ECE 271
Electronic Circuits I
Topic 5
Bipolar Junction Transistors
NJIT ECE271 Dr. Serhiy Levkov
Chap 5 - 1
Chapter Goals
• Explore physical structure of bipolar transistor
• Understand bipolar transistor action and importance of carrier transport
across base region
• Study terminal characteristics of BJT.
• Explore differences between npn and pnp transistors.
• Define four operation regions of BJT.
• Explore simplified models for each operation region.
• Study Q-point Biasing of BJT.
NJIT ECE271 Dr. Serhiy Levkov
Chap 5 - 2
Bipolar Transistor: Physical Structure
• Consists of 3 alternating layers of n- and ptype semiconductor called emitter (E), base
(B) and collector (C).
NJIT ECE271 Dr. Serhiy Levkov
Chap 5 - 3
Bipolar Transistor: Physical Structure
• Consists of 3 alternating layers of n- and ptype semiconductor called emitter (E), base
(B) and collector (C).
• Majority of current enters collector, crosses
base region and exits through emitter. A
small current also enters base terminal,
crosses base-emitter junction and exits
through emitter.
NJIT ECE271 Dr. Serhiy Levkov
Chap 5 - 4
Bipolar Transistor: Physical Structure
• Consists of 3 alternating layers of n- and ptype semiconductor called emitter (E), base
(B) and collector (C).
• Majority of current enters collector, crosses
base region and exits through emitter. A
small current also enters base terminal,
crosses base-emitter junction and exits
through emitter.
• Carrier transport in the active base region
directly beneath the heavily doped (n+)
emitter dominates i-v characteristics of BJT.
NJIT ECE271 Dr. Serhiy Levkov
Chap 5 - 5
npn Transistor and pn-junctions
• Base-emitter voltage vBE and
base-collector voltage vBC
determine currents in transistor
NJIT ECE271 Dr. Serhiy Levkov
Chap 5 - 6
npn Transistor and pn-junctions
• Base-emitter voltage vBE and
base-collector voltage vBC
determine currents in transistor
• They are said to be positive
when they forward-bias their
respective pn junctions.
NJIT ECE271 Dr. Serhiy Levkov
Chap 5 - 7
npn Transistor and pn-junctions
• Base-emitter voltage vBE and
base-collector voltage vBC
determine currents in transistor
• They are said to be positive
when they forward-bias their
respective pn junctions.
• The terminal currents are
collector current(iC ), base
current (iB) and emitter current
(iE).
NJIT ECE271 Dr. Serhiy Levkov
Chap 5 - 8
npn Transistor and pn-junctions
• Base-emitter voltage vBE and
base-collector voltage vBC
determine currents in transistor
• They are said to be positive
when they forward-bias their
respective pn junctions.
• The terminal currents are
collector current(iC ), base
current (iB) and emitter current
(iE).
• Primary difference between
BJT and FET is that iB is
significant while iG = 0.
NJIT ECE271 Dr. Serhiy Levkov
Chap 5 - 9
npn Transistor: How it Works (common emitter)
•
•
•
•
•
•
•
•
Look for relationship btw iB and iC.
Left pn junction is forward biased – open.
Right pn junction is reverse biased – closed.
If those would be regular diodes – no current
would exist btw emitter and collector.
But the width of the base is very narrow, two
back-to-back pn junctions are tightly coupled.
Electrons injected from emitter into base
region rush through it and are removed by
collector, creating collector current IC.
Some of the electrons will travel to the base,
creating base current IB .
Base current is usually quite smaller: iB  iC / b
where b is the common-emitter current gain
usually is in the range 50 to 200.
Thus transistor works as a current amplifier:
iC  b iB
Simulation: http://learnabout-electronics.org/bipolar_junction_transistors_05.php
NJIT ECE271 Dr. Serhiy Levkov
Chap 5 - 10
npn Transistor: How it Works (common base)
•
•
•
•
•
•
Left pn junction is forward biased – open.
Right pn junction is reverse biased – closed.
Similarly, since the width of the base is very
narrow, electrons injected from emitter into the
base region rush through it and are removed by
collector, creating collector current IC.
Some of the electrons will travel to the base,
creating base current IB .
Base current is usually quite small.
Considering transistor as a super node:


iE  iB  iC  iC / b  iC  iC  1 1  iC /


where
0.95   
b


b 1.0
b 1
is common-base current gain.
Look for relationship btw iE and iC.
NJIT ECE271 Dr. Serhiy Levkov
Chap 5 - 11
npn Transistor Model: Forward Characteristics
BJT is almost symmetrical, except
that usually emitter is more
heavily doped then collector.
Thus we consider two models:
1) when BE is forward biased and
BC is zero biased (forward
characteristics)
NJIT ECE271 Dr. Serhiy Levkov
Chap 5 - 12
npn Transistor Model: Forward Characteristics
BJT is almost symmetrical, except
that usually emitter is more
heavily doped then collector.
Thus we consider two models:
1) when BE is forward biased and
BC is zero biased (forward
characteristics)
2) when BC is forward biased
and BE is zero biased (reverse
characteristics).
NJIT ECE271 Dr. Serhiy Levkov
Chap 5 - 13
npn Transistor Model: Forward Characteristics


S 




 BE 


 T 
v
Forward transport current is iC  iF  I exp V





1
Where IS is saturation current 1018 A  IS 109 A

VT = kT/q =0.025 V at room temperature

BJT is almost symmetrical, except
that usually emitter is more
heavily doped then collector.
Thus we consider two models:
1) when BE is forward biased and
BC is zero biased (forward
characteristics)
2) when BC is forward biased
and BE is zero biased (reverse
characteristics).
NJIT ECE271 Dr. Serhiy Levkov
Chap 5 - 14
npn Transistor Model: Forward Characteristics


S 




 BE 


 T 
v
Forward transport current is iC  iF  I exp V





1
Where IS is saturation current 1018 A  IS 109 A

VT = kT/q =0.025 V at room temperature

Base current:
BJT is almost symmetrical, except
that usually emitter is more
heavily doped then collector.
iB 
iF




F 
IS
vBE  
exp
1
VT  




bF b
10  b F  500 is forward common-emitter
current gain
Thus we consider two models:
1) when BE is forward biased and
BC is zero biased (forward
characteristics)
2) when BC is forward biased
and BE is zero biased (reverse
characteristics).
NJIT ECE271 Dr. Serhiy Levkov
Chap 5 - 15
npn Transistor Model: Forward Characteristics


S 




 BE 


 T 
v
Forward transport current is iC  iF  I exp V





1
Where IS is saturation current 1018 A  IS 109 A

VT = kT/q =0.025 V at room temperature

Base current:
BJT is almost symmetrical, except
that usually emitter is more
heavily doped then collector.
Thus we consider two models:
1) when BE is forward biased and
BC is zero biased (forward
characteristics)
2) when BC is forward biased
and BE is zero biased (reverse
characteristics).
NJIT ECE271 Dr. Serhiy Levkov
iB 
iF




F 
IS
vBE  
exp
1
VT  




bF b
10  b F  500 is forward common-emitter
current gain
Emitter current is given by
iE  iC  iB 



F 
IS
vBE  
exp
1
VT  





bF
0.95 F 
1.0 is forward commonb F 1
base current gain
Chap 5 - 16
npn Transistor Model: Forward Characteristics


S 




 BE 


 T 
v
Forward transport current is iC  iF  I exp V





1
Where IS is saturation current 1018 A  IS 109 A

VT = kT/q =0.025 V at room temperature

Base current:
BJT is almost symmetrical, except
that usually emitter is more
heavily doped then collector.
Thus we consider two models:
1) when BE is forward biased and
BC is zero biased (forward
characteristics)
2) when BC is forward biased
and BE is zero biased (reverse
characteristics).
NJIT ECE271 Dr. Serhiy Levkov
iF
iB 




F 
IS
vBE  
exp
1
VT  




bF b
10  b F  500 is forward common-emitter
current gain
Emitter current is given by
iE  iC  iB 



F 
IS
vBE  
exp
1
VT  





bF
0.95 F 
1.0 is forward commonb F 1
base current gain
In the forward active operation region:
iC  bF iB ,
iC  F iE
Chap 5 - 17
npn Transistor Model: Reverse Characteristics
Reverse transport current is


S 




 BC 


 T 
v
iR  iE  I exp
V





1

NJIT ECE271 Dr. Serhiy Levkov
Chap 5 - 18
npn Transistor Model: Reverse Characteristics
0  b R 10
is reverse common-emitter
current gain
Reverse transport current is


S 









 BC 


 T 
v
iR  iE  I exp
V
1
Base current is given by

iR
IS







 BC 


 T 
v
iB 

exp
V
bR bR

NJIT ECE271 Dr. Serhiy Levkov





1
Chap 5 - 19
npn Transistor Model: Reverse Characteristics
0  b R 10
is reverse common-emitter
current gain
Base currents in forward and reverse modes
are different due to asymmetric doping levels
in emitter and collector regions.
Reverse transport current is


S 









 BC 


 T 
v
iR  iE  I exp
V
1
Base current is given by

iR
IS







 BC 


 T 
v
iB 

exp
V
bR bR

NJIT ECE271 Dr. Serhiy Levkov





1
Chap 5 - 20
npn Transistor Model: Reverse Characteristics
0  b R 10
is reverse common-emitter
current gain
Base currents in forward and reverse modes
are different due to asymmetric doping levels
in emitter and collector regions.
Emitter current is given by
IS
Reverse transport current is


S 









 BC 


 T 
v
iR  iE  I exp
V
1







 BC 


 T 
v
iC  
exp
V
R





1
bR
0  R 
 0.95
b R 1
is reverse commonbase current gain
Base current is given by

iR
IS







 BC 


 T 
v
iB 

exp
V
bR bR

NJIT ECE271 Dr. Serhiy Levkov






1
In the reverse active operation region:
iE  bRiB ,
iE  RiC
Chap 5 - 21
pnp Transistor: Structure
• Voltages vEB and vCB are positive when they forward bias their
respective pn junctions.
• Collector current and base current exit transistor terminals and
emitter current enters the device.
NJIT ECE271 Dr. Serhiy Levkov
Chap 5 - 22
pnp Transistor: Forward Characteristics
Base current is given by
iB 

Forward transport current is


S 




 EB 


 T 
v
iC  iF  I exp
V





iF
bF

IS
bF







 EB 


 T 
v
exp
V





1
Emitter current is given by

v
1 
 exp  EB
iE  iC  iB  I S 1 
b F 

 VT
 vEB  
IS 
  1

exp 
 F 
 VT  
1
0.95 F 
 
  1
 
bF
1.0
b F 1

NJIT ECE271 Dr. Serhiy Levkov

Chap 5 - 23
pnp Transistor: Reverse Characteristics
Base current is given by
iF
IS







 CB 


 T 
v
iB 

exp
V
bR bR

iC   I 1
 IS
Reverse transport current is


 CB 


 T 
v
iR  iE  I exp
V
1
Emitter current is given by



S




S 













b



R 
0  R 


 CB 




 T 
v
exp
V


 CB 




 T 
v
exp
V
1






R 
1




1




1
bR
 0.95
b R 1

NJIT ECE271 Dr. Serhiy Levkov
Chap 5 - 24
Operation Regions of Bipolar Transistors
Binary Logic States
NJIT ECE271 Dr. Serhiy Levkov
Chap 5 - 25
i-v Characteristics of BJT (Recall MOSFET)
NJIT ECE271 Dr. Serhiy Levkov
Chap 5 - 26
i-v Characteristics of BJT (npn):
Common-Emitter Output Characteristics
Circuit to measure output characteristic:
For iB = 0, transistor is cutoff.
When iB > 0, and increases, iC also increases.
For vCE > vBE, npn transistor is in forward-active
region, iC = bF iB is independent of vCE.
For vCE < vBE, transistor is in saturation (the voltage
btw
npn
collector and emitter is small, base collector diode conducts).
For pnp, iC vs. vEC
For vCE < 0, roles of collector and emitter reverse.
NJIT ECE271 Dr. Serhiy Levkov
Chap 5 - 27
i-v Characteristics of BJT (pnp):
Common-Emitter Output Characteristics
Circuit to measure output characteristic:
NJIT ECE271 Dr. Serhiy Levkov
Chap 5 - 28
i-v Characteristics of BJT (npn):
Common-Emitter Transfer Characteristic
Defines relation between collector current
and base-emitter voltage of transistor.
Almost identical to transfer characteristic
of pn junction diode
Setting vBC = 0 in the collector-current
expression yields


S 




 BE 


 T 
v
iC  I exp
V





1
Collector
current expression has the same

form as that of the diode equation
NJIT ECE271 Dr. Serhiy Levkov
Chap 5 - 29
Simplified Cutoff Region Model
The full BJT model is the so called Gummel-Poon transport model, which is relatively
complicated. For our purpose, it will be enough to use the simplified model.
NJIT ECE271 Dr. Serhiy Levkov
Chap 5 - 30
Simplified Cutoff Region Model
The full BJT model is the so called Gummel-Poon transport model, which is relatively
complicated. For our purpose, it will be enough to use the simplified model.
In cutoff region both junctions are reverse-biased, transistor is off state: vBE < 0, vBC < 0
If we assume that vBE  4VT and
vBC  4VT , where VT = kT/q =0.025 and
-4kT/q = -0.1 V, then exp(vBE / VT ) <exp(-4)<0.02, and the transport model terminal
current equations simplifies:
iC  
NJIT ECE271 Dr. Serhiy Levkov
IS
bR
,
iE  
IS
bF
, iB  
IS
bF

IS
bR
Chap 5 - 31
Simplified Cutoff Region Model
The full BJT model is the so called Gummel-Poon transport model, which is relatively
complicated. For our purpose, it will be enough to use the simplified model.
In cutoff region both junctions are reverse-biased, transistor is off state: vBE < 0, vBC < 0
If we assume that vBE  4VT and
vBC  4VT , where VT = kT/q =0.025 and
-4kT/q = -0.1 V, then exp(vBE / VT ) <exp(-4)<0.02, and the transport model terminal
current equations simplifies:
iC  
IS
bR
,
iE  
IS
bF
, iB  
IS
bF

IS
bR
As will be shown in the example (next slide) those currents are so small that for
practical purposes, they are essentially zero. Thus, equivalent circuit:

NJIT ECE271 Dr. Serhiy Levkov

Chap 5 - 32
Simplified Cutoff Region Model (Example)
•
•
•
•
Problem: Estimate terminal currents using simplified transport model
Given data: IS = 10-16 A, F = 0.95, R = 0.25, VBE = 0 V, VBC = -5 V
Assumptions: Simplified transport model assumptions
Analysis: From given voltages, we know that transistor is in cutoff.



S 


IC  I 1





R 
16
1
b

IS
R
 4 1016 A
I E  IS 10 A
IS
IB  
 31016 A
bR

NJIT ECE271 Dr. Serhiy Levkov
For practical purposes, all three
currents are essentially zero.
Chap 5 - 33
Simplified Forward-Active Region: Model
In forward-active region, emitter-base junction is forward-biased and collectorbase junction is reverse-biased: vBE > 0, vBC < 0
The simplified transport model terminal current equations:


 BE  ,


 T 
v
iC  IS exp
V
and
v 
IS
iE  exp  BE  ,
V 
F
 T 
v 
IS
iB  exp  BE 
V 
bF
 T 
iC  bF iB , iE  (bF 1)iB , iC   F iE
Conclusion. All currents are independent of the base-collector voltage vBC .
The collector current can be modeled as a current source that is controlled by
the base-emitter voltage.
NJIT ECE271 Dr. Serhiy Levkov
Chap 5 - 34
Simplified Forward-Active Region: Circuit
NL
CVD
• Current in base-emitter diode is amplified by common-emitter current gain
bF and appears at collector; base and collector currents are exponentially
related to base-emitter voltage.
NJIT ECE271 Dr. Serhiy Levkov
Chap 5 - 35
Simplified Forward-Active Region: Circuit
NL
CVD
• Current in base-emitter diode is amplified by common-emitter current gain
bF and appears at collector; base and collector currents are exponentially
related to base-emitter voltage.
• For simplicity, base-emitter diode can be replaced by constant voltage drop
model (VBE = 0.7 V) since it is forward-biased in forward-active region.
NJIT ECE271 Dr. Serhiy Levkov
Chap 5 - 36
Simplified Forward-Active Region: Circuit
or
NL
CVD
• Current in base-emitter diode is amplified by common-emitter current gain
bF and appears at collector; base and collector currents are exponentially
related to base-emitter voltage.
• For simplicity, base-emitter diode can be replaced by constant voltage drop
model (VBE = 0.7 V) since it is forward-biased in forward-active region.
• Like with the diode, using NL model circuit, requires solving nonlinear
diode equation in combination with other equations for the circuit in order
to find vBE , iB and iC .
NJIT ECE271 Dr. Serhiy Levkov
Chap 5 - 37
Simplified Forward-Active Region: Circuit
NL
CVD
• Current in base-emitter diode is amplified by common-emitter current gain
bF and appears at collector; base and collector currents are exponentially
related to base-emitter voltage.
• For simplicity, base-emitter diode can be replaced by constant voltage drop
model (VBE = 0.7 V) since it is forward-biased in forward-active region.
• Like with the diode, using NL model circuit, requires solving nonlinear
diode equation in combination with other equations for the circuit in order
to find vBE , iB , iC , and iE .
• When using CVD model, vBE is postulated as 0.7V, and iB , iC , and iE are
found in combination with other equations for the circuit.
NJIT ECE271 Dr. Serhiy Levkov
Chap 5 - 38
Simplified Forward-Active Region Model
(Example 1)
• Problem: Estimate terminal currents and base-emitter voltage
• Given data: IS =10-16 A, F = 0.95, VBC = VB - VC = -5 V, IE = 100 mA
• Assumptions: Simplified transport model assumptions, room
temperature operation, VT = 25.0 mV
Do example on the board
NJIT ECE271 Dr. Serhiy Levkov
Chap 5 - 39
Simplified Forward-Active Region Model
(Example 1)
• Problem: Estimate terminal currents and base-emitter voltage
• Given data: IS =10-16 A, F = 0.95, VBC = VB - VC = -5 V, IE = 100 mA
• Assumptions: Simplified transport model assumptions, room
temperature operation, VT = 25.0 mV
• Analysis: Current source forward-biases base-emitter diode, VBE > 0,
VBC < 0, we know that transistor is in forward-active operation region.
IC  F I E  0.95100mA  95mA
F
0.95
bF 

19
1  F 1 0.95
I
100mA
IB  E 
 5mA
b F 1
20






VBE VT ln
NJIT ECE271 Dr. Serhiy Levkov


 F I E 
IS
 0.69V




Chap 5 - 40
Simplified Forward-Active Region Model
(Example 2)
• Problem: Estimate terminal currents, base-emitter and base-collector
voltages.
• Given data: IS = 10-16 A, F = 0.95, VC = +5 V, IB = 100 mA
• Assumptions: Simplified transport model assumptions, room
temperature operation, VT = 25.0 mV
Do example on the board
NJIT ECE271 Dr. Serhiy Levkov
Chap 5 - 41
Simplified Forward-Active Region Model
(Example 2)
• Problem: Estimate terminal currents, base-emitter and base-collector
voltages.
• Given data: IS = 10-16 A, F = 0.95, VC = +5 V, IB = 100 mA
• Assumptions: Simplified transport model assumptions, room
temperature operation, VT = 25.0 mV
• Analysis: Current source causes base current to forward-bias baseemitter diode, VBE > 0, VBC <0, we know that transistor is in forward-active
operation region.
IC  bF IB 19100mA 1.90mA
I E  (bF 1)IB  20100mA  2.00mA






I






VBE VT ln C  0.764V
I
S
VBC VB VC VBE VC  4.24V
NJIT ECE271 Dr. Serhiy Levkov

Chap 5 - 42
Simplified Forward-Active Region Model
(Example 3)
• Problem: Find Q-point
• Given data: bF = 50, bR = 1 VBC = VB - VC = -9 V
• Assumptions: Forward-active region of operation, VBE = 0.7 V
Do example on the board
NJIT ECE271 Dr. Serhiy Levkov
Chap 5 - 43
Simplified Forward-Active Region Model
(Example 3)
•
•
•
•
Problem: Find Q-point
Given data: bF = 50, bR = 1 VBC = VB - VC = -9 V
Assumptions: Forward-active region of operation, VBE = 0.7 V
Analysis:
VBE  8200I E V EE  0
8.3V
I E 
1.01 mA
8200
I
1.02mA
IB  E 
19.8 mA
b F 1
51
IC  bF IB  0.990 mA
VCE VCC  I R (VBE )
C C
9 0.99mA(4.3K ) 0.7  5.44 V

NJIT ECE271 Dr. Serhiy Levkov
Chap 5 - 44
Simplified Reverse-Active Region: Model
In reverse-active region, base-collector junction is forward-biased and baseemitter junction is reverse-biased: vBE < 0, vBC > 0
The simplified transport model terminal current equations are:
v

vBC 
BC

,
iC  
exp
, iE   I S exp 

 V 
VT 
R
T 

IS
and




iE  bRiB ,
vBC 
iB 
exp
VT 
bR
IS




iE  RiC
Conclusion. All currents are independent of the base-collector voltage vBE .
The emitter current can be modeled as a current source that is controlled by the
base-collector voltage.
NJIT ECE271 Dr. Serhiy Levkov
Chap 5 - 45
Simplified Reverse-Active Region: Circuit
or
NL
CVD
• Current in base-collector diode is amplified by the gain bR and appears at
collector; base and collector currents are exponentially related to basecollector voltage.
NJIT ECE271 Dr. Serhiy Levkov
Chap 5 - 46
Simplified Reverse-Active Region: Circuit
or
NL
CVD
• Current in base-collector diode is amplified by the gain bR and appears at
collector; base and collector currents are exponentially related to basecollector voltage.
• Base-collector diode can be replaced by constant voltage drop model
(VBC = 0.7 V) since it is forward-biased in reverse-active region.
NJIT ECE271 Dr. Serhiy Levkov
Chap 5 - 47
Simplified Reverse-Active Region: Circuit
or
NL
CVD
• Current in base-collector diode is amplified by the gain bR and appears at
collector; base and collector currents are exponentially related to basecollector voltage.
• Base-collector diode can be replaced by constant voltage drop model
(VBC = 0.7 V) since it is forward-biased in reverse-active region.
• Like with the diode, using NL model circuit, requires solving nonlinear diode
equation in combination with other equations for the circuit in order to find
vBC , iB , iC and iE .
NJIT ECE271 Dr. Serhiy Levkov
Chap 5 - 48
Simplified Reverse-Active Region: Circuit
or
NL
CVD
• Current in base-collector diode is amplified by the gain bR and appears at
collector; base and collector currents are exponentially related to basecollector voltage.
• Base-collector diode can be replaced by constant voltage drop model
(VBC = 0.7 V) since it is forward-biased in reverse-active region.
• Like with the diode, using NL model circuit, requires solving nonlinear diode
equation in combination with other equations for the circuit in order to find
vBC , iB , iC and iE .
• When using CVD model, vBC is postulated as 0.7V, and iB , iC and iE are
found in combination with other equations for the circuit.
NJIT ECE271 Dr. Serhiy Levkov
Chap 5 - 49
Simplified Reverse-Active Region: Example
• Problem: Find Q-point
• Given data: bF = 50, bR = 1 VBE = VB - VE = -9 V. Combination of R
and the voltage source forward biases base-collector junction.
Do example on the board
NJIT ECE271 Dr. Serhiy Levkov
Chap 5 - 50
Simplified Reverse-Active Region: Example
• Problem: Find Q-point
• Given data: bF = 50, bR = 1 VBE = VB - VE = -9 V. Combination of R
and the voltage source forward biases base-collector junction.
• Assumptions: Reverse-active region of operation, VBC = 0.7 V
• Analysis:
0.7V-(-9V)
1.01 mA
8200
IC
1.01mA
IB 

 0.505 mA
b R 1
2
I E  IB  0.505 mA
IC 

NJIT ECE271 Dr. Serhiy Levkov
Chap 5 - 51
Simplified Saturation Region Model
• In saturation region, both junctions are forward-biased, and the
transistor operates with a relatively large current and a small voltage
between collector and emitter. This is vCESAT - the saturation voltage
for the npn BJT.
• No simplified expressions exist for terminal currents other than
iC + iB = iE.
• They are determined by external circuit elements.
Simplified Model
NJIT ECE271 Dr. Serhiy Levkov
Chap 5 - 52
Nonideal BJT Behavior
•
•
•
•
•
•
Junction Breakdown Voltages. If reverse voltage across either of the two pn
junctions in the transistor is too large, the corresponding diode will break
down.
Minority Carrier Transport effects in the Base Region.
Base transit time (associated with storing minority-carrier charge Q required to
establish career gradient in base region) places upper limit on useful operating
frequency of transistor.
Diffusion Capacitance: for vBE and hence iC to change, charge stored in
base region must also change.
b-Cutoff Frequency, Transconductance and Transit Time - forwardbiased diffusion and reverse-biased pn junction capacitances of BJT cause
current gain to be frequency-dependent.
Early Effect and Early Voltage - in a practical BJT, output characteristics
have a positive slope in forward-active region; collector current is not
independent of vCE.
NJIT ECE271 Dr. Serhiy Levkov
Chap 5 - 53
Biasing for BJT
•
•
Digital logic circuits and linear amplifiers use very different operating points of
transistors.
This circuit can be either a logic
inverter or a linear amplifier
depending on a choice of Qpoint
NJIT ECE271 Dr. Serhiy Levkov
Chap 5 - 54
Biasing for BJT
• Goal of biasing is to establish known Q-point which in turn establishes
initial operating region of the transistor.
• For a BJT, the Q-point is represented by (IC, VCE) for an npn transistor
or (IC, VEC) for a pnp transistor.
• In general, during circuit analysis, we use simplified mathematical
relationships derived for a specified operation region, and the Early
voltage is assumed to be infinite.
• Two practical biasing circuits used for a BJT are:
– Four-Resistor Bias network
– Two-Resistor Bias network
• The constant VBE is not practical because of very steep iv curve and
strong dependence on temperature.
• Much better circuits are those of 4-resistor and 2-resistor biasing.
NJIT ECE271 Dr. Serhiy Levkov
Chap 5 - 55
Two-Resistor Bias Network for BJT:
• Problem: Find Q-point for pnp transistor in 2-resistor bias circuit with
given parameters.
• Given data: bF = 50, VCC = 9 V
• Assumptions: Forward-active operation region, VEB = 0.7 V
Do example on the board
NJIT ECE271 Dr. Serhiy Levkov
Chap 5 - 56
Two-Resistor Bias Network for BJT:
• Problem: Find Q-point for pnp transistor in 2-resistor bias circuit with
given parameters.
• Given data: bF = 50, VCC = 9 V
• Assumptions: Forward-active operation region, VEB = 0.7 V
• Analysis:
9 V EB 18,000IB 1000(IC  IB )
9 V EB 18,000IB 1000(51)IB
9V 0.7V
120 mA
69,000
IC  50IB  6.01 mA
IB 
V EC  91000(IC  IB ) 2.88 V
VBC  2.18 V

NJIT ECE271 Dr. Serhiy Levkov
Forward-active region operation is
correct Q-point is : (6.01 mA, 2.88 V)
Chap 5 - 57
Four-Resistor Bias Network for BJT
One of the best circuits for stabilizing the Q-point. R1 and R2 - a voltage divider
used to establish a fixed voltage at the base . RE and RC a- define the emitter current
and CE voltage.
bF  75

Do example on the board
NJIT ECE271 Dr. Serhiy Levkov
Chap 5 - 58
Four-Resistor Bias Network for BJT
One of the best circuits for stabilizing the Q-point. R1 and R2 - a voltage divider
used to establish a fixed voltage at the base . RE and RC a- define the emitter current
and CE voltage.
bF  75
Transform the left (input) part of the circuit
with using Thevenin equivalent.

R1
=4V
R1  R2
RR
REQ  R1 R2  1 2  12k 
R1  R2
VEQ  VCC
NJIT ECE271 Dr. Serhiy Levkov
Chap 5 - 59
Four-Resistor Bias Network for BJT
bF  75

Left loop:
VEQ  REQ I B VBE  RE I E  0
4  12,000I B  0.7 16,000(b F 1) I B
IB 
VEQ VBE
REQ  (b F 1) RE
IC  b F I B  201 m A,
NJIT ECE271 Dr. Serhiy Levkov

4V-0.7V
 2.68 m A
6
1.2310 
I E  (b F 1) I B  204 m A
Chap 5 - 60
Four-Resistor Bias Network for BJT
Right loop:
bF  75
VCE  VCC  RC IC  RE I E






VCE  VCC  RC 


 C

F 
RF

I  4.32 V
Left loop:
VEQ  REQ I B VBE  RE I E  0
4  12,000I B  0.7 16,000(b F 1) I B
IB 
VEQ VBE
REQ  (b F 1) RE
IC  b F I B  201 m A,
NJIT ECE271 Dr. Serhiy Levkov

4V-0.7V
 2.68 m A
6
1.2310 
I E  (b F 1) I B  204 m A
Chap 5 - 61
Four-Resistor Bias Network for BJT
Right loop:
bF  75
VCE  VCC  RC IC  RE I E






VCE  VCC  RC 
Left loop:
VEQ  REQ I B VBE  RE I E  0
4  12,000I B  0.7 16,000(b F 1) I B
•
•
•
4V-0.7V
IB 

 2.68 m A
6
REQ  (b F 1) RE 1.2310 
NJIT ECE271 Dr. Serhiy Levkov

I  4.32 V
All calculated currents are > 0
VBC = VBE - VCE = 0.7 - 4.32 = - 3.62 V
Hence, base-collector junction is reversebiased, and assumption of forward-active
region operation is correct.
VEQ VBE
IC  b F I B  201 m A,


 C

F 
RF
F. A. region correct:
Q-point is (201 mA, 4.32 V)
I E  (b F 1) I B  204 m A
Chap 5 - 62
Four-Resistor Bias Network for BJT
(load line analysis)
• Load-line for the circuit is:



C




RF 
I 12 38,200I
VCE VCC  R 
C
C
 F 

The two points needed to plot the load
line are (0, 12 V) and (314 mA, 0).
Resulting load line is plotted on
common-emitter output characteristics.
IB = 2.7 mA, intersection of
corresponding characteristic with load
line gives Q-point.
NJIT ECE271 Dr. Serhiy Levkov
Chap 5 - 63
Four-Resistor Bias Network for BJT:
Design Objectives
•
The input loop :
•
Then:
•
Also:
VEQ  I B REQ  VBE  I E RE  0, I B  I E / (b F 1)
IE 
IE 
VEQ VBE
REQ /(b F 1)  RE
VEQ VBE  REQ I B
RE


VEQ VBE
RE
VEQ VBE
RE
for
REQ
b F 1
 RE
for REQ I B  (VEQ VBE )
Thus design objectives:
• The value of REQ is usually designed small, to neglect the voltage drop in it. Then IC , IE ,
are set by VEQ , VBE , RE
• Also, VEQ is designed to be large enough that small variations in the assumed value of VBE
won’t affect IE.
• This implies that IB << IR2, so that IR1 = IR2. So base current doesn’t disturb voltage divider
action.
• This implies that IB << IE, so that Q-point is independent of base current.
NJIT ECE271 Dr. Serhiy Levkov
Chap 5 - 64
Four-Resistor Bias Network for BJT:
Design Objectives
•
From the good engineering approximation for the 4 resistor biasing:
I E  bF
•
•
•
•
REQ  b F RE

VEQ VBE
REQ
bF

VEQ VBE
 RE
RE
for
REQ
bF
 RE
From the input loop:
IE 
•
VEQ VBE
VEQ VBE  REQ I B
RE

VEQ VBE
RE
for REQ I B  (VEQ VBE )
The value of REQ is usually designed small, to neglect the voltage drop in it. Then IC , IE ,
are set by VEQ , VBE , RE
Also, VEQ is designed to be large enough that small variations in the assumed value of VBE
won’t affect IE.
This implies that IB << IR2, so that IR1 = IR2. So base current doesn’t disturb voltage divider
action.
This implies that IB << IE, so that Q-point is independent of base current.
NJIT ECE271 Dr. Serhiy Levkov
Chap 5 - 65
Four-Resistor Bias Network for BJT:
Design Guidelines
VCC
V
VEQ  CC
4
2
• Choose Thévenin equivalent base voltage
• Select R1 to set I1 = 9IB.
• Select R2 to set I2 = 10I
.
 B
R1 
V EQ
9I B
R2 

VCC V EQ
10I B

• RE is determined by VEQ and desired IC.
• RC is determined by desired VCE.

RC 
RE 
V EQ VBE
VCC VCE
IC
IC
 RE

NJIT ECE271 Dr. Serhiy Levkov
Chap 5 - 66
Four-Resistor Bias Network for BJT:
Design Example
•
•
•
•
Problem: Design 4-resistor bias circuit with given parameters.
Given data: IC = 750 mA, bF = 100, VCC = 15 V, VCE = 5 V
Assumptions: Forward-active operation region, VBE = 0.7 V
Analysis: Divide (VCC - VCE) equally between RE and RC. Thus, VE = 5 V
and VC = 10 V
RC 
RE 
VCC VC
VE
IC
 6.67 k
 6.60 k
IE
VB V E VBE  5.7 V
I
IB  C  7.5 mA
bF
I R2 10I B  75.0 m A
I R1  9I B  67.5 m A
VB
 84.4 k
9I B
V V
R2  CC B  124 k
10I B
R1 

NJIT ECE271 Dr. Serhiy Levkov
Chap 5 - 67
Four-Resistor Bias Network for BJT
Saturation region
Consider the first example, where RC is replaced with 56 kOhm
Do example on the board
NJIT ECE271 Dr. Serhiy Levkov
Chap 5 - 68
Tolerances - Worst-Case Analysis: Example (1)
Typically, tolerance of discrete transistors is 10%. 5%, 1%. In IC – 30%. Power
supply – (5-10)%. Current gain even more. Thus: the problem of tolerance analysis.
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Problem: Find worst-case values of IC and VCE.
Given data: bFO = 75 with 50% tolerance, VA = 50 V, 5 % tolerance on VCC , 10%
tolerance for each resistor.
V VBE
Analysis:
IC  I E  EQ
RE
To max IC , VEQ should be maximized, RE should
beminimized and opposite for minimizing IC.
Extremes of RE are: 14.4 kand 17.6 k.
R1
VEQ VCC
R1  R2
To maximize VEQ, VCC and R1 should be
maximized,
R2 should be minimized and

opposite for minimizing VEQ.
NJIT ECE271 Dr. Serhiy Levkov
Chap 5 - 69
Tolerances - Worst-Case Analysis: Example (2)
Extremes of VEQ are: 4.78 V and 3.31 V.
Using these values, extremes for IC are: 283 mA and 148 mA.
VCE VCC  RC IC  RE IE VCC  RC IC 

VCE VCC  RC IC VEQ VBE
VEQ VBE
RE
RE
To maximize VCE , IC and RC should be minimized, and opposite for
minimizing VEQ.

Extremes of VCE are: 7.06 V and 0.471 V
The min is actually a saturated region, hence calculated values for
VCE and IC actually not correct.
NJIT ECE271 Dr. Serhiy Levkov
Chap 5 - 70
Tolerances - Monte Carlo Analysis
• In real circuits, it is unlikely that various components will
reach their extremes at the same time, instead they will
have some statistical distribution. Hence worst-case
analysis over-estimates extremes of circuit behavior.
• In Monte Carlo analysis, values of each circuit parameter
are randomly selected from possible distributions of
parameters and used to analyze the circuit.
• Random parameter sets are generated, and the statistical
behavior of circuit is built up from the analysis of many
test cases.
NJIT ECE271 Dr. Serhiy Levkov
Chap 5 - 71
Tolerances - Monte Carlo Analysis:
Example
• Full results of Monte Carlo analysis of 500 cases of the 4-resistor bias circuit
yields mean values of 207 mA and 4.06 V for IC and VCE respectively which
are close to values originally estimated from nominal circuit elements.
Standard deviations are 19.6 mA and 0.64 V respectively.
• The worst-case calculations lie well beyond the extremes of the distributions
NJIT ECE271 Dr. Serhiy Levkov
Chap 5 - 72
BJT SPICE Model
• Besides capacitances associated with the
physical structure, additional components
are: diode current iS and substrate
capacitance CJS related to the large area pn
junction that isolates the collector from the
substrate and one transistor from the next.
• RB is resistance between external base
contact and intrinsic base region.
• Collector current must pass through RC
on its way to active region of collectorbase junction.
• RE models any extrinsic emitter
resistance in device.
NJIT ECE271 Dr. Serhiy Levkov
Chap 5 - 73
BJT SPICE Model Typical Values
Saturation Current IS = 3x10-17 A
Forward current gain BF = 100
Reverse current gain BR = 0.5
Forward Early voltage VAF = 75 V
Base resistance RB = 250 
Collector Resistance RC = 50 
Emitter Resistance RE = 1 
Forward transit time TT = 0.15 ns
Reverse transit time TR = 15 ns
NJIT ECE271 Dr. Serhiy Levkov
Chap 5 - 74