How is the solution for \$\alpha\$ and \$\beta\$ current gain of a BJT derived


I'm just an enthusiast, and not too good at maths; I'm exploring constant current source circuits, in doing so I came across two equations for BJT current gain:

Could someone help me understand how \$\alpha\$ and \$\beta\$ are derived to the equations below:

\$\alpha=\frac{\beta}{\beta+1}\$ and \$\beta=\frac{\alpha}{1-\alpha}\$

I know that:

\$I_c=\alpha I_e\$ and \$I_c=\beta I_b\$

Any help would be much appreciated.


Best Answer

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α and β Relationship in a NPN Transistor enter image description here

The value of Beta for most standard NPN transistors can be found in the manufactures data sheets.