Lecture 19 Bipolar Junction Transistors (BJT): Part 3 Ebers Moll
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Lecture 19 Bipolar Junction Transistors (BJT): Part 3 Ebers Moll Large Signal BJT Model, Using CVD model to solve for DC bias point Reading: Pierret 11.1 Georgia Tech ECE 3040 - Dr. Alan Doolittle Bipolar Junction Transistor (BJT) Quantitative Solution Insight into transistor performance If LB>>W (most of the minority carriers make it across the base), α DC β DC 1 ⇒ = = 2 DEWN B 1 + β DC DEWN B 1 W 1+ 1+ + DB LE N E DB LE N E 2 LB 1 and β DC α DC DB LE N E ⇒ = = 2 DEWN B 1 − α DC DEWN B 1 W + D B LE N E 2 LB Georgia Tech 1 ECE 3040 - Dr. Alan Doolittle Development of the Large Signal Model of a BJT (Ebers-Moll Model) IF0 A coshW VEB D VCB L D p D p 1 B V e T − 1 − qA B Bo e VT − 1 I E = qA E n Eo + B Bo LB sinh W LE LB sinh W L L B B * W cosh L VCB D p VEB D D p 1 B V e T − 1 − qA C nCo + B Bo e VT − 1 I C = qA B Bo LB sinh W LB sinh W LC L L B B A IR0 VCB VT VEB VT I E = I F 0 e − 1 − A e − 1 VCB VT VEB VT I C = A e − 1 − I R 0 e − 1 Georgia Tech ECE 3040 - Dr. Alan Doolittle Development of the Large Signal Model of a BJT (Ebers-Moll Model) VCB VT VEB VT I E = I F 0 e − 1 − A e − 1 VCB VT VEB VT I C = A e − 1 − I R 0 e − 1 When VCB=0, IC IB VEB VT I E = I F 0 e − 1 and but , IF0 > A VEB IE VEB VT I C = A e − 1 Looks like an Ideal diode ( see *) Thus, VEB VT VEB VT IE = IF0 e − 1 and I C = α F I F 0 e − 1 but , I C = α F I E → α F = α DC common base current gain The collector current is the fraction of the emitter current “collected” Georgia Tech ECE 3040 - Dr. Alan Doolittle Development of the Large Signal Model of a BJT (Ebers-Moll Model) VCB VT VEB VT I E = I F 0 e − 1 − A e − 1 VCB VT VEB VT I C = A e − 1 − I R 0 e − 1 When VEB=0, VCB IC IB VCB VT I E = − A e − 1 and but , I R0 > A IE VCB VT I C = − I R 0 e − 1 Looks like an Ideal diode ( see *) Thus, VCB VT VCB VT I E = −α R I R 0 e − 1 and I C = − I R 0 e − 1 but , I E = α R I C → α R ≠ α DC In Inverse Active mode, the emitter current is the fraction of the collector current “collected” Georgia Tech ECE 3040 - Dr. Alan Doolittle Development of the Large Signal Model of a BJT (Ebers-Moll Model) Ideal Diodes PNP Note: A=αRIRo= αFIFo IF VEB VT I F = I F 0 e − 1 and IR Emitter VCB VT I R = I R 0 e − 1 Collector IE IC αRIR Base IB αFIF VCB VT VEB VT IE = IF0e − 1 − α R I R 0 e − 1 Georgia Tech VCB VT VEB VT IC = α F I F 0 e − 1 − I R 0 e − 1 ECE 3040 - Dr. Alan Doolittle Development of the Large Signal Model of a BJT (Ebers-Moll Model) Ideal Diodes NPN IF VBE VT I F = I F 0 e − 1 and IR Emitter VBC VT I R = I R 0 e − 1 Collector IE IC αRIR Base IB αFIF VBC VT VBB VT I E = I F 0 e − 1 − α R I R 0 e − 1 Georgia Tech VBC VT VBE VT I C = α F I F 0 e − 1 − I R 0 e − 1 ECE 3040 - Dr. Alan Doolittle Using the Ebers-Moll model requires mathematical complexity (and much pain). Thus, we have an approximate solution method* that allows a quick solution. *I refer to as the “CVD/Beta Analysis”. This is just my term, not a universal name. Georgia Tech ECE 3040 - Dr. Alan Doolittle Quick Solution using a CVD/Beta Approach Consider the following pnp BJT circuit with a common emitter current gain, βDC=180.7. Find Ib, Ic, and Ie assuming a turn on voltage of 0.7V. Neglect Leakage currents R1(Ib) I C = α dc I E + I CBo I C = β dc I B + I CEo I E = I B + IC Ic Ib Ie R3(Ie) 0=-4V+IB(12000)+VEB+IE(15000) 4V=IB(12000)+0.7V+IC(1/αDC)(15000) 4V=IB(12000)+0.7V+[βDCIB][(1+βDC)/ βDC](15000) 3.3V=IB[(12000)+(1+180.7)(15000)] IB= 1.2uA Georgia Tech IC=180.7IB=218uA IE=(181.7/180.7)IC=219uA ECE 3040 - Dr. Alan Doolittle Development of the Large Signal Model of a BJT (Ebers-Moll Model) Compare our results using the CVD/Beta model to the full Ebers-Moll solution used in PSPICE... Actual Ibase=1.05uA not 1.2uA as calculated Only 1% error in the collector and emitter currents Actual Vbe=0.662V not 0.7V as assumed Current into various nodes Georgia Tech Voltage at various nodes ECE 3040 - Dr. Alan Doolittle Development of the Large Signal Model of a BJT (Ebers-Moll Model) Common Base IV curve looks like a diode Input Real shows variation due to “base width modulation” dependent on the applied VCB Output Input Output IE and IC and VEB (-VCB) Georgia Tech After the basecollector junction is reverse biased (starts collecting), IE~=IC Real IV is limited by breakdown of the base-collector junction ECE 3040 - Dr. Alan Doolittle Development of the Large Signal Model of a BJT (Ebers-Moll Model) Common Emitter IV curve looks like a diode but has a DC shift associated with the reverse biased base-collector junction current Output Real IV is limited by breakdown of the basecollector junction Input Input Output IB and IC and VEB VEC Georgia Tech After the base-collector junction is reverse biased (starts collecting), IC=βIB Real shows finite slope due to “base width modulation” dependent on the applied VCB ECE 3040 - Dr. Alan Doolittle
