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Understanding BJT Operation: Ideal Transistor Analysis and Ebers-Moll Model

This lecture delves into the analysis of Bipolar Junction Transistors (BJTs), covering ideal transistor behavior, Ebers-Moll model, and base-width modulation. Detailed discussions include minority carrier diffusion equations in different regions (emitter, base, collector), terminal current calculations, and performance parameters necessary for high current gain. The significance of narrow base and emitter constructions for enhanced transistor efficiency is explored, along with methods to minimize base-width modulation. A comprehensive overview of voltage behaviors in active and saturation regions is provided.

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Understanding BJT Operation: Ideal Transistor Analysis and Ebers-Moll Model

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  1. Lecture 25 OUTLINE The BJT (cont’d) • Ideal transistor analysis • Narrow base and narrow emitter • Ebers-Moll model • Base-width modulation Reading: Pierret 11.1-11.2; Hu 8.2-8.6

  2. Notation (PNP BJT) NENAE DEDN tE tn LELN nE0 np0 = ni2/NE NBNDB DBDP tB tp LBLP pB0 pn0ni2/NB NCNAC DCDN tC tn LCLN nC0 np0ni2/NC EE130/230M Spring 2013 Lecture 25, Slide 2

  3. “Game Plan” for I-V Derivation • Solve the minority-carrier diffusion equation in each quasi-neutral region to obtain excess minority-carrier profiles • different set of boundary conditions for each region • Find minority-carrier diffusion currents at depletion region edges • Add hole & electron components together  terminal currents EE130/230M Spring 2013 Lecture 25, Slide 3

  4. Emitter Region Analysis • Diffusion equation: • General solution: • Boundary conditions: • Solution: EE130/230M Spring 2013 Lecture 25, Slide 4

  5. Collector Region Analysis • Diffusion equation: • General solution: • Boundary conditions: • Solution: EE130/230M Spring 2013 Lecture 25, Slide 5

  6. Base Region Analysis • Diffusion equation: • General solution: • Boundary conditions: • Solution: EE130/230M Spring 2013 Lecture 25, Slide 6

  7. Since we can write as EE130/230M Spring 2013 Lecture 25, Slide 7

  8. EE130/230M Spring 2013 Lecture 25, Slide 8

  9. BJT Terminal Currents • We know: • Therefore: EE130/230M Spring 2013 Lecture 25, Slide 9

  10. BJT with Narrow Base • In practice, we make W << LB to achieve high current gain. Then, since we have: EE130/230M Spring 2013 Lecture 25, Slide 10

  11. BJT Performance Parameters • Assumptions: • emitter junction forward biased, collector junction reverse biased • W << LB EE130/230M Spring 2013 Lecture 25, Slide 11

  12. BJT with Narrow Emitter Replace with WE’ if emitter is narrow EE130/230M Spring 2013 Lecture 25, Slide 12

  13. Ebers-Moll Model increasing (npn) or VEC (pnp) • The Ebers-Moll model is a large-signal equivalent circuit which describes both the active and saturation regions of BJT operation. • Use this model to calculate IB and IC given VBE and VBC EE130/230M Spring 2013 Lecture 25, Slide 13

  14. V V EB CB I B E B C I C If only VEB is applied (VCB = 0): aR : reverse common base gain aF : forward common base gain If only VCBis applied (VEB = 0): : Reciprocity relationship: EE130/230M Spring 2013 Lecture 25, Slide 14

  15. In the general case, both VEB and VCB are non-zero: IC: C-B diode current + fraction of E-B diode current that makes it to the C-B junction IE: E-B diode current + fraction of C-B diode current that makes it to the E-B junction Large-signal equivalent circuit for a pnp BJT EE130/230M Spring 2013 Lecture 25, Slide 15

  16. Base-Width Modulation Common Emitter Configuration, Active Mode Operation W IE IC P+ N P  + VEB DpB(x) IC (VCB=0) x VEC W(VBC) 0 EE130/230M Spring 2013 Lecture 25, Slide 16

  17. Ways to Reduce Base-Width Modulation Increase the base width, W Increase the base dopant concentration NB Decrease the collector dopant concentration NC Which of the above is the most acceptable action? EE130/230M Spring 2013 Lecture 25, Slide 17

  18. Early Voltage, VA Output resistance: A large VA (i.e. a large ro ) is desirable IC IB3 IB2 IB1 VEC 0 VA EE130/230M Spring 2013 Lecture 25, Slide 18

  19. Derivation of Formula for VA Output conductance: for fixed VEB where xnC is the width of the collector-junction depletion region on the base side xnC P+ N P EE130/230M Spring 2013 Lecture 25, Slide 19

  20. EE130/230M Spring 2013 Lecture 25, Slide 20

  21. Summary: BJT Performance Requirements • High gain (bdc >> 1) • One-sided emitter junction, so emitter efficiency g  1 • Emitter doped much more heavily than base (NE >> NB) • Narrow base, so base transport factor aT 1 • Quasi-neutral base width << minority-carrier diffusion length (W << LB) • IC determined only by IB (IC function of VCE,VCB) • One-sided collector junction, so quasi-neutral base width W does not change drastically with changes in VCE (VCB) • Based doped more heavily than collector (NB > NC) (W = WB – xnEB – xnCB for PNP BJT) EE130/230M Spring 2013 Lecture 25, Slide 21

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