ee 434 lecture 22 - iowa state university
TRANSCRIPT
![Page 1: EE 434 Lecture 22 - Iowa State University](https://reader031.vdocuments.site/reader031/viewer/2022012412/616c28392a15a2291307a50b/html5/thumbnails/1.jpg)
EE 434Lecture 22
Bipolar Device Models
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Quiz 14The collector current of a BJT was measured to be 20mA and the base
current measured to be 0.1mA. What is the efficiency of injection of electrons coming from the emitter to the collector?
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And the number is ….
631
24578
9
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And the number is ….
631
24578
9
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Quiz 14The collector current of a BJT was measured to be 20mA and the base
current measured to be 0.1mA. What is the efficiency of injection of electrons coming from the emitter to the collector?
Solution:
2001.
20===
mAmA
B
C
IIβ
α1αβ−
=
Efficiency = α
β1βα+
=
.9952001
200α =+
=
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– Bipolar device operation dependent upon how minority carriers in base contribute to collector current
– Bipolar model (in high gain region)• Diode model for BE junction, injection efficiency for IC α
– Bipolar transistor is inherently a current amplifier with exponential relationship between collector current and VBE
• This property makes BJT very useful
Review from Last Time
t
BEV
V
C eI SI~β=
t
BEV
V
B eI SI~=
t
BEV
V
C eI SI~β=
CB IIβ1
=
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Bipolar Models
Simple dc Model
Small SignalModel
Frequency-Dependent Small Signal Model
Better Analytical dc Models
Sophisticated Model for Computer Simulations
Better Modelsfor Predicting
Device Operation
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Bipolar Models
Simple dc Model
Small SignalModel
Frequency-Dependent Small Signal Model
Better Analytical dc Models
Sophisticated Model for Computer Simulations
Better Modelsfor Predicting
Device Operation
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Bipolar ModelsSimple dc Model
following convention, pick IC and IB as dependent variables and VBEand VCE as independent variables
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Simple dc model
t
BEV
V
B eI SI~=
t
BEV
V
C eI SI~β=
qkTVt =
From last time :
This has the properties we are looking for but the variables we usedin introducing these relationships are not standard
SI~
It can be shown that is proportional to the emitter area AE
Define and substitute this into the above equations ESAJ1~ −= βSI
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Simple dc model
t
BEV
V
B eI SI~=
t
BEV
V
C eI SI~β=
qkTVt =
t
BE
VV
ESB e
βAJI =
t
BE
VV
ESC eAJI =
qkTVt =
JS is termed the saturation current density
Process Parameters : JS,β
Design Parameters: AE
Environmental parameters and physical constants: k,T,qAt room temperature, Vt is around 26mVJS very small – around .25fA/u2
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Transfer CharacteristicsJS=.25fA/u2
AE=400u2
VBE close to 0.6V for a two decade change in IC around 1mA
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.1 1 10
IC (mA)
V BE
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Transfer CharacteristicsJS=.25fA/u2
AE=400u2
VBE close to 0.6V for a four decade change in IC around 1mA
0.45
0.50
0.55
0.60
0.65
0.70
0.75
0.001 0.01 0.1 1 10 100 1000
IC (mA)
V BE
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Simple dc model
0
50
100
150
200
250
300
0 1 2 3 4 5
Vds
IdIC
VCE
VBE or IB
t
BE
VV
ESC eAJI =
Output Characteristics
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Simple dc model
0
50
100
150
200
250
300
0 1 2 3 4 5
Vds
IdIC
VCE
VBE or IB
Better Model of Output Characteristics
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Simple dc model
VBE or IB
Typical Output Characteristics
0
50
100
150
200
250
300
0 1 2 3 4 5
Vds
Id
IC
VCE
Forward ActiveSaturation
Cutoff
Forward Active region of BJT is analogous to Saturation region of MOSFET
Saturation region of BJT is analogous to Triode region of MOSFET
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Simple dc model
VBE or IB
Typical Output Characteristics
0
50
100
150
200
250
300
0 1 2 3 4 5
Vds
Id
IC
VCE
Projections of these tangential lines all intercept the –VCE axis at the same place and this is termed the Early voltage, VAF (actually –VAF is intercept)
Typical values of VAF are in the 100V range
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Simple dc model
VBE or IB
Improved Model
0
50
100
150
200
250
300
0 1 2 3 4 5
Vds
Id
IC
VCE
⎟⎟⎠
⎞⎜⎜⎝
⎛+=
AF
CEVV
SC VV1eJI t
BE
t
BE
VV
ESB e
βAJI =
Valid only in Forward Active Region
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Simple dc model
VBE or IB
Improved Model
0
50
100
150
200
250
300
0 1 2 3 4 5
Vds
Id
IC
VCE
Valid in All regions of operation⎟⎟
⎠
⎞
⎜⎜
⎝
⎛−+
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛−−= 11 t
BC
t
BE
VV
SV
V
F
SE eJeJI E
E AAα
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛−−
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛−= 11 t
BC
t
BE
VV
SVV
SC eJeJIR
EE
AAα
qkTVt =
Not mathematically easy to work withNote dependent variables changes
Termed Ebers-Moll model
VAF effects can be added
Reduces to previous model in FA region
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Simple dc model
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛−+
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛−−= 11 t
BC
t
BE
VV
SV
V
F
SE eJeJI E
E AAα
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛−−
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛−= 11 t
BC
t
BE
VV
SVV
SC eJeJIR
EE
AAαq
kTVt =
Ebers-Moll model
Process Parameters: {JS, αF, αR}
Design Parameters: {AE}
αF is the parameter α discussed earlierαR is termed the “reverse α”
FF
F
αβ =1-α
RR
R
αβ =1-α
JS ~10-16A/µ2 βF~100, βR~0.4
Typical values for process parameters:
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Completely dominant!
Simple dc model
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛−+
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛−−= 11 t
BC
t
BE
VV
SV
V
F
SE eJeJI E
E AAα
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛−−
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛−= 11 t
BC
t
BE
VV
SVV
SC eJeJIR
EE
AAαq
kTVt =
Ebers-Moll model
JS ~10-16A/µ2 βF~100, βR~0.4
With typical values for process parameters in forward active region (VBE~0.6V, VBC~-3V), with Vt=26mV and if AE=100µ2:
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛−−
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛−= 11 t
BC
t
BE
VV
SVV
SC eJeJIR
EE
AAα
( ) ( )1410 1 128
-1410 -51
C
10I 1.05x10 7.7x10.
−= − − −
Makes no sense to keep anything other thanBE
t
VV
C SI J e
EA ⎛ ⎞= ⎜ ⎟⎝ ⎠
in forward active
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Simple dc model
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛−+
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛−−= 11 t
BC
t
BE
VV
SV
V
F
SE eJeJI E
E AAα
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛−−
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛−= 11 t
BC
t
BE
VV
SVV
SC eJeJIR
EE
AAαq
kTVt =
Ebers-Moll model
Alternate equivalent expressions for dependent variables {IC, IB} defined earlier for Ebers-Moll equations in terms of independent variables {VBE, VCE}
1CEBE
t t
-VVV VR
C S E
R
1+βI J A e eβ
⎛ ⎞⎡ ⎤= −⎜ ⎟⎢ ⎥
⎣ ⎦⎝ ⎠CEBE
t t
-VVV V
B S E
F R
1 1I J A e - eβ β⎛ ⎞
= ⎜ ⎟⎝ ⎠
No more useful than previous equation but in form consistent with notation Introduced earlier
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Simple dc modelSimplified Multi-Region Model
Ebers-Moll Model Simplified Multi-Region Model
1CEBE
t t
-VVV V CER
C S E
R AF
V1+βI J A e e 1+β V
⎛ ⎞⎡ ⎤ ⎛ ⎞= −⎜ ⎟⎜ ⎟⎢ ⎥
⎣ ⎦ ⎝ ⎠⎝ ⎠
⎟⎟⎠
⎞⎜⎜⎝
⎛+=
AF
CEVV
ESC VV1eAJI t
BE
VBE=0.7VVCE=0.2V
IC=IB=0
CEBE
t t
-VVV V
B S E
F R
1 1I J A e - eβ β⎛ ⎞
= ⎜ ⎟⎝ ⎠
t
BE
VV
ESB e
βAJI =
Forward Active
Saturation
Cutoff
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Simple dc modelSimplified Multi-Region Model
⎟⎟⎠
⎞⎜⎜⎝
⎛+=
AF
CEVV
ESC VV1eAJI t
BE
t
BE
VV
ESB e
βAJI =
qkTVt =
VBE=0.7VVCE=0.2V
IC=IB=0
Forward Active
Saturation
Cutoff
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Simple dc modelSimplified Multi-Region Model
⎟⎟⎠
⎞⎜⎜⎝
⎛+=
AF
CEVV
ESC VV1eAJI t
BE
t
BE
VV
ESB e
βAJI =
qkTVt =
VBE=0.7VVCE=0.2V
IC=IB=0
Forward Active
Saturation
Cutoff
VBE>0.4V
VBC<0
IC<βIB
VBE<0
VBC<0
A small portion of the operating region is missed with this model but seldom operate in the missing region
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Simple dc modelEquivalent Simplified Multi-Region Model
⎟⎟⎠
⎞⎜⎜⎝
⎛+=
AF
CEBC V
V1βII
t
BE
VV
ESB e
βAJI =
qkTVt =
VBE=0.7VVCE=0.2V
IC=IB=0
Forward Active
Saturation
Cutoff
VBE>0.4V
VBC<0
IC<βIB
VBE<0
VBC<0
A small portion of the operating region is missed with this model but seldom operate in the missing region