Lecture 19. ECE Dr. Alan Doolittle

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...
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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

    coshW   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 = IF0e − 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