1. ECE 3040 - Dr. Alan Doolittle
Georgia Tech
Lecture 21
Bipolar Junction Transistors (BJT): Part 5
Hand Example, SPICE Example, and Limits on
output swing imposed by having to stay within
Forward Active Mode
Reading:
Notes
2. ECE 3040 - Dr. Alan Doolittle
Georgia Tech
An Example that puts it all together!
Consider an Integrated Circuit npn BJT with:
Emitter Doping, NDE=7.5e18 cm-3
Base Doping, NAB =10e17 cm-3
Collector Doping, NDC=1.5e16cm-3
Substrate doping NSub= 5e15 cm-3
Minority Carrier Diffusion coefficient in the emitter, DpE-(holes) = 5 cm2/s
Minority Carrier Diffusion coefficient in the base, DnB-(electrons) = 10 cm2/s
Base Quasi-neutral width, W = 300 nm
Minority Carrier Diffusion length in the emitter, LE = 250 nm
Minority Carrier Diffusion length in the base, LB = 100 um
Areas:
Aemitter-base = 25 um2 , Acollector-Base = 100 um2 , Asubstrate-Collector = 500 um2
Resistances and Early Voltage: rb = 250 Ω , rc = 200 Ω , rex = 5 Ω, VA = 35 V
Find the complete small- signal model for:
IC =100 mA, VCE =2V, and VCS=2V and Vbe=0.5Vbi For the emitter-base
3. ECE 3040 - Dr. Alan Doolittle
Georgia Tech
An Example that puts it all together!
First recognize that W<<LB so we can use the simplest form of the
transport parameters.
Next, recognize that our choice of generic labeling allows us to use the
equations developed for the pnp transistor here even though you were
given a npn transistor.
992
.
0
1
1
1
2
1
1
1
125
1
2
1
1
2
2
=
+
=
+
⇒
+
+
=
=
−
=
⇒
+
=
DC
DC
E
E
B
B
E
B
E
E
B
B
E
DC
DC
DC
B
E
E
E
B
B
E
E
B
B
E
DC
N
L
D
WN
D
L
W
N
L
D
WN
D
WN
D
N
L
D
L
W
N
L
D
WN
D
β
β
α
α
α
β
Note: The formulas here were derived in the optional material but
are not considered optional
4. ECE 3040 - Dr. Alan Doolittle
Georgia Tech
An Example that puts it all together!
( )
value
e
l
a
still
k
I
V
y
r
solution
e
approximat
the
g
u
or
k
I
V
V
y
r
k
g
I
V
y
r
mS
V
I
y
g
C
A
o
C
CE
A
o
m
o
C
T
o
T
C
m
arg
,
350
1
,
sin
370
1
4
.
32
1
86
.
3
22
22
11
21
Ω
=
≈
=
Ω
=
+
=
=
Ω
=
=
=
=
=
=
=
β
β
π
Transconductance:
Input Resistance:
Output Resistance:
5. ECE 3040 - Dr. Alan Doolittle
Georgia Tech
An Example that puts it all together!
Forward Base Transport Time:
fF
g
C
pS
D
W
F
m
B
B
F
173
45
2
2
=
=
=
=
τ
τ
Base-Emitter Diffusion Capacitance:
Watch the units!
jE
B C
C
C +
=
π
Maximum base transport limited operational frequency ~ 3.5 GHz!
6. ECE 3040 - Dr. Alan Doolittle
Georgia Tech
An Example that puts it all together!
−
≡
≡
+
=
junction
B
E
the
for
voltage
in
built
V
ce
capaci
depletion
bias
zero
C
where
V
V
C
C
junction
that
for
bi
o
j
junction
that
for
bi
o
j
j
tan
,
1
?
??
?
?
General Zero-Bias Depletion Capacitance:
( ) ( )
bi
D
A
D
A
o
S
V
junction
o
J
V
N
N
N
N
qK
A
C
C A
1
2
0
?
+
=
= =
ε
= 2
ln
i
D
A
bi
n
N
N
q
kT
V
Junction VBI Area (cm2
) Cj?o fF Applied Voltage Cj? fF
E-B 0.947 2.50E-07 23.335 -0.473 33.000
B-C 0.786 1.00E-06 37.248 2.000 19.782
C-Substrate 0.768 5.00E-06 177.201 2.000 93.332
Thus,
fF
C
fF
C
fF
C
C
C
CS
jE
B
3
.
93
8
.
19
206
=
=
=
+
=
µ
π
7. ECE 3040 - Dr. Alan Doolittle
Georgia Tech
SPICE BJT Modeling
−
≡
−
≡
≡
−
=
profile
doping
the
to
related
factor
onential
C
B
MJC
junction
C
B
the
for
voltage
in
built
VJC
ce
capaci
depletion
bias
zero
CJC
where
VJC
VBC
CJC
C MJC
exp
tan
,
1
µ
SPICE models capacitors slightly different than we have discussed.
Consider for example the Base-Collector capacitance:
Note the negative sign here
8. ECE 3040 - Dr. Alan Doolittle
Georgia Tech
SPICE BJT Modeling
Most Common Model Parameters PSPICE Name Units
*Transport saturation current (IS) IS A
Ideal maximum forward bias beta (βF) BF -
Forward Early voltage (VA) VAF V
Ideal maximum reverse bias beta (βR) BR -
Base resistance (rb) RB Ω
Emitter resistance (rex) RE Ω
Collector resistance (rc) RC Ω
B- E zero- bias depletion capacitance (CjE0) CJE F
B- E built- in potential (Vbi or φBE) VJE V
B- E junction exponential factor MJE -
B- C zero- bias depletion capacitance (Cjµ0) CJC F
B- C built- in potential (Vbi or φBC) VJC V
B- C junction exponential factor MJC -
Substrate zero- bias depletion capacitance (CCS0) CJS F
Substrate built- in potential (Vbi or φBS) VJS V
Substrate junction exponential factor MJS -
Ideal forward transit time (τF) TF seconds
*The Transport saturation current (IS) results from the simplified model which assumes forward active operation.
This can optionally be replaced with the Ebers-Moll parameters:
Base-collector leakage saturation current (IR0αR) ISC A
Base-emitter leakage saturation current (IF0αF) ISE A
Substrate-collector leakage saturation current ISS A
9. ECE 3040 - Dr. Alan Doolittle
Georgia Tech
SPICE BJT Modeling
In class example: Simulate this circuit using Vs=1 mV and determine the
voltage gain via a transient analysis, and an AC analysis.
What happens to the gain when C3 is removed? Why?
What happens when you do a transient analysis using VinAC=1 µV and
when VinAc=1 V? Why is there a difference?
10. ECE 3040 - Dr. Alan Doolittle
Georgia Tech
Forward active mode lies between saturation and cutoff. Thus, the maximum
voltage extremes that one can operate an amplifier over can easily be found
by examining the boundaries between forward active and cutoff and ….
VC max= + Supply
VE min= - Supply/Gnd
What sets the Maximum Limits of operation of the BJT Circuit?
11. ECE 3040 - Dr. Alan Doolittle
Georgia Tech
… and the boundaries between forward active and saturation
VC min= + 0.7 V
VBE=0.7
VCB=0V
VCE=0.7V
What sets the Maximum Limits of operation of the BJT Circuit?
12. ECE 3040 - Dr. Alan Doolittle
Georgia Tech
What sets the Maximum Limits of operation of the BJT Circuit?
Putting the two limits together…
VC min= + 0.7 V
VC @DC
VC max= + Supply
Output signals that exceed the
voltage range that would keep
the transistor within it’s Forward
active mode will result in
“clipping” of the signal leading
to distortion. (Example: “Distortion
found in loud Rock Music” - Heavy Metal)
Unclipped Signal
Clipped Signal at Active-
Saturation boundary
Clipped Signal at both Active-
Saturation and Active-Cutoff
boundary
The
maximum
voltage
swing
allowed
without
clipping
depends on
your choice
of DC bias
points.
