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Noob question: why doesn't dropping the voltage increase the current?
Positive resistance (like a resistor) not negative resistance (like constant power output active power supply)

One way to look at it is the power in cmos gates is all burned up fighting capacitance. You can run a cmos ram in sleep mode for years off a watch battery, but they'll take "serious" power at MHz speeds.

Think of charging a capacitor and watch the voltage across the cap as it charges. As electrons trickle in (thats the current) the voltage slowly rises. It'll take longer to charge that cap up to 5 volts than 3.3 volts. (edited to add, next step in analogy is you could make that cap charge up to 5 volts just as fast as it charged to 3.3. volts by cranking up the current...) So by analogy in your cmos gates the higher the voltage you charge a binary one up to, the larger the current spikes to get to that voltage representing a binary one.

There are resistive losses, but not much. Those are positive resistances, too.

So everything comes up positive resistance aka "higher voltage = higher current" not the other way around.

Are you familiar with Ohm's Law?

    V = IR
That, in a word, is why. The DC circuit can be modeled as a bunch of resistors, capacitors, and inductors. Capacitors and inductors are more complicated than resistors, but similar.

Intuitively, voltage is the ability to force current through the devices. Reducing voltage reduces ability to force current through.

Your notion of dropping voltage increasing current is probably rooted in power. Perhaps you are thinking about AC transformers, where halving the voltage does lead to doubled current. You can think of a transformer as playing with this equation while maintaining static Power:

    P = VI
Just wanted to say that everything in this article about the MCU, capacitors and diodes is spot on. (I don't do work with coin cell batteries, but I do have experience with using very small rechargeables and very small solar panels.)

To add to it, don't use zener diodes for over-voltage protection. They are extremely leaky. And if you need high value MLCC capacitors you are better off making them yourself from a stack of (more common) 10uF ceramic caps.

Articles like these are great. For those working with ultra-low power MCUs, it's a gold mine of knowledge, data, and wisdom. For everyone else (like me), it finds value as an inspiration. The article stands as an example of what good engineering looks like; the kind of attention to detail and depth of thoughtfulness we should strive to pour into our own projects.