Some basic questions about Q

[wigginjs]

Sorry, I'm quite sure this has been covered before, but I could find the answers I was looking for in a search (both the forum and a google search).

Can someone give me a strong definition of "Q"? When people say this are they generally refering to Qtc? Also, equations that relate Qtc to Qts, Qms, Qes, etc. I know it is a ratio of energy stored to energy disipated, but I was hoping someone could explain it in specific context to loudspeakers and how it is useful...

[kelticwizard]

Well, about the only thing I actually know about Q is in relation to loudspeakers, so maybe this is a good conversation.

Qts=the speaker's rating outside any enclosure

Qtc=the total Q of a closed box loudspeaker system. Unless the box you are using is MUCH larger than the speaker's Vas, the Qtc will be higher than Qtc.

To see the the relationship between Qts, (speaker unenclosed), and Qtc, (speaker in a closed box), use the following equation:

[kelticwizard]

If you have both Qes, (electrical Q), and Qms, (mechanical Q), you can find Qts by the following formula:

Qts = (Qes X Qms) / (Qes + Qms)

Do I have an explanation as to what Qes actually is, or what Qms actually is? No.

I can tell you that if you put a resistor or reactance, (ohms from a capacitor or inductor), in series with a speaker, the Qes goes up, and the Qts along with it. However, don't ask me what they actually are. I don't know.

[kelticwizard]

Qts and Qtc are related to where the speaker output is in relation to the midband.

Suppose you have a speaker that is rated 88 dB @ 1 M/1 Watt. We take the frequency of response, which is called Fs for an unenclosed speaker, and Fc for a speaker in a closed box.

What will the SPL be at one watt at the resonance frequency?

SPL = 20 Log Q

Example: And 88 db @ 1M/1W speaker has a Q of 0.5. The resonance frequency is 40 Hz. What will be the SPL at 40 Hz?

20 Log Q = 20 Log 0.5 = minus 6.02 dB = 81.98 dB.

Or

An 88 dB @1W/1M has a Q of 0.3 and a resonant frequency orf 30 Hz. What is the SPL at 30 Hz?

20 Log Q = 20 Log 0.3 = minus 10.46 = 77.54 dB

This formula applies both for Qts, (unenclosed speaker) and Qtc, (speaker in a closed box).

[Ron E]

Q is the ratio of energy stored to energy dissipated - if you really understood that you woudn't ask the question. This means it is a measure of the strength of resonance. The louspeaker stores energy in its suspension stiffness and in its mass. IF you make a louspeaker stiffer or heavier, Stored energy (thus Q) goes up, and vice versa.

The dissipated energy comes from two factors: 1) there are friction losses internally in the suspension of the speaker and in the transfer of mechanical to acoustic energy, this is quantified as Rms, the higher Rms is, the lower the Qms of the speaker. 2) The movement of the voice coil in the magnetic field generates a current that generates an electrical fied that opposes the coil's own motion. This is electrical damping Qes - it depends on three things, Magnetic field strength, length of wire in the gap, and inversely on the resistance of the coil.

#2 above is by far the most dominant in most speakers, and

Qms = 2*pi*Fs*Mt/Rms
Qes = 2*pi*Fs*Mt*Re/(Bl)^2

Mt is moving mass, Re is voice coil DC resistance, Bl is the product of magnetic strength and length of wire in the magnetic gap.

What is important in driver design is Qts = Qes*Qms/(Qes+Qms)

Qts essentially just helps you figure out box size. Lower Q drivers wil go in a smaller box relative to Vas, but will have higher cutoffs relative to Fs, and higher Q drivers will require larger boxes and have cutoffs closer to Fs.

[wigginjs]

What is the most desirable value of Q? For accuracy, is it better to be above 0.5 or below it?

[Mr Evil]

There is no single most desireable value for Q. Different values have give different qualities. Q=0.5 is critically damped. This means that there will be no overshoot on transients. It seems to be a popular value at the moment. Q=0.71 gives a maximally flat frequency response, which is nice. Q~=1 has been shown to be subjectively the best sounding to a lot of people, due to the peak at resonance which can make bass sound stronger.

Depending on what you consider most important for accuracy, Q between 0.5 and 0.71 would be most accurate.

[kelticwizard]

This thread shows the response curves for various values of Qts or Qtc-makes no difference.
Response Shapes of Various Values of Qts and Qtc



This chart shows the step respnse at resonance for various values of Qts or Qtc.http://www.diyaudio.com/forums/attac...amp=1038550363

The greater the output at Fs or Fc, the greater the "overshoot". It is up to you to make the tradeoff.

All practical Qtc for closed box are superior to all practical alignments for ported boxes, in terms of "overhoot". But yet, ported boxes do sound good. So take that into account when making your decision-these are all pretty smooth responses, from Q = 1 on down.

[Ron E]

Originally posted by m0tion
What is the most desirable value of Q? For accuracy, is it better to be above 0.5 or below it?

There is no magic number for Qtc - the Q when the driver is mounted in a closed box. Qtc = Qts*sqrt((Vas/Vb+1)

You are not going to be able to listen to a speaker and say: "That is a Qtc of 0.5, or that is a Qtc of 1", or whatever. Qtc's less than 0.5 are overdamped and not very useful for speakers. Qtc anywhere between 0.5 and 1+ can sound accurate. I had a friend with a dual 12" car sub that had a Qtc of 1.3 or so and he and all his friends said it sounded tight and fast. It sounded fine. I had another friend with 4-6.5" woofers in a fairly big car box that had a Qtc of 0.5 or so ( in the same type of car) and I can tell you it sounded no better. I have had similar experiences with subs in homes, but these are the most dramatic examples.

Qtc is a small thing. Especially in the home, room acoustics and placement are much bigger factors.