Hello!
The secret is not in the current. It is in the voltage.
So, if you have some CMOS circuitry that are supposed to run off a 12 V supply voltage and consume arount 10 microamps, you can (in principle) connect that circuit directly to a 12 V bar battery that is capable of delivering hundreds of amperes for cranking. No probs there.
But, the standard way of doing it to
A Fuse the current (or, as it is, really, voltage source) where you connect to it.
B Add some filtering to avoid getting noise from other circuitry connected to same battery.
C Provide overvoltage protection. This is a must in mobile applications where a load dump can take the battery voltage up to 50+ volts for a few milliseconds. But long enough to fry anything electronic.
D If your voltage source is DC has wrong voltage, put a switcher in between so that you get the right voltage. You can also use a linear voltage regulator, but then the voltage source must be a couple volts more than your circuit needs. If you have very low current consumption and a decent difference between your available voltage and needed voltage, then a simple resistor/zener combination does the trick. Simple, cheap, reliable.
E If you have an AC source (mains, for instance) then you need some sort of power supply unit (PSU). There are ones that range from little wall-warts with a few volts at a few milliamps to large units with multiple outputs and capable of supplying hundreds of amps.
But, you can forget about constant current diodes. They are handy as electronic components. But don't use them to reduce voltage to micros and other electronic devices.
Google "power supply" for loads of info.
Gunnar Englund
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100 % recycled posting: Electrons, ideas, finger-tips have been used over and over again...