Some further thoughts on using Piezo Tweeters -
Using the KSN-1141A as an example, which is a 2x6 piezo horn.
Here is a link to the data sheet on this tweeter -
http://piezosource.com/general/datasheets/Piezo_1141_datasheet.pdf
First look at the Frequency Response Graph then scroll down to the Impedance Chart. Notice on the Freq Response graph, the peaks at about 8khz and 14khz.
This Tweeter appears as a 0.3uF load to the amp.
It's relative impedance according to the impedance chart at 2khz is about 210 ohms and at 20khz it is about 40 ohms. Though using 0.3uF and calculating the reactance, ignoring phase angle, gives us 256 ohm at 2khz, 26.5 ohms at 20khz, and a calculated 2.65 ohms at 200khz.
I would likely use a L-Pad to attenuate the Tweeter and stabilize the apparently load. But an L-Pad depends on having some resistance in parallel with it (R1 on the attached drawing). So, personally, I would likely use a 16 ohm L-Pad with a 15 to 20 ohm resistor(R1) in parallel (though a precisely 16 ohm resistor would be ideal). In this case, 16 ohms would be the value I would use to calculate the capacitor for my crossover.
However, many people suggest using a resistor in series (R2) with the Piezo to act as a frequency dependent attenuator, and to protect the circuit impedance from dropping too low at high harmonic frequencies. But you can see from the impedance chart for the KSN-1141A, that what we assume the impedance is can be very different from the actual apparent impedance. Consequently, you can only wisely chose a series resistor(R2), if you know or can calculate the impedance of the Piezo at various frequencies.
Now back to the Frequency Response chart and again, notice the peaks in the upper half of the chart. Some people think these peaks make the piezo sound a little harsh. By adding a series resistor, you can soften the high without reducing them too much.
For example, if we use a 5 ohm or 10 ohm resistor in series with this piezo, we have the following attenuation at various frequencies -
At 2khz, 5 ohm = 1.9%, 10 ohm = 3.6%
At 20khz, 5 ohm = 16%, 10 ohm = 27%
At 200khz, 5 ohm = 67%, 10 ohm = 79%
Note, that I based this on calculated impedances, rather than the impedance chart. Using the values from the chart, the attenuation at 20khz is going to be closer to 11% for the 5 ohm and 20% for the 10 ohm.
So, by adding a 5 ohm resistor we have created a gradual roll-off slope that goes from 1.9% at 2khz to 16% at 20khz. That should server to soften the high without wiping them out completely.
For this particular Piezo Tweeter, the perceived impedance seems to level off above 20khz, but adding a 5 or 10 ohm resistor can make sure that the impedance never drops below the value of the Resistor.
But to accurately pick a resistor for R2, you need to know the relative impedance of the actual tweeter you are using.
Steve/bluewizard