Is the function of 1N4001 before the 5V regulator reverse polarity protection?
Is this a fine method? And I sometimes see 1N4148. Can any diode(besides zener) be used for such function?
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Yes, this diode is probably for reverse polarity protection. It does its job but has the disadvantage that about 0.6 V is dropped across it. It needs to be rated for the current, both continuous and surge, as well as the reverse voltage it might encounter. 1N4148 is fine for lower current applications. A shunt diode with polyswitch/fuse is also an option. More elaborate schemes with MOSFETs are possible.
any diode that can handle the current and voltage.
zeners have a low breakdown voltage and are thus unsuitable as you surmise. IN4148 can only handle a few hundered milliamperes continuous and so could be used in low current applications.
IN4001 can handle 1A, enough for many small devices.
This is a correct reverse polarity circuit in any circumstance:
This is completely different from the circuit you provide:
The main reason is the moment you stop: the inductances in your circuit will tend to conserve the current, and the circuit tries to achieve it from anywhere it want, harming your ICs, sensitive MOSFETs, sensors, or other components you have connected.
When you stop the circuit, the inductive equivalent of your circuit will try to retain the current, but your "protection" current diode does not allow to do that. Its mission consists in breaking the current flowing in the wrong direction.
The first circuit, instead, allows the current go trough the diode, and taking the diode a correct reverse polarity diode protection: all the current goes through this diode, breaking it if required.