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 1...
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
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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
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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
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)
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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
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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