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this is a circuit in LM2596 datasheet which suggests using zener+bjt combo to protect against UnderVoltage in regulator input :

The UVLO circuit

it turns the regulator off using its ON/OFF pin.

I have many D882, 2SC3650 and BCP56T1 transistors in hand (all NPN). Can I replace the 2N3904 with one of these NPNs I have?

if not, what parameters should I look for in transistors to replace this 2N3904?

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The 2N3904 is a very "generic" NPN.

The D882 is more of a "Power NPN", it will probably just work in your circuit but since it works at quite low currents in that circuit, the other transistors might be better suited.

The 2SC3650 and BCP56T1 are more similar to the 2N3904 and should both work.

To quickly classify such NPNs I look at:

Vce,max, Ic,max and \$h_{fe}\$.

2N3904: Vce,max = 40 V; Ic,max = 200 mA; \$h_{fe}\$ = 30 to 300

D882: Vce,max = 30 V; Ic,max = 3 A; \$h_{fe}\$ = 30 to 300

2SC3650: Vce,max = 25 V; Ic,max = 1.2 A; \$h_{fe}\$ > 600

BCP56T1: Vce,max = 80 V; Ic,max = 1 A; \$h_{fe}\$ = 25 to 250

If you realize how the circuit works:

When the input voltage exceeds ~12.6 V then the \$V_{BE}\$ of the NPN will exceed ~0.6 V so the NPN starts to conduct. That will pull the voltage on the collector down and enable the LM2596.

This "start to conduct when \$V_{BE}\$ exceeds ~0.6 V" is something all NPNs do (Darlington transistors also but at a higher voltage) so basically any NPN will work.

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