tricky teensy power situation

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Hi, I need some power mgt advice:

My current project is a daughterboard that attaches to the back of a Pocket Operator drum machine.
The PO is a 3.3v device; it presents power and ground pads on the back, and my board routes
its 3.3v pad to Vin and Gnd on the Teensy 3.2 on my board, and that powers the Teensy.
(I believe this is a direct connection to the two AA batteries on the back of the PO.)

This setup also lets me power the PO with the Teensy's regulated
supply. Or so I thought. It all worked great on the breadboard!
Actually it works just fine when the PO doesn't have its 2xAAA batteries
installed. But when it does have its batteries installed, I'm finding
that the power regulator chip on the teensy is getting red hot,
which is no good. I guess maybe the regulator is just a little bit higher
voltage than the PO batteries, and is "charging" them?

For a future versions of this board, I'm wondering how I can attain
my preferred power nirvana, which would be:

-- if USB is present, it powers both teensy and the PO
-- if PO batteries are present, they power both teensy and the PO
-- if both power sources are present, both are powered & nothing catches fire.

I've read the PRJC page on working with battery and USB side by side,
splitting the 5v and 3.3v sections of the board with a knife and then
bridging them with a diode. I'm not sure that would work with this
situation, tho, where I actually do want to be able to send current back to the PO --
just a limited current. Is there a favorite circuit or chip
to solve this sort of problem? Or can it all be accomplished with
the right diodes?

All advice much appreciated & thanks for being a great resource!
The 3.3V pin on Teensy can only take a regulated 3.3V if feeding that.

If Feeding VIN on a T_3.2 the card spec shows 3.6 to 6.0 Volts. Any less than that and the Teensy can't assure 3.3V as there is some voltage drop in the regulator - when it doesn't get enough it may be heating from that or a lack of needed current - 2 AAA's or AA's likely won't be up to the task alone.
Thanks for the advice but I'm not sure I follow what you said.

The teensy runs just fine on 2.8vdc coming from the 2 AAAs. It's only when the USB is attached & the teensy is getting a full 3.3v that I see this problem.

I've been reading a little bit about reverse current flow being a problem in DC regulators. Could that be the problem?
But how could current flow backwards from the batteries through the regulator,
when the regulator output is at 3.3v and the batteries are at only 2.8v?
opps ... misread ... not an EE for solving the real problem then.

But do understand that having two supplies is a bad idea without diode protection, the VIN<>VUSB trace should be cut - why the lower volt batteries would heat the Teensy is odd - unless they are such a current sink the regulator is working over time trying to make them be 3.3V? Though if reading right the batteried are on VIN at 5V when USB connected?

Can you put an ammeter inline to the battery connect to see the flow rate? Being lower voltage it seems the USB powered supply would feed them and that isn't right.

Hadn't seen notes of using Teensy at that low a voltage ... but recent years have been more consumed with T_3.5 to T_4.1 units
Aha! Due to yet another bug in my schematic, I did not have it wired up like I said at all.

The USB 5v connection (Vin) was connected direct to the battery+ on the PO!
Which I would have thought would boil the batteries, and I don't get why it would make the regulator overheat ...
but anyway I fixed it to how I had described before (regulated 3.3v <-> battery+) and now it's not overheating --
tho still slightly warm.

Still, I think this is probably not ideal, cut it's got to be running a reverse current to those
batteries, which are alkalines and not designed to be charged. I don't want this thing
to cause fires or burst batteries.

I think I'm starting to imagine how I would solve it with two parallel diodes, wired in series
with the battery->3.3v line. With one schottky diode oriented to allow the battery to power
the PO without dropping the voltage much, and the other diode oriented in the opposite
direction, chosen with enough fwd voltage drop to bring the 3.3v down to whatever
is the minimum voltage to run the PO ... probably 2.something?

Maybe it'll work? Better suggestions welcome!
Hadn't seen notes of using Teensy at that low a voltage ... but recent years have been more consumed with T_3.5 to T_4.1 units

Yeah, I thought I had once read something about the Teensy being able to run at lower clock speeds on less voltage ... but I can't find that now.
I just tried it on the breadboard for a while & never saw it be a problem. But now I wonder, are there other symptoms besides
spontaneous reboots that I should look out for?
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