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Emitter follower augmented

Hello, I have this emitter follower augmented ( I think that's his name in english) but I don't know from where is the beta+1 on the Iin ecuation?

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  • \$\begingroup\$ You're asking why \$I_{B3} = \frac{I_{E3}}{\beta+1}\$? And "Q3 is in forward active mode" is not enough explanation? \$\endgroup\$
    – The Photon
    Sep 28 '17 at 17:31
  • \$\begingroup\$ Yes that's what I'm asking. Edit: I looked into that and it explains why. \$\endgroup\$
    – Fox Alex
    Sep 28 '17 at 17:33
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    \$\begingroup\$ Your circuit is a current-mirror with beta helper not an emitter follower \$\endgroup\$
    – sstobbe
    Sep 28 '17 at 17:40
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Q3 is in forward active mode because the base-emitter junction is forward biased and the base-collector junction is reverse biased.

In this mode we have the very well known characteristic $$I_c = \beta I_b .$$

Since the current coming out of the emitter is (by KCL) the sum of the base and collector currents,

$$I_e = I_b + I_c = I_b + \beta I_b$$

and thus

$$I_b = \frac{I_e}{1+\beta}.$$

(Note: circuit theory purists would normally take \$I_e\$ to mean the current going in to the emitter, so there'd be some sign changes in the equations above)

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