There are better, half way more understandable ways to get to these parameters. Especially those taken from the impedance curve.
Because using electrical parameters in the equations of mechanical parameters and vice versa doesn't untangle the mistery for us.
The higher Fs, the higher Qes. So you cannot say that the speaker with Qes of 0.6 is borderline weak while the speaker with Qes of 0.3 is strong, unless Fs is looked at. It's so much interconnected.
Because using electrical parameters in the equations of mechanical parameters and vice versa doesn't untangle the mistery for us.
The higher Fs, the higher Qes. So you cannot say that the speaker with Qes of 0.6 is borderline weak while the speaker with Qes of 0.3 is strong, unless Fs is looked at. It's so much interconnected.
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Oh, I had my rodeo with that one too. People claiming based on these simulations that High Le drivers are less sensitive and less efficient. So I took the box with my B&C 21DS115 to the colleague with more pro measurement tools. My box simulated hair close to the lossy Le functions DISABLED, and was far off from the predicted FR with these functions enabled.
Indeed things are very complex, and some of these still cannot be simulated.
The real world truth also is, that high motor force drivers have tighter suspension more often than not. So the efficiency is lost there too. As I have zero mechanical failures on my speakers, I often opt-out from B&C speakers choice, because their suspensions are tighter, and more force is spent on these. Real measurements AND klippel data with some more math support each other in that claim.
Indeed things are very complex, and some of these still cannot be simulated.
The real world truth also is, that high motor force drivers have tighter suspension more often than not. So the efficiency is lost there too. As I have zero mechanical failures on my speakers, I often opt-out from B&C speakers choice, because their suspensions are tighter, and more force is spent on these. Real measurements AND klippel data with some more math support each other in that claim.
The series of responses in your graph look same as if you took a woofer and then started to add series resistance to it, the resonance sticks out while everything else attenuates. And the explanation is the same.
If you manipulated just the Bl, then all the other parameters of system in the simulator are the same, like damping. Damping is combination of multiple things and electrical damping is one with low output voltage sources (basically a short between driver terminals), like simulators have as well.
As you increase Bl what you see is electrical damping increases, basically reduces system Q.
When you look at damping from the systems theory point of view, it turns out that this is local degenerative feedback in the driver.
To explain,
the terminal voltage on a driver at any given moment in time is Ut = Us + Ud.
Us is the static voltage, it simple is the momentary current times the static voice-coil impedance (impedance when measured with a blocked voice coil).
Ud is the dynamic voltage aka Back-EMF, which is proportional to momentary cone velocity.
When Ud is much larger than Us, so that Ut = Ud, -- like at resonance, where current is lowest -- then the amp voltage sort of impresses a constant velocity profile on the driver, basically velocity-based strong motional feedback.
That's why Q goes down and output is lowered around resonance vs away from it when BL is increased.
When we are away from Fs in either direction, Ud drops naturally (Ud basically has a bandpass function peaking at Fs) and Us quickly becomes dominant, reducing feedback.
When BL is increased (or Re and Le reduced, as it's basically (BL)²/Re what defines feedback and Qes accordingly), then Ud is becoming greater vs Us which mostly affects behavior around resonance. Also, general efficiency is increased as more force is impressed with the same current and same losses. I see it basically as a coincidence that the output at resonance happens to be decreased via more feedback by the same amount it goes up efficiency-wise, so net zero.
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Great! It took some imaginarion of imaginary spring. Once the movement is "done" to excite the spring resonance, it basically doesn't matter by how strong force it is done, because force here does not really fully represent how far will the cone travel. If ever so, then the spring will come back in equally opposite force to null it out. Now only looser spring can allow for further distance travelled.
I got it on the math part too now, it is just harder for such equation to click. Hmm. That's a mind*uck, seeing that in some mode, it almost doesn't matter how strong the motor is to drive the resonance. Funny thing is that I kind of knew that. As one preferably wants lower Qms to drive the driver with authority, not letting it swing by itself. Amplifier can provide some some additional braking of course, but this cannot be ignored. It feels like wandering in an unknown part of town, suddenly appearing in place I know. "Oh! So this is where it leads to!". Connecting bits and pieces. Knowledge CAN be surprisingly selective.
So the high motor force high stifness drivers like many B&C speakers drivers linearize this behavior between driving and ringing. The price is not low though. Also my approach basically lets the speaker ring more. The advantage of higher efficiency is to my own detriment.
Then comes the subjective part. I was happy with the loose LF21N551, while my colleague did not like sound of it compared to well damped 21DS115. I heard nothing. If ever noticable, it was completely negligible to my ears.
Oof, that will be some heavy head today, to make something out of it.
I got it on the math part too now, it is just harder for such equation to click. Hmm. That's a mind*uck, seeing that in some mode, it almost doesn't matter how strong the motor is to drive the resonance. Funny thing is that I kind of knew that. As one preferably wants lower Qms to drive the driver with authority, not letting it swing by itself. Amplifier can provide some some additional braking of course, but this cannot be ignored. It feels like wandering in an unknown part of town, suddenly appearing in place I know. "Oh! So this is where it leads to!". Connecting bits and pieces. Knowledge CAN be surprisingly selective.
So the high motor force high stifness drivers like many B&C speakers drivers linearize this behavior between driving and ringing. The price is not low though. Also my approach basically lets the speaker ring more. The advantage of higher efficiency is to my own detriment.
Then comes the subjective part. I was happy with the loose LF21N551, while my colleague did not like sound of it compared to well damped 21DS115. I heard nothing. If ever noticable, it was completely negligible to my ears.
Oof, that will be some heavy head today, to make something out of it.
I have sealed box with Q of 0.806 (recommended by Alpine ) with Alpine SWR 1542D 15" at 750W RMS. I found out that it's not loud enough below 35 Hz and I don't even listen very loud. 100dB is too loud for me. If I ever build another sealed I am aiming for 0.707 or lower and a lot more power.
A point to consider: the stronger a driver is, the better it takes massive EQ to bump up the response to a, say Q=0.71 target when the natural response is quite over-damped with a Qb of 0.2 or so, coming from a hypothetical brutally strong driver ;-) Preferably using a big class-D amp which can handle the voltages and reactive load gracefully.
But we cannot shift the limits of the driver, of course. And the stronger feedback can make the driver potentially more unstable under certain conditions once nonlinearities start to rise. No free lunch. Natural Q of any sealed box works best around 0.5 to 1 for stable and predictable behavior.