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Chapter 4 – Bipolar Junction Transistors (BJTs)
Introduction
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Physical Structure and Modes of Operation
A simplified structure of the npn transistor.
Physical Structure and Modes of Operation
A simplified structure of the pnp transistor.
Physical Structure and Modes of Operation
Mode
EBJ
CBJ
Active
Cutoff
Saturation
Forward
Reverse
Forward
Reverse
Reverse
Forward
Operation of The npn Transistor Active Mode
Current flow in an npn transistor biased to operate in the active mode, (Reverse current components due to drift of thermally generated
minority carriers are not shown.)
Operation of The npn Transistor Active Mode
Profiles of minority-carrier concentrations in the base and in the emitter of an npn transistor
operating in the active mode; vBE  0 and vCB  0.
Operation of The npn Transistor Active Mode
The Collector Current
v BE
iC
I S e
VT
The Base Current
v BE
iB
iC
IS


e
VT
Physical Structure and Modes of Operation
iE
iC  iB
1

 iC
vBE 



VT
1 
 i I
 IS e
E
 C
 


1
Equivalent Circuit Models
Large-signal equivalent-circuit models of the npn BJT operating in the active mode.
The Constant n
The Collector-Base Reverse Current
The Structure of Actual Transistors
The pnp Transistor
Current flow in an pnp transistor biased to operate in the active mode.
The pnp Transistor
Two large-signal models for the pnp transistor operating in the active mode.
Circuit Symbols and Conventions
C
C
B
B
E
E
Circuit Symbols and Conventions
Example 4.1
VCC  15
IC1  0.001
  100
VBE  0.7
VEE  15
VT  0.025
Design circuit such that
VC  5
RC 
IC2  0.002
VCC  VC
IC2
C
B
3
RC  5  10
Since VBE=0.7V at IC=1mA, the value of VBE at IC=2mA is
E
VBE  0.7  VT ln 
2
VBE  0.717

 1
VE  VBE
 
v BE
iC
I S e
VT

IE 
1
RE 
VE  0.717
VE  ( VEE)
IE
3
IC2
IE  2.02  10

3
RE  7.071  10
IB 
IC2

5
IB  2  10
Example 4.1
Example 4.1
IB 
IC2

5
IB  2  10
Summary of the BJT I-V Relationships in the Active Mode
vBE
iC
IS e
VT
vBE
iB
iC
IS


e
vBE
VT
iE
iC
IS


Note : for pnp transitor, replace vBE for vEB
iC
  iE
iB
 1     iE
iC
  iB
iE
   1  iB

  iE


1
iE
1
VT
25mV
e
VT
Exercise 4.8
Exercise 4.9
The Graphical Representation of the Transistor Characteristics
The Graphical Representation of the Transistor Characteristics
Temperature Effect (10 to 120 C)
Dependence of ic on the Collector Voltage
The iC-vCB characteristics for an npn transistor in the active mode.
Dependence of ic on the Collector Voltage
Dependence of ic on the Collector Voltage – Early Effect
v BE
VA – 50 to 100V
IC
I S e
VT
v CE 

 1 

VA


(a) Conceptual circuit for measuring the iC-vCE characteristics of the BJT. (b) The iC-vCE characteristics of a practical BJT.
Dependence of ic on the Collector Voltage – Early Effect
Nested DC Sweeps
Example
Example
Example
Monte Carlo Analysis – Using PSpice
Monte Carlo Analysis – Using PSpice
Monte Carlo Analysis – Using PSpice
Monte Carlo Analysis – Using PSpice
Probe Output
Ic(Q), Ib(Q), Vce
The Transistor As An Amplifier
(a) Conceptual circuit to illustrate the operation of the transistor of an amplifier.
(b) The circuit of (a) with the signal source vbe eliminated for dc (bias) analysis.
The Collector Current and The Transconductance
The Base Current and the Input Resistance at the Base
The Emitter Current and the Input Resistance at the Emitter
The Transistor As An Amplifier
Linear operation of the transistor under the small-signal condition: A small signal vbe with a triangular waveform is superimpose din the
dc voltage VBE. It gives rise to a collector signal current ic, also of triangular waveform, superimposed on the dc current IC. Ic = gm vbe,
where gm is the slope of the ic - vBE curve at the bias point Q.
Small-Signal Equivalent Circuit Models
Two slightly different versions of the simplified hybrid- model for the small-signal operation of the BJT. The equivalent circuit in
(a) represents the BJT as a voltage-controlled current source ( a transconductance amplifier) and that in (b) represents the BJT as a
current-controlled current source (a current amplifier).
Small-Signal Equivalent Circuit Models
Two slightly different versions of what is known as the T model of the BJT. The circuit in (a) is a voltage-controlled current source
representation and that in (b) is a current-controlled current source representation. These models explicitly show the emitter resistance
re rather than the base resistance r featured in the hybrid- model.
Signal waveforms in the circuit of Fig. 4.28.
Fig. 4.30 Example 4.11: (a) circuit; (b) dc analysis; (c) small-signal model; (d) small-signal analysis performed directly on the
circuit.
Fig. 4.34 Circuit whose operation is to be analyzed graphically.
Fig. 4.35 Graphical construction for the determination of the dc base current in the circuit of Fig. 4.34.
Fig. 4.36 Graphical construction for determining the dc collector current IC and the collector-to-emmiter voltage VCE in the circuit of
Fig. 4.34.
Fig. 4.37 Graphical determination of the signal components vbe, ib, ic, and vce when a signal component vi is superimposed on the dc
voltage VBB (see Fig. 4.34).
Fig. 4.38 Effect of bias-point location on allowable signal swing: Load-line A results in bias point QA with a corresponding VCE which
is too close to VCC and thus limits the positive swing of vCE. At the other extreme, load-line B results in an operating point too close to
the saturation region, thus limiting the negative swing of vCE.
Fig. 4.44 The common-emitter amplifier with a resistance Re in the emitter. (a) Circuit. (b) Equivalent circuit with the BJT replaced
with its T model (c) The circuit in (b) with ro eliminated.
Fig. 4.45 The common-base amplifier. (a) Circuit. (b) Equivalent circuit obtained by replacing the BJT with its T model.
Fig. 4.46 The common-collector or emitter-follower amplifier. (a) Circuit. (b) Equivalent circuit obtained by replacing the BJT with
its T model. (c) The circuit in (b) redrawn to show that ro is in parallel with RL. (d) Circuit for determining Ro.
A General Large-Signal Model For The BJT:
The Ebers-Moll Model
 vBE 


 VT

iDE ISE  e
 1
 vBC 


 VT

iDC ISC  e
 1
ISC > ISE (2-50)
An npn resistor and its Ebers-Moll (EM) model. ISC and ISE are the scale or saturation
currents of diodes DE (EBJ) and DC (CBJ).
More General – Describe Transistor in any mode of operation.
Base for the Spice model.
Low frequency only
A General Large-Signal Model For The BJT:
The Ebers-Moll Model
 vBE 


 VT

IDE ISE  e
 1
 vBC 


 VT

IDC ISE  e
 1
F
forwarded  of the transistor source (close to 1)
R
reverse  of the transistor source (0.02 - 0.5
A General Large-Signal Model For The BJT:
The Ebers-Moll Model – Terminal Currents
 F ISE
 R  ISC
IS
iE
iDE   R  iDC
iB
1   F iDE  1   R iDC
iE
iC
iB


IS 
 e
vBE
VT
F


IS 
 e
vBE
VT
F


IS 
 e
F






 1   IS  e


IS

 1 
R
vBE
VT
iDC   R  iDE
iC
vBC



 e


IS

 1 
R
VT



 1
vBC
VT



 e



 1
vBC
VT



 1
F
R
F
1  F
R
1  R
A General Large-Signal Model For The BJT:
The Ebers-Moll Model – Forward Active Mode
vBE
iE
IS
F
e
 IS 
1 
VT


F 

1
vBE
iC
IS e
VT
 IS 

1
 R
 1


vBE
iB
IS
F
e
VT
 IS 

1
 F


R 

1
Since vBC is negative and its magnitude
Is usually much greater than VT the
Previous equations can be approximated
as
A General Large-Signal Model For The BJT:
The Ebers-Moll Model – Normal Saturation
Collector current will be
 forced  IB
 forced   F
In saturation both junctions are forwarded biased.
are positive and their values greater than VT.
Making these approximations and substituting
iB
IB
and
iC
Thus VBE and VBC
 forced  IB
results in two equations that can be solved to obtain VBE and VBC.
The saturatuion voltage can be obtained as the difference between the two:
VCEsat
 forced  1 


1 

R


VT ln 

 forced
 1



F


A General Large-Signal Model For The BJT:
The Ebers-Moll Model – Reverse Mode
I1
Note that the currents indicated have positive values.
Thus, since ic = -I2 and iE = -I1, both iC and IE will be
negative. Since the roles of the emitter and collector are
interchanged, the transistor in the circuit will operate in
the active mode (called the reverse active mode) when the
emitter-base junction is reverse-biased. In such a case
I1 = beta_R . IB
IB
I2
This circuit will saturate (reverse saturation mode) when
the emitter-base junction becomes forward-biased.
I1/IB < beta_R
A General Large-Signal Model For The BJT:
The Ebers-Moll Model – Reverse Saturation
We can use the EM equations to find the expression of VECSat
 1  1   I1    1  
 


 F  IB    F 


VECsat  V T ln 

I1
1 

1     


IB   R 



 
From this expression, it can be seen that the minimum VECSat is obtained when
I1 = 0. This minimum is very close to zero.
The disadvantage of the reverse saturation mode is a relatively long turnoff time.
A General Large-Signal Model For The BJT:
The Ebers-Moll Model – Example
For the circuit below, let
RB  1000
VI  5
 R  0.1
VCC  5
VBC  0.6
 F  50
Calculate approximate values ofe VE for the following cases:
RC = 1K, 10K, 100K
From VBC = 0.6
IB 
VI  VB
RB
VB  0.6
3
IB  4.4  10
a) for RC = 1 K, assume that the transitor is in the reverse active mode. thus
I1   R IB
VE  VCC  I1 RC
4
I1  4.4  10
VE  4.56
RC  1000
A General Large-Signal Model For The BJT:
The Ebers-Moll Model – Example
b) For RC = 10K, assume reverse active mode
RC  10000
4
I1   R IB
I1  4.4  10
VE  VCC  I1 RC
VE  0.6
Since VE = VB, the BJT is still in the reverse active mode.
b) For RC = 100K, assume reverse saturation mode
RC  10000
Since VECsat is liekly to be very small, we can assume VE = 0, and
I1 
VCC  0
RC
4
I1  5  10
VT  25
a better estimate for VE is to use the equation below (4.115)
 1  1   I1    1  
 


 F  IB    F 
 
VECsat  VT ln 

I1   1 

1




 IB    R  

Since
I1   R IB
the BJT is saurated
VECsat
3.5
mV
A General Large-Signal Model For The BJT:
The Ebers-Moll Model – Transport Model npn BJT
The transport model of the npn BJT. This model is exactly equivalent to the Ebers-Moll model. Note that the saturation currents of the
diodes are given in parentheses and iT is defined by Eq. (4.117).
Basic BJT Digital Logic Inverter.
vi high (close to power supply) - vo low
vi low
vo high
Basic BJT digital logic inverter.
Basic BJT Digital Logic Inverter.
Sketch of the voltage transfer characteristic of the inverter circuit of Fig. 4.60 for the case RB = 10 k, RC = 1 k,  = 50, and VCC =
5V. For the calculation of the coordinates of X and Y refer to the text.
The Voltage Transfer Characteristics
(a) The minority-carrier concentration in the base of a saturated transistor is represented by line (c). (b) The minority-carrier charge
stored in the base can de divided into two components: That in blue produces the gradient that gives rise to the diffusion current across
the base, and that in gray results in driving the transistor deeper into saturation.
Complete Static Characteristics, Internal Impedances,
and Second-Order Effects – Common Base
Avalanche
Saturation
Slope
The ic-vcb or common-base characteristics of an npn transistor. Note that in the active region
there is a slight dependence of iC on the value of vCB. The result is a finite output resistance
that decreases as the current level in the device is increased.
Complete Static Characteristics, Internal Impedances,
and Second-Order Effects – Common Base
The hybrid- model, including the resistance r, which models the effect of vc on ib.
Complete Static Characteristics, Internal Impedances,
and Second-Order Effects – Common-Emitter
Common-emitter characteristics. Note that the horizontal scale is expanded around the origin to show the saturation region in some
detail.
Complete Static Characteristics, Internal Impedances,
and Second-Order Effects – Common-Emitter
An expanded view of the common-emitter characteristics in the saturation region.
The Transistor Beta
Transistor Breakdown
Internal Capacitances of a BJT
Cde
Cje
C
C
F
IC
Base charging or Diffusion capacitance
VT
Cje0

1 

Base Emitter Junction capacitance
VBE 
V0e
m


m - 0.2 - 0.5 grading coefficient
C0
m
VCB 

1  V 
0c 

Collector Base Juntion Capacitance
Cde  Cje
rx
The Cut-Off Frequency
The Spice BJT Model and Simulation Examples
The Spice BJT Model and Simulation Examples
The Spice BJT Model and Simulation Examples
The Spice BJT Model and Simulation Examples
.model Q2N2222-X NPN(
Rc=1
Is=14.34f
Cjc=7.306p
Xti=3
Mjc=.3416
Eg=1.11
Vjc=.75
Vaf=74.03
Fc=.5
Bf=200
Cje=22.01p
Ne=1.307
Mje=.377
Ise=14.34f
Vje=.75
Ikf=.2847
Tr=46.91n
Xtb=1.5
Tf=411.1p
Br=6.092
Itf=.6
Nc=2
Vtf=1.7
Isc=0
Xtf=3
Ikr=0
Rb=10)
*National pid=19
case=TO18 88-09-07 bam
creation
The Spice BJT Model and Simulation Examples
BJT Modeling - Idealized Cross Section of NPN BJT
The Spice BJT Model and Simulation Examples
12V REG
RX MIX ER
C1
0 .0 1 uF
0.1uF
C7
0.01uF
6.8pF
C21
C18
120pF
C20
C23
180pF
10uF NP
TRI XFMR
D2
R7
560
C16
Q4
2N2222A
C13
C12
0 .0 6 8u F 0 .0 4 7u F
C15
1 0u F
C14
0 .0 6 8u F
R10
1K
1mH
R13
4.7
2.0uH
L4, L5
26t AWG32 ON
AMIDON T37-6
R15
75
R3
10K
PHJACK
10uF
+
Q1
2N2222A
Q2
2N2222A
R9
100
Q3
2N2222A
RX
GAIN
HEADPHONES
(LO-Z)
12 OHM
2K/SPKR
R6
10K
F-LP = 2.5KHz / F-BP = 800Hz
0 .0 2 2u F
RX_ BFO
C6
R8
1K POT
C17
T3
TRIFILAR XFMR
3 x 10t AWG32 ON
AMIDON FT37-61
L3
C24
8-80pF
L5
C11
C10
0 .0 6 8u F 0.1uF
J1
T2
2K
L2 82mH
RC VR F ILT ER
56pF
R1
1K
R2
10K
+
C9
0 .0 4 7u F
R5
1K
C8
0 .0 1 uF
1N4148
180pF
C22
8-80pF
L4
2.0uH
82mH
C3
0.1uF
C102
0.47uF
DET_ AUD
T3
R4
3.2K
L1
+
C2
1 00 u F
S5
C5
T2
PRI: 650t AWG40
SEC: 50t AWG32
ON AMIDON
PC1408-77 POT CORE
12V REG
C101
0.47uF
D1
1N4148
C4
RF
PR EAMP
C19
BP
T1
BIF XFMR
T1
BIFILAR XFMR
2 x 10t AWG32 ON
AMIDON FT37-61
RX_ IN
LP
10uF NP
RX AUD IO AMP
R11
R14
10K
BA L
MO DULA TOR
R12
51K
27K
+
TX VFO
C25
10uF
D3
1N4148
T4
TRIFILAR XFMR
3 x 12t AWG32 ON
AMIDON FT37-61
C26
0.01uF
CARRIER
BALANCE
R16
12V REG
+
C27
100uF
L6
C?
0.01uF
C31
0.01uF
D5:
18-36pF
(6 - 1.5V)
6.95 7.35 MHz
R31
L10 1mH
C48
0.01uF
TO
LO-Z
MIC
5.6uH
R35
15.0K/1%
C47
3-36pF
TX_ ON
Q9
2N2222A
L15
100uH
C54
1000pF
T6:
PRI: 36t AWG 32
SEC: 4t AWG 32
ON AMIDON T50-6
0.022uF
33K
D8
1N4148
R44
330
R43
10K
R45
1.00K/1%
D7
1N4148
R42
15K
L17 100uH
Q13
2N2222A
R48
J2
C64
0.01uF
Q11
2N2222A
82pF
C65
0.01uF
R49
220
R50
47
16 VDC
UNREG
220uF
C75
1.0
R65
12V REG
Q17
2N2222A
10-1/2W
R66
I-LIM =
0.42A
0.1uF
1.0
R67
+
C76
47uF
8V REG ULA TOR
R68
C83
0.1uF
+
T7
12 V RE GUL ATO R
R72
357/1%
R73
475/1%
C89
D16
6.2V/1W
0.1uF
R77
475/1%
S3
0dB
TX_ ON
C70
20dB
15K
C71
Q15
2N2222A
R56
R57
15K
D14
1N4148
120pF
T8
BIF CHOKE
1.0uH
L20
1.0uH
L21
C79
4 70 p F
C80
1 00 0 pF
R60
36
R63
20
BNC
ANTENNA
50 OHMS
T9
R61
36
J5
C81
470pF
DRV_ COL L
C86
82pF
C84
0.01uF
3:1:1
C85
8-80pF
T7:
PRI: 36t AWG 32
SEC: 2 x 9t AWG 32
ON AMIDON T50-2
R70
20
R74
2K POT
220
D18
8.2V/1W
T9:
PRI: 2 x 8t AWG 26
SEC: 7t AWG 26
ON AMIDON T68-6
Q21
2N2222A
C90
2K
D17
0.1uF
0.01uF
C87
T8: BIFILAR CHOKE
2 x 8t AWG26 ON
AMIDON FT50-61
L22 22uH
1N4148
0.1uF
BIAS
(SET FOR
Ic=1.5mA
QUIESCENT)
LO W-PA SS
RF FIL TER
C88
R76
TX_ ON
R75
D19
6.2V/1W
C68
0 .0 1 uF
1mH
L19
C73
0.01uF
0.1uF
C91
RC VR
AT TEN
R53
39
5uH
R69
75.0/1%
R71
Q22
2N2222A
R52
220
C78
0.1uF
C77
47uF
0.1uF
Q20
2N2222A
470-1/2W
RX_ IN
R51
TBD
39-200
AS REQD
TO ADJ
GAIN
0.1uF
R62
20
1K
Q19
2N2222A
TX_ ON
1K
0.01uF
2K
8V REG
C82
C69
C72
0.1uF
10-1/2W
Q18
2N2222A
+
R58
20
1N4002
R64
Q16
2N2222A
R33
RX_ ON
D12
10-1/2W
S7
R55
D9
1N5822
D11
R59
1N4002
CW
R36
1K
DRV_ COL L
0.01uF
12V REG
13 VDC (BATT)
D10
DSB
51K
Q12
2N2222A
C62
8 -8 0 pF
CO NTRO L C KT
1A SB
R47
1K
C63
2N2222A
Q14
1N4002
PWR
ON/OFF
+
C58
0.1uF
DSB
0.022uF
TX_ ON
J3
F2
R30
27K
L14
1 00 u H
C61
470-1/2W
R54
1 50 0
RF
DR IVER S
2.2K
0.01uF
RX_ ON
0 .0 1 uF
TX_ ON
C60
E4
C67
0.01uF
S1
C46
10uF
T6
R46
L18 100uH
R29
R34
10K
5uH
C57
0.1uF
TX_ VFO
C66
0.01uF
R25
100
TX_ ON
C59
KEY
C38
0 .0 3 3u F
C55
0.1uF
9:1
1mH
1 2V REG
0 .0 1 uF
L16
E3
PTT
R23
100
TX AUD IO AMP
10uF NP
R39
47
L13
1 00 u H
1mH
C30
Q7
2N2222A
T5
PRI: 360t AWG40
SEC: 800t AWG40
ON AMIDON
PC1408-77 POT CORE
12V REG
TX_ ON
L7
C34
10uF
C37
T5
C43
0.1uF
C42
0 .0 4 7u F
RX_ ON
1mH
D6
1N4148
R40
3.2K
C56
0.01uF
C41
0 .0 3 3u F 0 .2 2 uF
C40
L12
Q10
2N2222A
C53
R41
USB O/S
CENTER = ZERO O/S
C74
Q5
2N2222A
Q6
2N2222A
47mH
C44
C39
0.1uF
10K
0.01uF
RX_ ON
S2
L9
R37
C51
LSB O/S
47mH
E2
R32
1K
C49
1000pF
L8
600/3K
Q8
2N2222A
L11
C52
2-22pF
J4
R20
10K
2. 75 K Hz LOW PAS S F ILT ER
C36
10uF NP
E1
R26
47
R27
27.4K/1%
C45
0.01uF
D5
42pF
R38
33.2K/1%
C35
0.01uF
VF 0 / BFO
C50
56pF
1.00M/1%
100K POT
R28
F3
1A SB
C29
10uF
R22
+
10K
12V REG
MAIN
TUNE
R19
2K
+
C33
10uF
C32
0.01uF
R24
5K POT
BANDSPREAD
DSB
D4
1N4148
100uH
8V REG
C?
0.01uF
100 POT
TRI XFMR
R18
10K
100uH
8V REG
R21
49.9K/1%
T4
R17
1K
+
L?
C28
0.1uF
1 2V REG
C92
(THERMAL COUPLING)
0.01uF
PU SH-P ULL
PO WER AMP
1. 5W P EP
+
C93
47uF
C94
0.1uF
Titl e
N5FC 2 N22 2 2 DSB/CW TRANSCEIVER
DE SIGNE D BYSiz e
M. NORTHRUP C
N5FC
Date :
Doc u me nt Num be r
{Doc}
Sunday, March 08, 1998
Rev
-She e t
1
of
2