8 - EE 2001 Fall 2008 Problem Set 9 BJT Biasing Derive an...

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EE 2001 Fall 2008 Problem Set 9 ______________________________________________________________________ BJT Biasing Derive an equation for V CE in terms of beta. (use V BE,on = 0.7 volts) Plot V CE vs beta. Note: V CE approaches a steady value as beta becomes very large. It doesn’t collapse to saturation level, 0.2V, as we might expect. In a sense, large transistor gains “buy” us a stable operating point. Sort of like credit default swaps buy us a stable market (but with transistor circuits this actually works). Solution: IB = (VCE – 0.7)/R1 – 0.7/R2 KCL at the collector-- (VCE – 0.7)/R1 + beta*IB + (VCE – VCC)/RC = 0 (VCE – 0.7)/R1 + beta*((VCE – 0.7)/R1 – 0.7/R2) + (VCE – VCC)/RC = 0 VCE(1/R1 + beta/R1 + 1/RC) = 0.7/R1 + beta*0.7/R1 + beta*0.7/R2 + VCC/RC VCE = (0.7/R1 + beta*0.7/R1 + beta*0.7/R2 + VCC/RC)/ (1/R1 + beta/R1 + 1/RC) VCE = (k1 + k2*beta)/(k3 + k4*beta) where k1 = 0.7/R1 + VCC/RC = 0.0535; k2 = 0.7/R1 + 0.7/R2 = 0.0105; k3 = 1/R1 + 1/RC = 0.01; k4 = 1/R1 = 0.005; Plot of VCE starts at k1/k3, that is 5.35V, for beta = 0, and approaches k2/k4, that is 2.1V, as beta approaches infinity. RC (200 ) R1 (200 ) +10 v I C + V CE _ R2 (100 )

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