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correct me please


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When one design  preamplifier using BJT voltage-divider unbupassed Emitter config, one want max symetrical signal swing at the collector. To do this, VCE = 0.5 VCC &
I (saturation) = 2 IC = VCC/(RC+RE)
If I want a voltage gain = A, then

A= RC/(RE+re), where re = 0.026/IE, so

RC = A(RE+re) --------------(eq.1)

as said before, for max symetrical signal swing at the collector,

2 IC = VCC/(RC+RE)  ==>

RC = (VCC/2IC) - RE  ------(eq.2)

From (eq.1) & (eq.2) we get:

A(RE+re)= (VCC/2IC) - RE, solvig for RE yields:

RE = {VCC/2(1+A)IC} - (A/A+1)re

question #1: Is there any error in either equations or concepts
If yes, corrected me, please

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