Gang...
Here are the details of a completely
new and MUCH superior design...
This new approach is 3 to 4 times more efficient, in that it's able to put a MUCH more pure sine wave -- nearly perfect -- of 70-80 volts p-p (27 Vrms) across our piezo tweeters while consuming less than 100mA. This moves its power consumption down into the range that a single 9v "transistor radio" battery can easily handle -- so that's the operating voltage it is designed to use. This new design employs only one inductor, plus one active and three passive components. It's AMAZING. :)
It is NOT dynamically tunable (I will be working on that next), but I have chosen and documented a very nice and inexpensive line of inductors, with a large variety of available values surrounding 1000uH. So you can purchase a range (at 42 cents each) to set the operating frequency wherever you choose, given your component tolerances, individual tweeter capacitance, and personal frequency preference.
Here's what happened...
As I last wrote, I was working on the problem of a continuously tunable system. (That problem remains outstanding, and I will return to it now that this most recent breakthrough is detailed and documented.) I have always been annoyed by my original use of a "buck-style" voltage boost converter, since it inherently wastes so much power while the transistor is on. In looking at the wave shapes and frequency responses of the resonating filter being driven by the buck-style booster, I was wishing that I could provide not only a positive impulse to the resonator, but also a equal negative impulse. My feeling was that if I could drive the resonator with something even a bit "less of a spike" -- perhaps more of a square -- then the wave shapes I was seeing might have at least some better chance of being less unruly.
Then I remembered the beautiful little Microchip MOSFET driver IC I had used in the first "Big Mama Mega Blaster" I built for Mark. Because I was building only one, and I didn't want to spend my life optimizing it, I used a MONSTER overkill power MOSFET. But a MOS transistor necessarily has a large enhancement mode channel to suppor large current flow. And that requires a large gate and accompanying gate capacitance. Since that first device was driven by a simple 555 timer, the timer's output drive was limited. So I added a "MOSFET Driver IC" between the 555 timer and the overkill power MOSFET's gate. Such a driver has a beefy complementary MOS (CMOS) output stage... essentially two large MOS transistors, one N-channel and one P-channel which are used to rapidly charge and discharge an external power MOSFET's large gate capacitance. That's all it does. The front end of a MOSFET driver is typically a high-impedance input, and this one also had 300mV of hysteresis to eliminate output jitter and uncertainty if the input is noisy or wandering around a bit. These MOSFET drivers are available in both inverting and non-inverting versions. I always over-order parts from Digikey on the theory that (a) if I order 10 they're cheaper each, and (b) something I used once is more likely to be used again... that was certainly the case this time. So I already had some of those $2 MOSFET driver ICs on hand.
I assembled the bits the pieces of a now-familiar architecture: an inverting driver, driving a high-Q resonator consisting of an inductor and capacitor in series (the capacitor being both the circuit's load and our tweeter), taking feedback from the inductor/capacitor junction, through an RC phase-shifting filter, and back to the input of the inverting driver...

It took off like a bat out of hell and began to sing!
I then spent the next 24 hours or so studying it closely and optimizing its operation. As you can see, it could not possibly be any simpler.
I believe we have our final design for a non-tunable, high-frequency, high-power audio oscillator. When I saw that the circuit was drawing so little power, I experimented with raising its operating voltage from 6 to 9 volts... and it only made it louder. I am getting NO distortion, NO harmonics, and NO misbehavior of any kind. The R1 and C2 values are non-critical, though I think they are optimal for the frequency range we want.
One thing we learned during the past few weeks, is that the tweeter capacitances vary widely, but so too do the inductors (10%). And we've also seen that people have varying preferences for the operating frequency of their devices. Some people don't mind if it's audible to humans, others prefer to be completely stealthy. So rather than specifying a single value for the device's frequency-setting inductor, I selected a very nice, Digikey-stocked, family of inexpensive (42 cents each) inductors. The family offers a full range of values clustered around 1000uH (1mH). My advice would be for people to purchase as many different values in the region as they may need and want. Lower inductance values will yield higher frequencies, whereas higher values will bring the frequency down. The mid-point of the range I have provided is 1000uH, which nominally oscillates at 12 to 16 kHz depending upon the individual tweeter's capacitance.
The rule of thumb should be to use the lowest frequency (highest inductance value) that you're comfortable with, since we don't yet have sufficient experience with the response of these piezo tweeters to know how much power they emit at super-sonic frequencies -- nor for that matter with canine responses.
In conclusion...
I am EXTREMELY pleased with the surprising evolution this aspect of the project has taken. I believe that armed with the schematic and bill-of-materials (attached to this post), anyone with basic electrical/electronics assembly skills can now quickly, easily, and inexpensively assemble a state-of-the-art fixed (or incrementally variable), high-performance high-power acoustic sound generator.
It is my hope that the people here will be interested in assembling this much-superior, version 2.2.0 of the fixed-frequency oscillator system, so that we might all share in everything that can be learned about it. It is absolutely true that all of the feedback provided about the performance of the previous design was instrumental in getting me to the place where this one would be born.
Thanks everyone!! :)
/Steve.