmonic oscillators that is usually taught in introductory college physics courses. Here are some sources: [16], [17], [18] The fact that the less damping a resonator has, the narrower it's resonance curve, is one of the most basic properties of resonance, used throughout engineering and physics. I do think the article needs a more rigorous derivation of it. --Chetvorno^TALK 11:12, 4 December 2020 (UTC)

I tried to do a good job of this in chapter 8 "Resonators" of my book, in case anyone wants to cobble from there. Dicklyon (talk) 04:29, 7 December 2020 (UTC)

What a fascinating book! Incredibly comprehensive and authoritative. I had no idea so many different mathematical approaches had been applied to modeling the vocal tract and auditory apparatus. Very kind of you to let us look at it. The chapter on Q and resonators is great. If you don't mind I am going to cite it in the article. --Chetvorno^TALK 22:45, 8 December 2020 (UTC)

It looks to me like at low Q values, say below 3, the whole relation between Q, resonance width, and bandwidth breaks down, since the 3dB resonance width begins to be distorted by the other poles and zeros of the system. --Chetvorno^TALK 22:45, 8 December 2020 (UTC)

Of course I'd be pleased to be cited. The relations don't quite break down – they're just not as simple as the usual high-Q approximations. Dicklyon (talk) 05:08, 9 December 2020 (UTC)