08-1 BJT Models - brd4.braude.ac.il
Theory of Analog Electronics
BJT
Part 1. BJT Models
* In this presentation definitions and examples
from Wikipedia, HowStaffWorks and some other sources
were used
ORT Braude Engineering College. Course: Theory of Analog Electronics 31401.
Lecturer: Dr. Samuel Kosolapov ksamuel@braude.ac.il
Quiz 08. 1 (before the start):
Do You need this lecture ?
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Items to be
defined/refreshed/discussed
• BJT appearance
• Ebers-Moll Model
• BJT Characteristics
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BJT
BJT – Bipolar Junction Transistor
Transistor – TRANsformer of reSISTance
P-N-P BJT Transistor
N-P-N BJT Transistor
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BJT: 4 Operation Modes
Operating Modes in the BJT (2 Junctions 4 combinations are possible)
Mode
Forward-active
Cutoff
Saturation
Reverse-active
Emitter-Base
Junction State
Forward biased
(open)
R
F
R
Collector-Base
Junction State
Reverse biased
(closed)
R
F
F
For Analog Electronics: only Forward-Active Mode (Region) is relevant
Other modes are used in Digital Electronics
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BJT: Modes for Digital Electronics
Cut-Off state: (VCE>0, VBE<0.7V all currents are very small)
Both diodes are Reverse-Biased ; transistor equivalent is “OPEN SWITCH”:
Saturation State: (Left non-linear part of IC - F(VCE, IB) curves. IB > ICsat/HFE )
Both diodes are Reverse-Biased; transistor equivalent is “CLOSED SWITCH”:
More info (and info about Reverse-Active mode) sees in Digital Electronics books
(Mauro, and Millman course). Used in 74** TTL gates.
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BJT: Idea Device Nobel Prize Hard Work
Non-Linear Model (DC & AC) Linear Small-signal AC model
Ebers-Moll Model of BJT NPN Transistor
(By P.Lynch. Worked Examples in Physical Electronics, 1972 (absent in ORT Library)
See also Millman-Hakias. Integrated Electronics, pp. 147-148
Millman-Grabel. Microelectronics. 621.381 MIL pp. 87-89
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BJT: Ebers-Moll Model
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BJT: Ebers-Moll Model Input Characteristics
IB=F1( VBE, VCE )
~ Simple Diode.
Nearly no influence of Vce:
(0.3V and 10 V)
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BJT: Ebers-Moll Model Input Characteristics
IB=F1( VBE, VCE ) in 3D
Taylor Approximation will be
good here !!!
Attention:
For Vce < ~0.2 V
more complex graph
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BJT: Ebers-Moll Model Output Characteristics
IC=F2( Vce, IB ) {MAPLE: Symbolic formula is ~ 6 pages}
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BJT: Ebers-Moll Model Output Characteristics
IC=F2( Vce, IB ) in 3D
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BJT: Ebers-Moll Model H-Parameters
Feedback: ~ 0
Good
H12=HFE = b ~ 100:
Current Gain
H22=HOE :
Exaggeration
H11=HIE = 1kW:
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BJT: Ebers-Moll Model Large Signal Model #1
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BJT: Ebers-Moll Model Large Signal Model #2
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BJT: Ebers-Moll Model Large Signal Model #3
Rebf
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BJT: Example: Common Base Amplifier
Results of Simulation:
Mode test:
Inspecting E-B-C Voltages:
VEB < 0 VBE>0 BE diode is Forward-Biased
VCB > 0 CB diode is Reverse-Biased
Forward-Active Mode
Voltage Gain: (10.06-10.55) /( (-2.8) – (-2.7 ) = +4.9
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BJT: Example: Common Base Amplifier
Manual Solution with simplest model
No sub-division for DC and AC !!!!!
SUPPOSE (and this MUST be CHECKED at the end,
(otherwise we CAN NOT use this model),
that transistor is in Forward-Active state.
First step: REPLACE transistor to its model (Model 2 here):
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BJT: Example: Common Base Amplifier
Manual Solution with simplest model
Calculate Voltages and Currents
IE
V
signal
V0
Rsignal
F
VC F I E RC VCC ;
b
;
1 F
F Vsignal V0 RC
b RC
Vsignal V0 VCC
VC
VCC
Rsignal
b 1 Rsignal
1
VC
RC
1
F I E VCC
RC
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BJT: Example: Common Base Amplifier
Manual Solution with simplest model
Get Numerical Results
b = 100 – parameter of the transistor.
VC1 = (100/(1+100))*(5/1)*(2.7-0.7)= 9.900990100 V
VC2 = (100/(1+100))*(5/1)*(2.8-0.7) = 10.39603961 V
“Voltage Gain” = 4.96
DC Test: For Vsignal used, VBE >0 ( VEB<0) , VBC<0 (VCB>0) Forward-Active Region,
By the way, Vc ~ Vcc/2
RESULT: DC state wasestimated. Voltage/Current Gain was estimated.
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BJT: More Models
More BJT Models:
Reminder:
Original Ebers-Moll Model:
Active Region:
Dbe if Forward Biased (open)
Battery 0.7 V + resistor
Dbc is Reverse Biased (closed)
No connection Icr = 0
Ar*Icr = 0
Ebers-Moll for Active Region is
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BJT: Model and Relevant Equations
I C F I E ; I E I B I C I B F I E ;
IB
F IB
IE
; I C F I E
; I C H FE I B ;
1F
1F
F
H FE {b }
; {H FE H 21 } {FE : Forward Emitter}
1F
Example : F 0.99 H FE 99 ~ 100
I E I B I C I B H FE I B 1 H FE I B
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BJT: Alternative Drawing
I EF I E ;
F IB
F I EF F I E I C
H FE I B b I B
1F
b ~ 100
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BJT: Addition to Ebers-Mall Model Model for AC
Generally, “BASE” is “inside” the transistor, so RBB must be added
(“bad wire” from the B pin to Base junction).
(X point is “real “BASE” )
RBE is practically very small (dynamic resistance of the diode ~ 5 W )
RBB ~ 100W.. 1 kW
For AC Analysis Vbeo must be shorten,
RBE is practically very small ( ~ 5 W ),
so
AC model from here is: ( X E )
~H
parameters
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BJT: From H to Y parameters
Problem with nodes analysis:
Current IB in current controlled voltage source must be replaced to some voltage.
Ib = Vbe / H11 ;
IC = HFE*IB = (HFE/H11)* (VB - VE)
~ Y parameters Gm ? + Rce
Q. What is the difference from FET AC model ???
A. Value of “Input resistance”
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BJT Model: Practical Remarks
Basically Ebers-Moll original model may be (and was) used for
calculations of ALL states of the BJT.
Practically, in Analog Electronics “DC” and “small-signal AC” analyses are used for
Active Region only.
Parameters of full Ebers-Moll Model are parameters evaluated from physical and
geometry properties of the specific BJT.
Parameters of “small-signal AC model” depends on chosen Q-point
DC parameters != AC parameters
HFE for DC != Hfe for AC
To distinguish:
hFE - means DC parameters hfe – means AC small-signal parameters
BUT in most “electronics books” “good value” ~ 100 is used as b
as for AC as for DC.
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Control Questions
•
•
•
•
•
What have I learned
Questions
Why did I learn it
How can I apply this (We’ll use this for…)
Challenge
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Literature to read
1. TBD
2. Mauro
3. (See Roland E. Thomas. The Analysis and Design of Linear
Circuits 621.319.2 THO)
4. http://users.ece.gatech.edu/~alan/ECE3040/Lectures/Lectur
e19-BJT%20Ebers-MollModel.pdf
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