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## Lecture 25

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**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**Notation (PNP BJT)**NENAE DEDN tE tn LELN nE0 np0 = ni2/NE NBNDB DBDP tB tp LBLP pB0 pn0ni2/NB NCNAC DCDN tC tn LCLN nC0 np0ni2/NC EE130/230M Spring 2013 Lecture 25, Slide 2**“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**Emitter Region Analysis**• Diffusion equation: • General solution: • Boundary conditions: • Solution: EE130/230M Spring 2013 Lecture 25, Slide 4**Collector Region Analysis**• Diffusion equation: • General solution: • Boundary conditions: • Solution: EE130/230M Spring 2013 Lecture 25, Slide 5**Base Region Analysis**• Diffusion equation: • General solution: • Boundary conditions: • Solution: EE130/230M Spring 2013 Lecture 25, Slide 6**Since**we can write as EE130/230M Spring 2013 Lecture 25, Slide 7**EE130/230M Spring 2013**Lecture 25, Slide 8**BJT Terminal Currents**• We know: • Therefore: EE130/230M Spring 2013 Lecture 25, Slide 9**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**BJT Performance Parameters**• Assumptions: • emitter junction forward biased, collector junction reverse biased • W << LB EE130/230M Spring 2013 Lecture 25, Slide 11**BJT with Narrow Emitter**Replace with WE’ if emitter is narrow EE130/230M Spring 2013 Lecture 25, Slide 12**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**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**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**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**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**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**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**EE130/230M Spring 2013**Lecture 25, Slide 20**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