Power Regulators Question

Understood, okay then, I will rebuild it with 3AA batteries supply, thanks for pointing out the potential issue.
What about the voltage/current spike that may be caused by induction coil in parallel circuit? Is that even a concern I should have at all?

PS: Also, just thinking out loud, the pro mini 3.3v has MIC5205 voltage regulator and just looked into datasheet, seems that it can take input voltage in 2.5-16V range, so if I understand correctly powering form 3V pack should be okay then, or still not a good idea?

Minor detail, but it's called a "voltage" regulator, rather than "power" regulator. ( don't ask me why. That's just the conventiion)

A power regulator would lower the voltage if the current increased and vise versa.

Still not a good idea. You can power a pro Mini with 4.5 V on the Vin pin. The 3.3 V regulator is an LDO.
(Low DropOut )

With no actual waveform data on the coil, no vendor's link for the coil , no electrical specificatiins on the coil, not even a photo of the coil, all I can say is :

"did you already post these or am I supposed to have a crystal ball ?"

raschemmel:
"did you already post these or am I supposed to have a crystal ball ?"

No, have not posted that yet, did not know you need to know exact specifications, this is what I have in mind,

http://www.mbedded.ninja/wp-content/gallery/electronics-misc/piezo-drive-circuit-parallel-inductor.jpg

39mH coil,not sure which one to buy yet, but somethign generic off digikey like this one:

You'll need a 1N4001 flyback diode across the coil:
flyback diode

as well as a decoupling cap and electrolytic cap across the supply that will power the coil.
You should have at least a 220 uF filter cap on that supply and a 0.1 uF decoupling cap also.

It is quite possible the diode might affect the timing for the coil. You'll have to do some empirical testing and try the coil without a diode , then try it with a diode to see what effect it has on the sound. If if does affect the sound you can try inserting a resistor in series with the diode. Experiment with the resistor value, starting low (47 ohms) and increasing it to 100, 220, 330, 470, 1 k 2.2 k until the effect on the piezo sound decreases , (if at all). I have never tried it but worst case, if none of the above is successful in elimating the effect of the diode on the coil turn-off time, you will have to eliminate the diode and use a transistor rated for Vce breakdown of 60V+.

What is the switching frequency of the coil driving squarewave on the base resistor ?

raschemmel:
You'll need a 1N4001 flyback diode across the coil:
flyback diode

as well as a decoupling cap and electrolytic cap across the supply that will power the coil.
You should have at least a 220 uF filter cap on that supply and a 0.1 uF decoupling cap also.

It is quite possible the diode might affect the timing for the coil. You'll have to do some empirical testing and try the coil without a diode , then try it with a diode to see what effect it has on the sound. If if does affect the sound you can try inserting a resistor in series with the diode. Experiment with the resistor value, starting low (47 ohms) and increasing it to 100, 220, 330, 470, 1 k 2.2 k until the effect on the piezo sound decreases , (if at all). I have never tried it but worst case, if none of the above is successful in elimating the effect of the diode on the coil turn-off time, you will have to eliminate the diode and use a transistor rated for Vce breakdown of 60V+.

What is the switching frequency of the coil driving squarewave on the base resistor ?

Switching frequency is 2.5 - 3.5kHz, thanks for all the great info.

Inductive reactance of the coil at that frequency is 612 ohms to 857 ohms.

Let R = 612 ohms

Vcc = 12V
Vce = 1 V
Vcoil = 12V-1V == 11V

Icoil =11V/612 ohms = 0.0179 V = 18 mA

Part number of coil driver transistor ?

raschemmel:
Part number of coil driver transistor ?

I am not sure yet, I need to buy most parts so I will perhaps be ordering a bunch of transistors and picking up what fit the best, whatever you suggest basically :). I'm new to this, what you already know and can calculate in your mind will take me some time to wrap my mind around.
This is the transistor I have immediately available: BD679AS onsemi | Discrete Semiconductor Products | DigiKey

datasheet

You might have a problem.
VCEO(SUS) is 50 mA.

Icoil =11V/612 ohms = 0.0179 V = 18 mA

Your load is barely more that 1/3 of the sustaining collector current.
What this means is that the transistor may not even turn on .

I think you don't have to worry about the transistor being damaged by the reverse voltage on coil turn off.
Try and see what happens.