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jbjb
11-05-2009, 04:54 PM
I read that the system Q is 0.3 but how does this number tally with the damping settings where Hi = Q 0.5, mid = Q 0.7 and low = Q 1.1 ?

If I have my damping on Hi, is the Q at 0.5 or 0.3?

RythmikAudio
11-09-2009, 06:50 PM
I read that the system Q is 0.3 but how does this number tally with the damping settings where Hi = Q 0.5, mid = Q 0.7 and low = Q 1.1 ?

If I have my damping on Hi, is the Q at 0.5 or 0.3?

The system Q value of 0.3 is the system intrinsic Q value. The Q value associated with damping setting is the time domain Q value that controls the amount of ringing in the reproduced signal. The best way to understand this difference is to examine the case where the intrinsic Q value is 0.3, but the time domain Q value is 0.7. What is the output of a system with intrinsic Q value of 0.3? It is very fast and quick and no ringing. Now since we would like to "emulate" the time domain output of Q=0.7, which has a slight ringing. There is a filter circuit (called pre-emphasis circuit) added in front of the system in order to generate an system output signal with ringing like Q=0.7. What this circuit does is to produce a "biased" input signal with ringing and feed that to the system input (with Q value of 0.3) to produce a final output with ringing. That is how we produce the those 3 different damping in timing domain. It is very easy to design the pre-emphasis circuit to reproduce signal with Q of say 0.5 (no ringing), 0.7(small ringing), and 1.1 (big ringing) in one circuit. The ringing implemented in this fashion is actually the most stable as will be explained later.

Now, we can take the opposite case, where the intrinsic Q value is 0.9 and we would like to reproduce the output such that it does not have any ringing. Since the intrinsic system already have ringing, the pre-emphasis circuit needs to generate a system input signal to cancel the ringing of 0.9 at the output. It is more difficult if we consider the real world scenario that the intrinsic Q value can change over time. For instance, let us the first week the customers receive a subwoofer, the system Q value is 0.9. Assume the pre-emphasis is a perfect cancellation. However, as he plays more and voice coil gets hotter, the intrinsic Q value changes to let us say 1.0. Now, we have a mixture of two high Q ringing at the output: one is from the intrinsic Q ,which is now 1.0 and there is no pre-emphasis to cancel that, and the other is the Q of pre-emphais circuit which still stays at 0.9 (because eletronic circuit has much less variability than the subwoofer itself) and it passes the system without being cancelled.

So the best strategy is to keep intrinsic Q as low as possible so that it does not have any ringing at all. It is far easier to add ringing if we ever want it.

So even though in our servo sub, we can have 3 damping settings, the system intrinsic Q value is always kept at 0.3. So the question naturally arises: why not offering a damping setting of 0.3 so that there is no pre-emphasis circuit. The reason is Q value of 0.3 attenuates the bass too gradually and the sound becomes lean and the excursion requirement at the bottom end becomes excessively large. A Q value of 0.3 means the roll-off starts at 6db/oct and gradually changes to 12db/oct. So the price to pay is the perception of quantity in bass energy. So far it has proven to be a commercially viable setting.

Even though Q=0.3 is considered to be over-damped, it is actually a better intrinsic Q value when we factor in the real world situation where actual Q value for sure will change due to nonlinearity, time, or any other reason. Q=0.5 is not really the best if we consider the potential of drift. It can drift from 0.5 to 0.6 over time. Of course one can argue it can also drift from 0.5 back to 0.4 but in reality it is more likely the former case, not the latter case. For instance, if the magnet lose strength, that actually increases Q value, it is very hard to decrease Q value. So with Q=0.3, there is a lot of room for the drift before it ever becomes critically damped. There is another reason of choosing Q value of 0.3. The large damping associated with Q=0.3 means the system can act very fast. If we think of instrinsic system as a black box system, the intrinsic Q is like how fast it can respond internally. It is like acting. You can pretend you are slow even though internally you are fast. That just makes keeping up the signal easier.

jbjb
11-09-2009, 06:55 PM
Thanks for the detailed explanation Brian!