Lecture19 BJT Ebers MollModel
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Transcript of Lecture19 BJT Ebers MollModel
ECE 3040 - Dr. Alan DoolittleGeorgia Tech
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
ECE 3040 - Dr. Alan DoolittleGeorgia Tech
Bipolar Junction Transistor (BJT) Quantitative SolutionInsight into transistor performance
If LB>>W (most of the minority carriers make it across the base),
DC
DC
BE
EEB
BEEB
BE
DC
DC
DC
EEB
BE
BEEB
BE
DC
WNDNLD
LW
NLDWND
and
NLDWND
LW
NLDWND
αα
β
ββ
α
−=⇒
+
=
+=
+⇒
++
=
1
21
1
11
1
211
1
2
2
ECE 3040 - Dr. Alan DoolittleGeorgia Tech
−−
−=
−−
−=
11
11
0
0
TCB
TEB
TCB
TEB
VV
RV
V
C
VV
VV
FE
eIeAI
eAeII
−
+−
−
=
−
−
−
+=
1sinh
cosh1
sinh
1
1sinh
11sinh
cosh
TCB
TEB
TCB
TEB
VV
B
B
B
BoBCo
C
CVV
B
B
BoBC
VV
B
B
BoBVV
B
B
B
BoBEo
E
EE
e
LW
LW
LpD
nLD
qAe
LWL
pDqAI
e
LWL
pDqAe
LW
LW
LpD
nLD
qAI
IF0
IR0
A
A
*
Development of the Large Signal Model of a BJT (Ebers-Moll Model)
ECE 3040 - Dr. Alan DoolittleGeorgia Tech
−−
−=
−−
−=
11
11
0
0
TCB
TEB
TCB
TEB
VV
RV
V
C
VV
VV
FE
eIeAI
eAeII
When VCB=0,
gaincurrentbasecommonIIbut
eIIandeII
ThusseeAI
but
eAIandeII
DCFEFC
VV
FFCV
V
FE
F
VV
CV
V
FE
TEB
TEB
TEB
TEB
ααα
α
=→=
−=
−=
>
−=
−=
,
11
,*)(
,
11
00
0
0
VEB
IB
IC
IE
Looks like an Ideal diode
Development of the Large Signal Model of a BJT (Ebers-Moll Model)
The collector current is the fraction of the emitter current “collected”
ECE 3040 - Dr. Alan DoolittleGeorgia Tech
−−
−=
−−
−=
11
11
0
0
TCB
TEB
TCB
TEB
VV
RV
V
C
VV
VV
FE
eIeAI
eAeII
When VEB=0,
DCRCRE
VV
RCV
V
RRE
R
VV
RCV
V
E
IIbut
eIIandeII
ThusseeAI
but
eIIandeAI
TCB
TCB
TCB
TCB
ααα
α
≠→=
−−=
−−=
>
−−=
−−=
,
11
,*)(
,
11
00
0
0VCB
IB
IC
IE
Looks like an Ideal diode
In Inverse Active mode, the emitter current is the fraction of the collector current “collected”
Development of the Large Signal Model of a BJT (Ebers-Moll Model)
ECE 3040 - Dr. Alan DoolittleGeorgia Tech
Note: A=αRIRo= αFIFo
IE IC
IB
Collector
Base
Emitter
αFIFαRIR
IF IR
−=
−= 11 00
TCB
TEB
VV
RRV
V
FF eIIandeII
DiodesIdeal
−−
−=
−−
−=
11
11
00
00
TCB
TEB
TCB
TEB
VV
RV
V
FFC
VV
RRV
V
FE
eIeII
eIeII
α
α
Development of the Large Signal Model of a BJT (Ebers-Moll Model)
PNP
ECE 3040 - Dr. Alan DoolittleGeorgia Tech
Development of the Large Signal Model of a BJT (Ebers-Moll Model)
IE IC
IB
Collector
Base
Emitter
αFIFαRIR
IF IR
−=
−= 11 00
TBC
TBE
VV
RRV
V
FF eIIandeII
DiodesIdealNPN
−−
−=
−−
−=
11
11
00
00
TBC
TBE
TBC
TBB
VV
RV
V
FFC
VV
RRV
V
FE
eIeII
eIeII
α
α
ECE 3040 - Dr. Alan DoolittleGeorgia Tech
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.
ECE 3040 - Dr. Alan DoolittleGeorgia Tech
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.
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 IC=180.7IB=218uA IE=(181.7/180.7)IC=219uA
CBoEdcC III +=α
CEoBdcC III += β
Neglect Leakage currents
R1(Ib)
R3(Ie)
Ie
Ib
Ic
CBE III +=
ECE 3040 - Dr. Alan DoolittleGeorgia Tech
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 Vbe=0.662V not 0.7V as assumed
Actual Ibase=1.05uA not 1.2uA as calculated
Only 1% error in the
collector and emitter
currents
Current into various nodes Voltage at various nodes
ECE 3040 - Dr. Alan DoolittleGeorgia Tech
IV curve looks like a diode
Real shows variation due to “base width modulation” dependent on the applied VCB
After the base-collector junction is reverse biased (starts collecting), IE~=IC
Real IV is limited by breakdown of the base-collector junction
Development of the Large Signal Model of a BJT (Ebers-Moll Model)Common Base
Input
IE and VEB
Output
IC and (-VCB)
Input Output
ECE 3040 - Dr. Alan DoolittleGeorgia Tech
IV curve looks like a diode but has a DC shift associated with the reverse biased base-collector junction current
After the base-collector junction is reverse biased (starts collecting), IC=βIB
Development of the Large Signal Model of a BJT (Ebers-Moll Model)
Input
IB and VEB
Output
IC and VEC
Real IV is limited by breakdown of the base-
collector junction
Real shows finite slope due to “base width modulation” dependent on the applied VCB
Input
Output
Common Emitter