Lowering Fs, trade-offs?

That’s mean decreasing the impedance level at the Fs frequency is preferred. The reason is the flatter the impedance curve, less impedance spike at the Fs frequency, the more it’s desired. Am I correct?
Yes, a flatter impedance curve can have some benefits when it comes to crossover filter design. However, one needs to keep in mind the desired acoustic target response.

Consider the following 2-inch (50mm) midrange driver, the Visaton G 50 FFL - 8 ohm unit. It has a resonance frequency of 455Hz, and its low-frequency rolloff appears to follow a 2nd-order response with a Qtc = 0.71.

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A quickly-created VituixCAD model of the electrical impedance of this driver is shown below.

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The SPL response model is shown below. It represents the main features of the low-frequency and high-frequency response, but omits the wiggles in the passband.

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Adding a simple 2-component (C and L) 2nd-order high-pass filter network to this driver produces the following response. This filtered response is −3dB at about 450Hz. This shows that the impedance peak of the driver at 455Hz can be worked with using a simple filter network. It's possible to adjust the –3dB low-frequency cut-off frequency by varying the values of C and L in the filter network.

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The VituixCAD circuit used to produce the above response is shown below. Note that Z = 10,000 ohms and SPL = 90dB for Driver #1 in this reduced-order model.

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Are you quite sure that the L880/2 did not have a cup installed? The midrange driver needs to be isolated from the low-frequency high-amplitude pressure variations inside the enclosure that are produced by the movement of the woofer. It could be expected that, without a cup/rear chamber, the 2-inch midrange unit would probably end up being damaged.
Yes, I’m sure. The 880’s 2” midrange doesn’t have rear cup installed. But, I believe it should have resembled structure to the conventional tweeters—it’s sealed even if it has no cup equipped. See the attached for an illustration.

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From the information that's been provided, the 2-inch midrange in the L880/2 has a sealed enclosure, which will have a particular volume that produces a given resonance frequency for that driver. The variant with the cup installed has a larger enclosure volume, resulting in lower added stiffness from the air in the enclosure, and therefore that driver's resonance frequency will be lower, all other things being equal.
 
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Not at all.
More probably a lowering of Fb by lowering the Qtc from 1 to something lower as I mentioned earlier. As you were informed earlier the tweeter is a "closed system" like a woofer in a sealed box but much much smaller.
There are open backed tweeters and these usually came with a reasonably big plastic cup that integrated with the drivers surround.
I've attached pix of the small drivers made by Coral that are /were made this way
 

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Hi, all kinds of technical answers already, so a philosphical one as greetings from morning coffee table 🙂

Any driver was very likely manufactured to certain goals, like some particular frequency response for some particular reason. Since Fs is from spring and mass, you could just increase mass which is relatively easy retroactive mod, much easier than loosening the spring. As you increase mass at least sensitivity drops as the motor needs to work harder now, frequency response changes. If this is for good then it is, so if the driver was designed bad and got better now. But if the driver was good set of compromises it likely got worse with the mod, at least for the initial intent the driver was designed for.

So, sometimes you have to work with what you've got and perhaps manipulate the driver if it then works better for what you have in mind. If there is luxury to buy new driver, it's just matter of choosing the suitable one that needs no modification. This is why drivers are bought about last, first there needs to be a plan to know what kind of drivers are needed.
 
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