ESE319 Introduction to Microelectronics
BJT Intro and Large Signal Model
2008 by Kenneth R. Laker (based on P.V. Lopresti 2006) update 09Sep08 KRL)
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ESE319 Introduction to Microelectronics
Why BJT?
What's the competition to BJT and bipolar technologies?
What advantages does the competition have over BJT?
What advantages does BJT and bipolar have over their competition?
What circuit applications benefit from BJT and bipolar technologies?
2008 by Kenneth R. Laker (based on P.V. Lopresti 2006) update 09Sep08 KRL)
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ESE319 Introduction to Microelectronics
Why BJT
What's the competition to BJT and bipolar technologies?
MOSFET, in particular CMOS is the leading competitor
What advantages does the competition have over BJT?
Small size (die area), low cost and low power dissipation
What advantages does BJT and bipolar have over their competition?
High frequency operation, high current drive, high reliability in
severe environmental conditions.
What circuit applications benefit from BJT and bipolar technologies?
RF analog and digital circuits,power electronics and power amplifiers, automobile electronics, radiation hardened electronics
2008 by Kenneth R. Laker (based on P.V. Lopresti 2006) update 09Sep08 KRL)
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ESE319 Introduction to Microelectronics
BJT Physical Configuration
NPN
PNP
Closer to actual layout
Each transistor looks like
two back-to-back diodes,
but each behaves much differently!
2008 by Kenneth R. Laker (based on P.V. Lopresti 2006) update 09Sep08 KRL)
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ESE319 Introduction to Microelectronics
NPN
BJT Symbols and Conventions
PNP
Note reversal in current directions and voltage signs for PNP vs. NPN!
2008 by Kenneth R. Laker (based on P.V. Lopresti 2006) update 09Sep08 KRL)
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ESE319 Introduction to Microelectronics
NPN BJT Modes of Operation
Forward-Active Mode
EBJ forward bias (VBE > 0)
CBJ reverse bias (VBC < 0)
iE = iC + iB
vCE = vCB + vBE
Mode
Forward-Active
VBE
VBC
>0
<0
Reverse-Active
<0
<0
>0
>0
<0
>0
Cutoff
Saturation
2008 by Kenneth R. Laker (based on P.V. Lopresti 2006) update 09Sep08 KRL)
VBC = -VCB
Not Useful!
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ESE319 Introduction to Microelectronics
NPN BJT Forward-Active Mode Basic Model
Collector-base diode
is reverse biased
V CB0
( or VBC < 0)
Base-emitter diode is
forward biased
saturation current
V BE ≈0.7
AE
W
NA
Dn
ni
A E q D n ni
I s=
N AW
2
Area of base-emitter junction
Width of base region
Doping concentration in base
Electron diffusion constant
Intrinsic carrier concentration = f(T)
iC ≈ I S e
v BE
VT
VT=
kT
o
≈ 25 mV @ 25 C
q
iC
i B=

i E =i B i C =1i B
=common−emitter current gain
2008 by Kenneth R. Laker (based on P.V. Lopresti 2006) update 09Sep08 KRL)
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ESE319 Introduction to Microelectronics
Note that the iC equation looks like that of a forward-biased
diode.
Is it?
2008 by Kenneth R. Laker (based on P.V. Lopresti 2006) update 09Sep08 KRL)
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ESE319 Introduction to Microelectronics
Note that the iC equation looks like that of a forward-biased
diode. Is it?
v BE
VT
i C =I S e −1
By using the other two equations the question can be answered
1
1
i E =i B i C = 1i C =
iC


=common−emitter current gain
=common−base current gain
and write:
v
v
1
1
V
V
i E=
I S e −1= I S e −1


BE
BE
T
T
AhHa! This iE equation describes a forward-biased emitter-base
“diode”.
2008 by Kenneth R. Laker (based on P.V. Lopresti 2006) update 09Sep08 KRL)
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ESE319 Introduction to Microelectronics
So the new set of
equations is:
v BE
VT
IS
i E = e −1

v BE
VT
i C =I S e −1= i E
iC
i B=

A E q D n ni 2
I s=
N AW
Where:

=
1
Typically:
50200
10−18 I S 10−12 A.
Is is strongly temperaturedependent, doubling for a
5 degree Celsius increase
in ambient temperature!
2008 by Kenneth R. Laker (based on P.V. Lopresti 2006) update 09Sep08 KRL)
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ESE319 Introduction to Microelectronics
Two equivalent large signal circuit models for
the forward-active mode NPN BJT:
Nonlinear VCCS
Nonlinear CCCS
Key Eqs.
= F
v BE
VT
iC ≈ I S e = F i E
IS
i E≈ e
F
V BE
VT
2008 by Kenneth R. Laker (based on P.V. Lopresti 2006) update 09Sep08 KRL)
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ESE319 Introduction to Microelectronics
Yet another NPN BJT large signal model
i C = i B ≈ I S e
v BE
VT
IS
⇒ iB≈ e

v BE
VT
iB
This “looks like” a diode
between base and emitter
and the equivalent circuit
becomes:
iC
iE
Note that in this model, the diode current is represented in
terms of the base current. In the previous ones, it was represented in terms of the emitter current.
2008 by Kenneth R. Laker (based on P.V. Lopresti 2006) update 09Sep08 KRL)
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ESE319 Introduction to Microelectronics
NPN BJT Operating in the Reverse-Active Mode
Recall for NPN Reverse-Active Mode VBE < 0 & VBC > 0
●
●
We also have transistor action if we:
●
Forward bias the base-collector junction and
●
Reverse bias the base emitter junction
The physical construction of the transistor, however, leads to betas on the order of 0.01 to 1 and
correspondingly smaller values of alpha, e. g.:
R
0.1
R=
≈
≈0.091
 R1 1.1
for
 R =0.1
2008 by Kenneth R. Laker (based on P.V. Lopresti 2006) update 09Sep08 KRL)
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ESE319 Introduction to Microelectronics
The equivalent large signal circuit model for
the reverse-active mode NPN BJT:
RVRS
Active
FWD
Active
iC
Sat. or Scale Current Eq.
 F I SE = R I SC =I S
iB
iE
BJT is non-symmetrical
Key Eqs.
−I S
iC ≈
e
R
i E ≈−I S e
v BC
VT
v BC
VT
2008 by Kenneth R. Laker (based on P.V. Lopresti 2006) update 09Sep08 KRL)
 R ≪ F
R ≪F
AC A E
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ESE319 Introduction to Microelectronics
The Ebers-Moll Large Signal Model
The E-M model combines
the FWD & RVRS Active
equivalent circuits:
Note that the lower left
diode and the upper right
controlled current source
form the forward-active
mode model, while the upper left diode and the lower
right source represent the
reverse-active mode model.
i C = F i DE −i DC
i E =i DE − R i DC
i b =1− F  I DE 1− R  I DC
2008 by Kenneth R. Laker (based on P.V. Lopresti 2006) update 09Sep08 KRL)
i DE =I SE e
v BE
VT
−1
v BC
VT
i DC =I SC e −1
 F I SE = R I SC =I S
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ESE319 Introduction to Microelectronics
Operation in the Saturation Mode
Recall for Saturation Mode VBE > 0 & VBC > 0 (or VCB < 0)
Consider the E-M model for collector current. We will
include the “-IS” term in the ideal diode equation.
i C = F i DE −i DC
v BE
VT
IS
i C = I S e −1− e
R
v BC
VT
−1
The first term is the forwardv mode collector current:
BE
VT
 F i DE = I S e −1
The second is the reverse mode collector current:
v
IS V
i DC = e −1
R
BC
T
2008 by Kenneth R. Laker (based on P.V. Lopresti 2006) update 09Sep08 KRL)
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ESE319 Introduction to Microelectronics
Combining terms:
Using typical values:
v BE
VT
v BC
IS V
iC = I S e −1− e −1
R
[
i C = e
v BE
VT
 R1
−1−
e
R
We obtain:
i C =[ e
40 v BE
 R =0.1
T
−v CB
VT
1 R 1
=
R
R
−40 v CB
−1−11e
]
−1 I S
I S =10
−14
A.
V T =0.025 V.
−1 ] 10−14
Let's plot iC vs. vBC (or vCB) with vBE = 0.7 V
2008 by Kenneth R. Laker (based on P.V. Lopresti 2006) update 09Sep08 KRL)
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ESE319 Introduction to Microelectronics
Scilab Saturation Mode Calculation
//Calculate and plot npn BJT collector
//current in saturation mode
vBE=0.7;
VsubT=0.025;
VTinv=1/VsubT;
betaR=0.1;
IsubS=1E-14;
alphaR=betaR/(betaR+1);
alphaInv=1/alphaR;
ForwardExp=exp(VTinv*vBE)-1;
vCB=-0.7:0.001:-0.1;
vBC=-vCB;
ReverseExp=alphaInv*(exp(VTinv*vBC)-1);
iC=(ForwardExp-ReverseExp)*IsubS;
signiC=sign(iC);
iCplus=(iC+signiC.*iC)/2; //Zero negative values
plot(vCB,1000*iCplus); //Current in mA.
2008 by Kenneth R. Laker (based on P.V. Lopresti 2006) update 09Sep08 KRL)
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ESE319 Introduction to Microelectronics
Saturation Mode Plot
Forward-active
Recall for Sat.
Mode
VBE > 0
&
VBC > 0
(or VCB < 0)
Saturation
A
2008 by Kenneth R. Laker (based on P.V. Lopresti 2006) update 09Sep08 KRL)
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ESE319 Introduction to Microelectronics
pnp
npn
The PNP Transistor
Mode
Forward-Active
VEB
VCB
>0
<0
Reverse-Active
<0
<0
>0
>0
<0
>0
Cutoff
Saturation
2008 by Kenneth R. Laker (based on P.V. Lopresti 2006) update 09Sep08 KRL)
VCB = -VBC
Not Useful!
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ESE319 Introduction to Microelectronics
PNP BJT Forward-Active Mode Basic Model
Collector-base diode
is reverse biased
V BC 0
Emitter-base diode is
forward biased
V EB≈0.7
Note reversal in voltage
polarity and in current
directions!
i C =I S e
iC
i B=

v EB
VT
−1
i E =i B i C =1i B
2008 by Kenneth R. Laker (based on P.V. Lopresti 2006) update 09Sep08 KRL)
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ESE319 Introduction to Microelectronics
PNP BJT Large Signal Model
FWD. Active
i C =I S e
iC
i B=

v EB
VT
−1
i E =i B i C =1i B
Substituting, as in the
npn case, we get:
Note reversal in current
directions!
2008 by Kenneth R. Laker (based on P.V. Lopresti 2006) update 09Sep08 KRL)
v EB
IS V
i E = e −1

T
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ESE319 Introduction to Microelectronics
Yet another PNP BJT large signal model
v EB
VT
v EB
VT
IS
IS
i C = i B = I S e −1⇒ i B = e −1≈ e


v EB
VT
This “looks like” a diode
between base and emitter
and the equivalent circuit
becomes:
iB
iC
Again, in this model, the diode carries only base current,
not emitter current.
2008 by Kenneth R. Laker (based on P.V. Lopresti 2006) update 09Sep08 KRL)
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ESE319 Introduction to Microelectronics
Scilab Plot of NPN Characteristic
(iC vs. vCE and vBE)
//Calculate and plot npn BJT collector
//characteristic using Ebers-Moll model
VsubT=0.025;
VTinv=1/VsubT;
betaR=0.1;
alphaInv=(betaR+1)/betaR;
IsubS=1E-14;
for vBE=0.6:0.02:0.68
ForwardExp=exp(VTinv*vBE)-1;
vCE=-0:0.001:10;
vBC=vBE-vCE;
ReverseExp=alphaInv*(exp(VTinv*vBC)-1);
iC=(ForwardExp-ReverseExp)*IsubS;
signiC=sign(iC);
iCplus=(iC+signiC.*iC)/2; //Zero negative vals
plot(vCE,1000*iCplus); //Current in mA.
end
2008 by Kenneth R. Laker (based on P.V. Lopresti 2006) update 09Sep08 KRL)
i C = F i DE −i DC
where
v BE
VT
i DE =I SE e −1
i DC = I SC e
v BC
VT
−1
v BC =v BE −v CE
No Early effect
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ESE319 Introduction to Microelectronics
Plot Output
saturation mode
forward-active mode
v BE =0.68 V
Early effect
not included.
v BE =0.66 V
v BE =0.64 V
2008 by Kenneth R. Laker (based on P.V. Lopresti 2006) update 09Sep08 KRL)
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ESE319 Introduction to Microelectronics
More on NPN Saturation
The base-collector diode has much larger
area than the base-emitter one.
●
●
●
Therefore, with the same applied voltage, it will
conduct a much larger forward current than will
the base-emitter diode.
When the collector-emitter voltage drops below
the base-emitter voltage, the base-collector
diode is forward biased and conducts heavily.
v CB =v CE −v BE
when
v CE ≈V CE sat 
2008 by Kenneth R. Laker (based on P.V. Lopresti 2006) update 09Sep08 KRL)
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ESE319 Introduction to Microelectronics
IC Expansion Around Zero VCE
IC (mA)
IC = 0
VCE (V)
Note that the collector current is zero at about VCE 0.06 V., not 0 V.!
Also note the large reverse collector-base current below 0.06 V.
2008 by Kenneth R. Laker (based on P.V. Lopresti 2006) update 09Sep08 KRL)
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ESE319 Introduction to Microelectronics
Voltage
at
Zero
Collector
Current
v
v
IS V
iC = I S e −1− e −1
R
BE
BC
VT
T
v BE
VT
 R e −1=e
−
 R 1−e
v BE
VT
=e
 v BE −vCE 
VT
−
v CE
VT
V BE
≈40∗0.7⇒ e
VT
−
IC = 0 =>
v
v
IS V
V
e −1= I S e −1
R
 R e
BC
BE
T
T
v BE
VT
−1=e
v BC
VT
−
 R =e
vCE
VT
−1
−
−e
v BE
VT
v BE
VT

≪1
⇒ vCE =−V T ln  R 
v CE =−0.025⋅ln 
−1
2008 by Kenneth R. Laker (based on P.V. Lopresti 2006) update 09Sep08 KRL)
0.1
=0.0599V.
0.11
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