BJT - Principles of Operation
• Different concentrations of donors and acceptors in BJT regions
PE >> NB >> PC
• Very narrow base thickness compared with diffusion length LD
WB << LD
Emitter
(p++)
Base
(n+)
Collector
(p)
Typical Doping [1/cm3]: PE~1020; NB~1018; PC~1017
• Current gain β = ∆iC / ∆iB
P
β≈ E
NB
 WB 

⋅ 1 −
LD 

Bipolar Junction Transistor (BJT)
Symbolic representation of BJT in circuits
VCB
IC
Collector
IB
VCE
Base
VBE
IE
Emitter
• BJT is a three-terminal device
• The “arrow” shows the direction of current in an emitter
• Only two voltages and two currents are independent
VCE = VBE+ VCB
IE = IB + IC
Identification of BJT terminals
How to recognize the terminals using Ohmmeter
• A stand alone transistor can be represented as two p-n
junctions. They can be tested separately
1) Type of BJT (n-p-n or p-n-p)
2) Which terminal is the base
n
Base
p
n
p
Base
n
p
3) Which one is the emitter
• Emitter-Base is the most heavily doped p-n junction
Reverse Bias Resistance of B-E junction is much
lower than that of C-E junction: RBE << RCE
Types of BJT
• There are two basic types of BJT
n-p-n
p-n-p
and
C
n-type
B
p-type
C
p-type
B
n-type
E
n-type
E
p-type
• This notation comes from the type and sequence of the
semoconductor layers
• Direction of the “arrow” specifies the type of BJT in
circuit diagrams
Regimes of BJT
Forward active
•
•
+
iC
n
VCB > 0
p
iB
+
iE
VBE >0
-
N
• B-E junction is forward biased, the typical VBE ≈ 0.7 V
• C-B junction is reverse biased
• The most remarkable propety is that collector current
reflects the base current
∆iC = β . ∆iB
• Typical current gain β ~ 70-200
•
Collector and emitter currents close to each other iC ≈ iE
Family of Input characteristics of BJT
n-p-n
iB=f(VBE)
iC
VCE
+
+
VBE
VCE=const
iB (µA)
30
VCE=10V
VCE=0
VCE=5V
∆iB
1
=
rπ ∆VBE
20
10
0.7
VBE (V)
• Input characteristic is a weak function of VCE
• iB(VBE) can be approximated as a step function at VBE ≈0.7V
Family of Output characteristics of BJT
iC=f(VCE)
n-p-n
iB=const
VCE
+
+
VBE
-
iC (mA)
30 µA
3
20 µA
2
iB=10 µA
1
0.5
5
10
• Saturation region: VCE < 0.5V
• Active region: iC is a weak function of VCE
15
VCE (V)
Small signal parameters of BJT
collector
base
iC=β iB
iC =gm VBE
r0
rπ
emitter
• Current gain (empirical parameter) β ≈
• Transconductance gm=iC/VT
gm ≈
• Input resistance rπ = β/gm= VT/iB rπ ≈
• Output resistance r0 =VA/ iC
r0 ≈
iC
10…500
0.1…2A/V
10Ω…1kΩ
1…100 kΩ
1/ r0
Early voltage VA
VA ≈ 100…200 V
0
VCE
Configurations of BJT in stages
Vin
Vout
• One node in common for input and output circuits
Common emitter
Common Collector
Common Base
Biasing of BJT with constant iB
• A FORWARD ACTIVE regime requires a forward
biased B-E junction and a reverse biased C-B junction
RB*
iC
iB
+VCC
VBE ≈ 0.7V
• RB defines the base current in steady state conditions
iB =
VCC − 0.7
RB
Loading of BJT
• RC converts the current iC into output voltage
RB
RC
*
iC
+VCC
iB
VCE
VBE ≈ 0.7V
• The voltage drop across RC decreases VCE
VCE = VCC – iC.RC
Biasing of BJT with constant VBE
•
The voltage divider (R1, R2) stabilises VBE
+VCC
RC
R1
i1
iC
iB
R2
VBE
• The values of R1 and R2 are chosen:
1) to satisfy i1 >> iB
2) to provide proper biasing
VCC
>> iB
R1 + R2
VBE = VCC
R2
= 0.7V
R1 + R2
Thermal stabilization with RE
• Introducing RE is an effective way of thermal
stabilization of iC
+VCC
RC
R1
VB = const
VBE
R2
RE
VRE = RE iE
• Increase of iC with temperature increases the voltage
drop across RE and leads to the reduction of VBE, iB and iC
respectively
VB = VBE +iERE = const
High gain with good temperature stability
• Capacitor CE shunts RE for AC (signal) current
iC
RC
R1
CE
R2
RE
DC
AC
• The capacitor value should be large enough to short out
RE at the lowest frequency fL of AC signal
CE >>
1
2πf L RE
BJT gain stage
Amplitude and phase relationships
VC = VCC - iCRC
VE = iERE ≈ +iCRE
∆V
B
∆VC
t
VCC
+10V
t
iC
R1
8k2
RG C
1
100k
RC
2k
VC
VB
VCE
VOUT
VE
VIN
R2
2k
E
V∆V
OU
∆VE
RE
1k
t
iE
∆VC
R
≈− C
∆VB
RE ;
∆ϕCB=1800
∆VE
=1
;
∆VB
∆ϕEB=0
BJT in gain stages
I. COMMON EMITTER
• High Voltage gain AV
+VCC
RB
• High Current gain AI
Vout
RC RB
Vin
t
t
• Inverting: ∆ϕ = 180o
II. COMMON BASE
• Voltage gain AV in high
+VCC
RB
• Low Rin, high Rout
RC
frequency bandwidth
Vout
• No Current gain: AI = 1
Vin
t
t
• Low Rin, high Rout
• Inverting: ∆ϕ = 180o
t
III. COMMON COLLECTOR
+VCC
Vin
RB
• High Rin, low Rout
• No Voltage gain: AV = 1
Vout
• High Current gain AI
t
R
RE
t
• Non-inverting: ∆ϕ = 0o
Small signal parameters of BJT stage
+VCC (const)
∆iRc
∆iR1
∆Vout
∆Vin
∆iro
∆iR2
R1
rπ
∆iB
R2
Rin = R1 || R2 || rπ
rπ
ro
Rout = RC || ro
• For AC current the resistances are connected in
parallel
r0
RC
Temperature dependence of BJT
characteristics
• The input characteristic is a strong function of
temperature
iB (µA)
30
T2 > T1
T1
20
10
- 2mV/oC
0.7
VBE (V)
• Current gain β increases with temperature
Steady state collector current iC requires
temperature stabilization
BJT equivalent circuit for small signals
BJT Input Resistance rπ
⇒
B
B
Vin
~
Vin
E
0.7 V
rπ
~
E
rπ is a differential input resistance
Operating point
(bias)
IB
10 µA
Iin
∂I B
1
=
rπ ∂VBE
0.7 V
Vin
VBE
VBE= 0.7 + Vincos(ωt)
IB= 10 + Iincos(ωt)
Vin
rπ =
I in
BJT equivalent circuit for small signals
BJT Output Resistance r0
~
C Vout
⇒
5V
Vout
C
r0
E
~
E
r0 is a differential output resistance
IC
Operating point
VCE= 5 + Voutcos(ωt)
Iout
1 ∂I C
=
r0 ∂VCE
1 mA
5V
Vout
VCE
IC= 1 + Ioutcos(ωt)
Vout
r0 =
I out
Small signal parameters of BJT
base
collector
iC=β iB
iC =gm VBE
r0
rπ
emitter
• Current gain (empirical parameter) β ≈
• Transconductance gm=iC/VT
gm ≈
• Input resistance rπ = β/gm= VT/iB rπ ≈
• Output resistance r0 =VA/ iC
r0 ≈
iC
10…500
0.1…2A/V
10Ω…1kΩ
1…100 kΩ
1/ r0
Early voltage VA
VA ≈ 100…200 V
0
VCE
Stage with Common Emitter
+VCC
RB
RC
Vin
t
Vout
t
• High Voltage gain AV
• High Current gain AI
• Inverting: ∆ϕ = 180o
• Low Rin,≈ rπ
• High Rout ≈ (ro || RC)
Stage with Common Collector
• Suitable as a current buffer
+VCC
RB
Vin
Vout
Vin
VBE
VE
RE
• High input resistance Rin = Vin/iB ≈ β RE
Vin = VBE +VE = iB rπ + (iB + iC) RE =
= iB [rπ + (1+β)RE] ≈ iBβ RE
•
Low output resistance Rout
• No Voltage gain AV ≈ 1
Stage with Common Base
+VCC
RB
RC
Vout
Vin
t
• High bandwidth of voltage gain
• Low input resistance Rin,≈ rπ
• High output resistance Rout ≈ (ro || RC)
• Inverting: ∆ϕ = 180o
• No Current Gain: α = ∆iC / ∆iE ≤ 1
α=
β
≈1
β +1
Load line and Q-point of the gain stage
VCE =VCC - iC RC
• The load line can be determined using two points:
1) VCE = VCC at iC = 0
2) iC= VCC /RC at VCE = 0
Load line
iC (mA)
3
Q-point
2
iB = 20 µA
1
tan ϕ= 1/RC
0.5
5
ϕ
10
15
VCE (V)
• Quiescent (or Q) point is the intersection of the load line with
the corresponding output characteristic
• The slope of the load line equals 1/RC
• Setting the Q-point in the middle of the load line allows to
obtain the maximum swing of output signal
Load Line
Load line
iC (mA)
∆iB
30 µA
3
Q-point
2
20 µA
10 µA
1
0.5
5
10
15
∆VCE
time
• The load line defines the relationship between the
variation of iB and the variation of VBE
time
VCE (V)
Optimization of the Q-point
iC (mA)
Q1
3
Optimum Q
2
1
Q2
0.5
5
10
15
VCE (V)
• The maximum undistorted swing of the output voltage
depends on the position of Q-point
1) Optimum Q
t
2) Q1 or Q2
t
t
∆VCE
Operating point of a BJT stage
+VCC
RC
R1
VB = const
VBE
R2
VB = VCC
RE
VRE = RE iE
R2
= VBE + iE RE ≈ 0.7 + iC RE
R1 + R2
VB − 0.7
iC ≈
RE
VCE = VCC − iC [ RE + RC ]
• The desirable operating point is VCE ≈ VCC/2
Load line and Q-point for AC signal
• If capacitor CE is in parallel to RE, the AC load line is
VCE = V * − iC RC
DC Load line
iC (mA)
AC Load line
3
Q-point
iCQ
2
1
1/(RC+RE)
1/RC
0.5
5
15 VCE (V)
10
V*
VCC
max Vout
• Q-point is the same for DC and AC load lines
•
V * = VCC − iCQ RE ,
iCQ - the current corresponding to Q-point
Properties of BJT at High Frequencies
• At high frequencies the gain is mainly limited by the
diffusion time τD of minor carriers through the base
β
dB
static gain
10
3
30
102
20
10
10
slope
10 dB/dec
fT
1
0.1
1
10
100 f (GHz)
• Cut–off frequency fT corresponds to unity gain β =1
1
fT =
2πτ D
•
Gain-bandwidth product β .∆f =fT allows to estimate
the number of stages to obtain the required gain in the
specified bandwidth