The capacitor in your tweeter is most likely there to protect it from high frequency signals that could damage the tweeter.

Absolutely not!. A Tweeter is designed to play high audio frequencies. Powerful low frequencies will destroy it.
A woofer plays low frequencies.

 

The capacitor in your tweeter is most likely there to protect it from high frequency signals that could damage the tweeter.

Where did you get that strange idea?
As AGa noted, not true.
The capacitor passes the high frequencies (which the tweeter is there to reproduce), not block them.
And there is generally not much energy in the high musical frequencies the tweeter sees so, unless there is a deliberate generation of large high frequency signals (such as from an audio generator) there is little chance of overloading a tweeter connected to a proper crossover network.
Most musical energy is in the bass and mid-range frequencies.

 

The crossover shown in post #20 has first-order filters. A second order crossover has steeper cutoff slopes but causes phase shift that causes cancellation of frequencies at the crossover frequency. All ever-order filters have a 180 degrees phase shift.

The best sounding speaker I designed has 3rd-order highpass and lowpass filters. It produces no awful woofer cone breakup sounds and no awful tweeter resonant sounds.

 

Even if the tweeter is rated power matches the rated amplifier power (truthful ratings, not exaggerations) then if the amplifier's volume control is turned up too high (or if acid rock "music" is played) causing clipping distortion, then the tweeter will probably be destroyed by the continuous full power high frequencies.

Many tweeters have a power rating when playing pink noise (equal power per octave).

 

(such as from an audio generator)

or a home-made amplifier that has gone unstable!

The inductance of a moving-coil tweeter tends to protect it from really high frequencies. An unstable amplifier is instant death to piezo tweeters!

 

I have never uses a piezo tweeter because its frequency response is all over the place and sounds awful.
Rock groups use them for the "distinctive" sound.

 

I have never uses a piezo tweeter because its frequency response is all over the place and sounds awful.
Rock groups use them for the "distinctive" sound.

Agreed - they are dreadful, but I thought that rock groups used them for no better reason than because they are cheap. I thought that there is so much variation from device to device, even in the same batch that it would be difficult to have a "distinctive sound".
If you cheap out on the amplifier so that it is permanently in clipping, the extra high-frequency content soon evaporates the metallising that makes the contents to the PZT. And cheap amplifiers often give a nice burst of high frequency instability as they come out of clipping.

 

I am wondering just what the mechanism of "improving the quality" would be that would come from changing to a more complex crossover circuit. That is a big assumption based on what??
What would be improved?? Not the linearity of the frequency response, not harmonic distortion, and not power sensitivity.
See post #12 also.
We are not told what the rest of the package is, but if it is similar to all of the dual speakers I have seen, the way to improve the quality is to replace the whole assembly with some speakers that are actually better, that is, better linearity and flatter frequency response across your listening spectrum.
The series capacitor is there to keep the lower frequencies from overdriving the smaller higher frequency speaker into the high distortion travel range.
By installing an actual crossover there will probably be a dip in the middle frequency range that will discolor the sound of your music. Other posts have mentioned that as well.

 

to get the full benefit of the new Crossover-Network
the original Capacitor should be removed to prevent altering
the Tuning / Frequency-Response of the new Crossover-Network.

A crossover network that is a "better crossover circuit" has a much steeper cutoff slope than a simple capacitor. The better circuit completely removes the tweeter resonant frequency.

Excellent points. Points I had overlooked.

Still, it's easy enough to bypass the original cap with a jumper. If it produces a desired affect to have it in - or jumped out - it comes down to what the end user wants and finds most pleasing. Me? I have tinnitus. I constantly hear high frequency buzzing and whistling. I have to boost the high end in order to meet a pleasing sound quality. While it sounds good to me, to others it is often tinny and lacks full range. Well, full range may be there, but the high end is boosted more so than mid range and low range audio. To each his (or her) own ear.

 

How a Speaker "Sounds" is a very "subjective" thing.

You can't really judge a Speaker's Sound before You take care of the listening environment,
which makes a massive difference.

Many changes that people want to make to their Speakers are based of of
a bunch of blarney that may be floating around the internet that
promises to make your ordinary junk into perfect "sound-transducers".
Most of the time they have no clue as to what it takes to
reproduce sounds in the most satisfactory manner possible, to that particular persons taste.

I have a check-list that has been very successful in the past,
but it involves developing a good understanding of the important factors
that must be taken into consideration when designing any sound-system.
But I have no idea of how much effort You want to put into improving your sound-system.

Why are You installing new Crossover-Networks in your Speakers ?
There may be many other, more productive, changes that You can make.

Pictures, of both the Speaker-Components, the Box, and the usual listening environment,
would go a long way towards helping to make any recommendations.
.
.
.

 

Adding to what LQC mentioned, the fact is that a "perfect" sound system will seem to be lacking for those of us who are more used to "hearing what we like." I once was allowed to listen for a bit to a "perfectly flat response, no audible distortion" system that was installed in an isolated anechoic room, which was even suspended off the building structure. It may have been great for listening to Mozart at medium volume, I guess, but not very interesting.