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Plans. What does MCDE give us for the gain? How can we use the equation to improve the gain? Can we develop a compact circuit model for a BJT?. BJT Coordinate system and parameters. Forward Active minority carrier distribution. P. N. P+. p B (x). n E (x’). n E0. p B0. n C0.
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Plans • What does MCDE give us for the gain? • How can we use the equation to improve the gain? • Can we develop a compact circuit model for a BJT? ECE 663
Forward Active minority carrier distribution P N P+ pB(x) nE(x’) nE0 pB0 nC0 nC(x’’) ECE 663
Emitter Region • Minority carrier diffusion equation: • Boundary conditions: P N P+ pB(x) nC0 pB0 nE(x’) nC(x’’) nE0 Wide emitter region Law of the junction ECE 663
Base Region • Minority carrier diffusion equation: • Boundary conditions: P N P+ pB(x) nC0 pB0 nE(x’) nC(x’’) nE0 Law of the junction(s) ECE 663
Collector Region • Minority carrier diffusion equation: • Boundary conditions: P N P+ pB(x) nC0 pB0 nE(x’) nC(x’’) nE0 Wide collector region Law of the junction ECE 663
Currents ECE 663
Solutions in the Base Region • Need to keep both positive and negative exponential terms in the general solution. • Apply Boundary conditions: • Solve for A1 and A2 and plug-in to general solution ECE 663
Base solutions ECE 663
Currents: Emitter hole current ECE 663
Collector hole current IE IC IEp ICp C E IEn ICn IB ECE 663
Simplify • Active mode biasing: VEB>0 (forward bias) and VCB<0 (reverse bias) • Can keep only terms with emitter-base exponential ECE 663
Emitter Efficiency • Want to express in terms of doping: ECE 663
Common Emitter Gain ECE 663
Can also calculate total emitter and collector currents by adding up electron and hole currents in the collector and emitter Fortunately, for usable transistors (high gain) usually, the base is small Compared to the minority carrier diffusion length and the equations simplify ECE 663
Narrow Base Approximation: W<<LB • Can simplify hyperbolic functions involving W/LB • If <<1, then sinh() and cosh ()1 + 2/2 Linear concentration dependence across the base ECE 663
Narrow Base Emitter Efficiency • has If you want high emitter injection efficiency, then NB/NE << 1 High emitter doping ECE 663
Performance factors: Base Transport factor aT If you want high base transport (T 1) then you want as small of a Base as possible W << LB or alternatively large LB = large p ECE 663
Performance factors: Common Base Gain adc Want both high emitter doping and narrow base for high gain ECE 663
Performance factors: Common Emitter Gain bdc Want both high emitter doping and narrow base for high gain ECE 663
Circuit models • If VCB=0 then the equation for the emitter current looks like the ideal diode equation: ECE 663
Circuit models If VEB=0, then the collector current equation also reduces to one that looks like an ideal diode equation: ECE 663
Ebers-Moll Model The exp(VCB) term in the emitter equation and the exp(VEB) term in the collector current equation have the same prefactor: The emitter and collector current equations can be written in terms of four parameters (three are independent): Can show thatF= dc ECE 663
Characteristics: Common Base Input Output Ebers-Moll equation After some manipulation ECE 663
IC IB IE Common Emitter Characteristics Output Input Start with Ebers-Moll equations and some algebra to get them into the right form: ECE 663
Common Base Characteristics Output Input ECE 663
NEW Common Emitter Characteristics Input (Forward Biased PN junction) Output (Reverse biased PN junction .. Is controlled by IB) ECE 663
NEW Resistor-Transistor Logic (RTL) ECE 663