# 基宽调制与巴斯-莫尔模型

1. Lecture #16 OUTLINE The Bipolar Junction Transistor – Narrow-emitter and/or narrow-collector – Ebers-Moll model – Base-width modulation, Early voltage Reading: Chapter 11.2 Spring 2003 EE130 Lecture 16, Slide 1 Narrow-Emitter and Narrow-Collector cosh(WE ' / LE ) qVEB / kT I En = qA DLEE nE 0 (e − 1) sinh(WE ' / LE ) cosh(WC ' / LC ) qVCB / kT I Cn = − qA DLCC nC 0 (e − 1) sinh(WC ' / LC ) I E = qA [( DE WE′ nE 0 + DB LB pB 0 cosh(W / LB ) sinh(W / LB ) )(e qVEB / kT − 1) − ( DB LB )( pB 0 sinh(W1 / LB ) e qVCB / kT − 1 )] = qA[( ) ( )(e )] cosh(W / LB ) IC DB LB pB 0 sinh(W1 / LB ) (e qVEB / kT − 1) − DC WC′ nC 0 + DB LB pB 0 sinh(W / LB ) qVCB / kT −1 Spring 2003 EE130 Lecture 16, Slide 2 1

2. Performance Parameters (revisited) 1 γ = n iE 2 1 + n DD NN LW 2 E B B Replace with W ’ if short emitter E E E iB 1 αT = 1 + 12 ( ) W 2 LB 1 α dc = 1+ ni E 2 D N W E B ni B 2 DB N E LE + 12 ( ) W 2 LB 1 β dc = ni E 2 D N W E B ni B 2 DB N E LE + 12 ( ) W 2 LB Spring 2003 EE130 Lecture 16, Slide 3 Ebers-Moll Model IC IB saturation active region region V CE 0 The Ebers-Moll model is a large-signal equivalent circuit which describes both the active and saturation regions of BJT operation. Spring 2003 EE130 Lecture 16, Slide 4 2

3.IC is driven by two forces, VEB and VCB . V EB V CB If only VEB is applied (VCB = 0): IB I E = I F 0 ( e qVEB / kT − 1) I C = α F I F 0 ( e qVEB / kT − 1) E B C I B = (1 − α F )I F 0 ( e IC qVEB / kT − 1) If only VCB is applied (VEB = 0): : αR : reverse common base gain αF : forward common base gain I C = − I R 0 (e qVCB / kT − 1) I E = −α R I R 0 (e qVCB / kT − 1) I B = I R 0 (1 − α R )(e qVCB / kT − 1) Spring 2003 EE130 Lecture 16, Slide 5 In the general case, both VEB and VCB are non-zero: I C = α F I F 0 ( e qVEB / kT − 1) − I R 0 ( e qVCB / kT − 1) IC: C-B diode current + fraction of E-B diode current that makes it to the C-B junction I E = I F 0 ( e qVEB / kT − 1) − α R I R 0 ( e qVCB / kT − 1) IE: E-B diode current + fraction of C-B diode current that makes it to the E-B junction Spring 2003 EE130 Lecture 16, Slide 6 VCE (V) 3

4. Reciprocity Relationship DB pB 0 α F I F 0 = α R I R 0 ≡ qA LB sinh(W / LB ) Spring 2003 EE130 Lecture 16, Slide 7 Base-Width Modulation VBE B E + N C N P V CE emitter base collector } WB 3 reduction of base width WB 2 VCE 1 < VC E2 <VC E3 WB 1 ∆nn' B 1 β dc = niE 2 DE N B W niB 2 DB N E LE + 12 ( ) W 2 LB x How can we reduce the base-width modulation effect? Spring 2003 EE130 Lecture 16, Slide 8 4

5. V BE B E + N C The base-width modulation N P VCE emitter base effect is reduced if we collector } WB 3 reduction of base width (A) Increase the base width, WB 2 VCE 1 < VC E2 <VC E3 (B) Increase the base doping WB 1 n' concentration, NB , or (C) Decrease the collector doping concentration, NC . x Which of the above is the most acceptable action? Spring 2003 EE130 Lecture 16, Slide 9 Early Voltage Output resistance : −1  ∂I  V r0 ≡  C  = A  ∂VCE  IC IC IB3 (b) IB2 A large VA (i.e. a VA : Early Voltage IB1 larger ro ) is desirable VA 0 VCE Spring 2003 EE130 Lecture 16, Slide 10 5

6. Punchthrough Spring 2003 EE130 Lecture 16, Slide 11 Summary: BJT Performance Requirements • High gain (βdc >> 1) → One-sided emitter junction, so emitter efficiency γ ≈ 1 • Emitter doped much more heavily than base (NE >> NB) → Narrow base, so base transport factor αT ≈ 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) Spring 2003 EE130 Lecture 16, Slide 12 6

7. Review: Modes of Operation Common-emitter output characteristics (IC vs. VCE) IC Note that βdc = is lower for inverted mode operation. Why? IB Spring 2003 EE130 Lecture 16, Slide 13 7