Qms, Qes, and Qts

[Jason]

Couldn't decide which forum to post this, but since I'm specifically asking about sub drivers, I figured here..

Ok, I'm trying to gain a better understanding about the Q of subwoofers. I think I understand the Qms, as that is a measurement of the dampening ability of the transducer from a mechanical standpoint. Spider/surround compliance and mass/weight of the cone mainly I guess??

And Qts is the total combined of (Qms*Qes)/(Qms+Qes), that is basically a combined system Q rating, right?

Where I'm having a brain block is the Qes. How does a transducer have an electrical Q? I think of Q as the ability of the cone to stop, or its ability to not store kinetic energy and continue moving after the signal is no longer present. As I've read, Qes is a measurement of the transducers control from it's electrical system...but in going with my 'vision' that Q measures how fast the cone will stop, as in stopping with an absence of signal, how is there an electrical Q. Without signal, the electromagnet of the voice coil doesn't exist..nothing to react to the permanent magnet. What am I missing??

I'm obviously not looking at this properly, or I'm sure the light bulb would go off. :idea:

[Jason]

I guess there's nobody as nerdy as me....

I figured dweekie or someone else would straighten me out :dizzy:

[Jason]

Hmm, that's a little different than what I had read. I thought all the Q measurements had to do with the drivers dampening ability.

I don't have a specific reason to want this info, other than I'm a nerd at heart and love this stuff.

[Mark Seaton]

Couldn't decide which forum to post this, but since I'm specifically asking about sub drivers, I figured here..

Ok, I'm trying to gain a better understanding about the Q of subwoofers. I think I understand the Qms, as that is a measurement of the dampening ability of the transducer from a mechanical standpoint. Spider/surround compliance and mass/weight of the cone mainly I guess??

And Qts is the total combined of (Qms*Qes)/(Qms+Qes), that is basically a combined system Q rating, right?

Where I'm having a brain block is the Qes. How does a transducer have an electrical Q? I think of Q as the ability of the cone to stop, or its ability to not store kinetic energy and continue moving after the signal is no longer present. As I've read, Qes is a measurement of the transducers control from it's electrical system...but in going with my 'vision' that Q measures how fast the cone will stop, as in stopping with an absence of signal, how is there an electrical Q. Without signal, the electromagnet of the voice coil doesn't exist..nothing to react to the permanent magnet. What am I missing??

I'm obviously not looking at this properly, or I'm sure the light bulb would go off. :idea:

Q is a measure of resonance strength and damping of that resonance, depending on perspective. Many love to chase what they consider an ideal Q, and some designers swear by it. I take a more holistic/systemic approach. The end combined result is what matters. The parts have to not overly misbehave in the context you are using them, but many overlook very workable solutions for the end result when chasing some alleged ideal in one detail.

As adobo suggested, check out the Loudspeaker Design Cookbook, or even www.diysubwoofers.org and many other DIY oriented websites.

Getting back to the question, Q basically relates to damping at the resonance of the driver. The Qts is the combined mechanical and electrical damping which contributes significantly to the frequency response shape around the low frequency corner of a given driver in a given box. Qes is the contribution of the electrical damping. You might better conceptualize this as how much braking of driver motion there is when you short the VC terminals. Very low Qes means the driver gets much stiffer when you short the VC, as the electromagnetic force provides a lot of damping. Qms is similar, where this is the damping of the surround and spider on the resonance of the driver.

Another important understanding is that if either the Qms or Qes is MUCH higher than the other, Qts approaches the smaller one. As such, Qts can NEVER be higher than Qes or Qms, as Qts is the combined damping of the two. High Q contributes little to the damping, so as an example, you could hypothetically have a Qms of 20 and a Qes of 0.15, where the driver Qts would then be effectively 0.15. In reality it is some fraction smaller than Qes, and if you then lowered only Qms you would see Qts start to drop further, but it wouldn't round to 0.14 until Qms was ~4.00.

While some will disagree and hold fast to the importance of Q of the driver, I design with the interest of having the right damping for the enclosure and application. Of course I only look at Q as a quick approximation when I can't immediately see the parameters that really matter. The reality is that these "Q"s are not tangible things you can change singularly. They are a lumped parameter indicating the relative balance between the physical parameters of a driver. When it comes to the low frequency sensitivity and frequency response of a driver (separate from max output), you can only change the cone size (Sd), stiffness of the suspension (Cms), mass of the cone, VC etc (Mmd), and the electromagnetic strength of the motor (BL^2/Re). Those 5 values define all of the other Thiele-Small parameters. Add definitions of Le and Xmax and you have the small signal, low frequency behavior of a driver covered.

[Jason]

You might better conceptualize this as how much braking of driver motion there is when you short the VC terminals. Very low Qes means the driver gets much stiffer when you short the VC, as the electromagnetic force provides a lot of damping. .

Hi Mark....thanks for chiming in. I doubt I'd find a better source of knowledge than you on this...

About the above...How would there be any electrical braking energy if we short the VC? There wouldn't be any magnetic field in the VC to react to the permanent magnet. I'm still a little confused. I'm curious as to where electrical dampening happens to stop cone motion when there is no signal, ie inbetween fast kick drum tracks.

I can appreciate the big picture viewpoint of yours. To me it's obvious that a sealed enclosure would create an air spring that would increase the dampening. Conversely I guess an IB designs end Q would be equal to the actual drivers Qts?

I'll have to look up that book, thanks guys

[Mark Seaton]

Hi Mark....thanks for chiming in. I doubt I'd find a better source of knowledge than you on this...

About the above...How would there be any electrical braking energy if we short the VC? There wouldn't be any magnetic field in the VC to react to the permanent magnet. I'm still a little confused. I'm curious as to where electrical dampening happens to stop cone motion when there is no signal, ie inbetween fast kick drum tracks.

Take any speaker you have around that is easy to move with finger pressure on the cone and short the terminals (with the amp disconnected!). The driver will be damped much more. This goes back to basics of currents and wires in magnetic fields and can be reviewed in various speaker books as well as basic physics books usually under topics of magnets & motors. Short explanation is that a wire moving through a fixed magnetic field (VC inside the magnetic gap) creates Voltage and current. If you short the VC terminals, the Voltage is small, and current flows through the coil... creating a force opposite of it's motion. In effect, the Qes is inversely related to how much the shorted coil resists motion in the gap.

Turning to the case of a quiet passage after a loud passage, just as the amplifier sends Voltage to the speaker, it can dictate zero Voltage to the best of its ability. Amplifier damping factor basically tells you how well the amplifier can hold the terminals of the voice coil to zero Volts. This means the cone of a speaker will be more damped when an amplifier is turned on, which can be readily observed. The lower the Qes of the driver, the greater this damping will be for a given amplifier.

While many look to various damping values to predict the responsiveness of a woofer, many love the performance of amplifiers with very low damping factors like tube amplifiers. In the end it is the behavior of the entire connected system. Too much electrical damping often means too little bass or very non-flat response. As usual, getting the right balance which best meets your goals gives the best result.

I can appreciate the big picture viewpoint of yours. To me it's obvious that a sealed enclosure would create an air spring that would increase the dampening. Conversely I guess an IB designs end Q would be equal to the actual drivers Qts?

I'll have to look up that book, thanks guys

Actually, the Qb always raises above Qts in a sealed box. Don't confuse damping for stiffness. A spring can require more force to move but have less damping of the resonance. You are correct that for all practical purposes the Q of an IB is that of the driver's Qts.

[Jason]

Take any speaker you have around that is easy to move with finger pressure on the cone and short the terminals (with the amp disconnected!). The driver will be damped much more. This goes back to basics of currents and wires in magnetic fields and can be reviewed in various speaker books as well as basic physics books usually under topics of magnets & motors. Short explanation is that a wire moving through a fixed magnetic field (VC inside the magnetic gap) creates Voltage and current. If you short the VC terminals, the Voltage is small, and current flows through the coil... creating a force opposite of it's motion. In effect, the Qes is inversely related to how much the shorted coil resists motion in the gap.

I wasn't thinking about how the coil moving through the magnet created current. I was just thinking about how there wasn't a magnetic charge on the coil. OK thanks, this works in my head now.

Turning to the case of a quiet passage after a loud passage, just as the amplifier sends Voltage to the speaker, it can dictate zero Voltage to the best of its ability. Amplifier damping factor basically tells you how well the amplifier can hold the terminals of the voice coil to zero Volts. This means the cone of a speaker will be more damped when an amplifier is turned on, which can be readily observed. The lower the Qes of the driver, the greater this damping will be for a given amplifier.

While many look to various damping values to predict the responsiveness of a woofer, many love the performance of amplifiers with very low damping factors like tube amplifiers. In the end it is the behavior of the entire connected system. Too much electrical damping often means too little bass or very non-flat response. As usual, getting the right balance which best meets your goals gives the best result.

I was going to ask about this before, but I didn't really know if it fit in with what I was talking about. I read a little about global negative feedback and all, and it seems like this is a bandaid to a certain extent. From what I read, with a well designed amp, low dampening is fine

Actually, the Qb always raises above Qts in a sealed box. Don't confuse damping for stiffness. A spring can require more force to move but have less damping of the resonance.

So the 'air spring' effect can contribute to ringing at the resonance?

You are correct that for all practical purposes the Q of an IB is that of the driver's Qts.

At least I got that one right :woo:

Thanks alot for the info