BJT Circuit Configurations
~
V be
vs
RL
Rs
V cc
Common base
~
vs
RL
Rs
V cc
Common emitter
~
vs
Rs
RL
V cc
Common collector
Common emitter current gain
BJT Current-Voltage Characteristics
VCE, V
Very small base current (~5-75 μA)
causes much higher collector current (up to 7.5 mA).
The current gain is ~ 100
BJT amplifier circuit analysis: Operating point
RL
VCE, V
Collector current depends on two circuit parameters:
the base current and the collector voltage.
At high collector voltage the collector current depends on the base
current only.
For Ibase = 40 μA, Icoll = 4 mA for any EC-E greater than 1.5 V
BJT amplifier circuit analysis: Operating point
VCC
RL
VCE
VCE, V
For an arbitrary collector voltage, collector current can be found using the KVL.
The KVL for the collector – emitter circuit, VCC = IRL×RL + VCE;
V −V
I RL = CC CE The RL current depends linearly on the collector voltage VCE
RL
Resistor RL and the C-E circuit of BJT are connected in series, hence IRL = IC
For Ib = 40 μA and VCC = 13V, the collector current IC = 4 mA
For Ib = 75 μA and VCC = 14V, the collector current IC = 4 mA
BJT amplifier gain analysis: 1
1. Input circuit
The input voltage has two components: the DC bias and the AC signal
Vin
AC signal amplitude
DC bias
Time
DC voltage component biases the base-emitter p-n junction in the forward direction
AC component is the input signal to be amplified by the BJT.
BJT amplifier gain analysis: 2
VCE, V
2. Output circuit
The collector current has two components too.
IC
AC current amplitude
Base current
DC current
DC and AC collector currents flow through the BJT
in accordance with its I-V characteristics
Time
BJT amplifier gain analysis: 3
VCE, V
The resistance of the B-E junction is very low when VBE ≥ VBE0 ≈ Vbi≈ 0.7 V.
Hence the base current IB ≅ (Vin-VBE0)/R1 = (VinDC-VBE0+VinAC)/R1
The collector current IC does not depend on the collector voltage if the latter is high
enough.
Hence, IC ≅ β IB;
The voltage drop across the load resistance R2: V2= IC R2;
The output voltage Vout = VCC - V2 = VCC - IC R2;
Vout = VCC - IC R2 = VCC - β IB R2 = VCC - β R2(VinDC-VBE0+VinAC)/R1;
In signal amplifiers only AC component of the output voltage is important:
VoutAC = - β R2VinAC/R1;
The amplifier voltage gain: kV
= VoutAC/VinAC= - β R2/R1;
BJT amplifier gain analysis: 4
VCE, V
Common emitter gain summary:
Current gain: kI = β
Voltage gain: kV
= VoutAC/VinAC= - β R2/R1;
Power gain: kP = kV × kI = - β2 ×
R2/R1
BJT design and factors affecting the performance
Base resistance and emitter current crowding in BJTs
The voltage drop along the base layer
Vbb = rbb Ib,where rbb is called the base
spreading resistance.
The p-n junction current decreases
rapidly when the voltage drops by
ΔVbb ~ Vth = kT/q
Δde
⎛ VV
⎞
⎛ qV
⎞
kT
TH
I = I S ⎜ e − 1⎟ = I S ⎜ e − 1⎟
⎜
⎟
⎝
⎠
⎝
⎠
The length of the edge region, Δde, where most of
the emitter current flows may be estimated from:
Vth = I b Rb max
Δd e
≈ I b ρb
te W
Emitter current crowding in BJTs (cont.)
Vth = I b Rb max
Δde
Δd e
≈ I b ρb
te W
1
ρb =
qN b μb
From these,
Vth te W Vth
q N b μ b te Wb
Δd e ≈
=
Ib ρb
Ib
Example
Estimate the effective emitter
length, Δde for the BJT having
the following parameters:
Ib = 50 μA;
Nb = 1017 cm-3
Δde
μb = 400 cm2/V-s
Wb = 0.1 μm
te = 100 μm
Vth
q N b μ b te Wb
Δd e ≈
Ib
Δde = 3.33 e-4 cm = 3.33 μm
Large periphery B JT Design
Base narrowing (Early effect)
The depletion width of the p-n junction depends on the applied voltage:
(Here W is the depletion region width
not the width of the base as in BJT!)
In the BJT, this effect means that the effective width of the base is less than Wb:
Weff = Wb - Xdeb - Xdcb
where Wb is the physical thickness of the base,
xdeb and xdcb are the depletion region widths from the emitter and collector sides.
The depletion widths are given by (Ne>>Nb):
⎡ 2εε 0 (Vbi − Vbe ) ⎤
xdeb = ⎢
⎥
q
N
b
⎣
⎦
1/ 2
⎡ 2εε 0 (Vbi + Vcb ) N c ⎤
x dcb = ⎢
⎥
2
qN b
⎢⎣
⎥⎦
1/ 2
xdcb is usually the most important factor since the voltage applied to collector is
high.
The doping level in collector, NDC has to be lower than that of the base, NAB, to
reduce the Early effect:
NC << NB
Due to Early effect the effective base thickness depends on the collector voltage.
In the gain expression, W should be replaced with Weff:
β rec =
2 L2p
2
Weff
The Early effect decreases the output resistance, and hence the voltage
gain of BJTs.
Punch-through breakdown in BJTs - the result of the Early effect
The punch-through breakdown voltage Vpt:
W = xdcb
q W 2 N b (N c + N b )
V pt =
2 εε 0
Nc
BJT Model
• Gummel-Poon model used in SPICE and other
simulators
Ie
Ic
Applying KCL to the BJT terminals:
Ie = Ic + Ib
Collector – emitter current relationship:
Ic = α Ie
Ib
where α is called a common base current gain
Hence,
I c = α ( I c + Ib )
α
Ic =
Ib
1−α
Common emitter current
gain is defined as:
I c = β Ib
α
β=
1−α
β
α=
1+ β
The last two expressions link common emitter and common base current gains
Simplified Gummel-Poon BJT equivalent circuit
αnIe
αiIc
Ic
Ie
Emitter
Ideal diode
Ideal diode
Leakage diode
Collector
Leakage diode
Base
• Emitter junction:
⎛ Vbe ⎞ ⎤
I se ⎡
I be =
⎢exp ⎜
⎟ − 1⎥
β F ⎣ ⎝ nFVth ⎠ ⎦
• Collector junction:
⎛ Vbc ⎞ ⎤
I sc ⎡
I bc =
⎢exp ⎜
⎟ − 1⎥
β R ⎣ ⎝ nRVth ⎠ ⎦
Vth = kT/q = 0.026 V at 300 K
Gummel-Poon BJT equivalent circuit accounting
for the leakage currents
αnIe
αiIc
Ic
Ie
Emitter
Ideal diode
Ideal diode
Leakage diode
Collector
Leakage diode
Base
•Emitter –base leakage
Collector –base leakage diode:
diode:
I Leak _ be
⎡
⎛ Vbe ⎞ ⎤
= I se ⎢exp ⎜
⎟ − 1⎥
⎝ nEVth ⎠ ⎦
⎣
I Leak _ bc
⎡
⎛ Vbc ⎞ ⎤
= I sc ⎢exp ⎜
⎟ − 1⎥
⎝ nCVth ⎠ ⎦
⎣