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Unit II
BJT Amplifiers
Outline
• Small signal analysis of common Emitter
• Small signal analysis of common Base
• Small signal analysis of common Collector
• Differential Amplifiers-CMRR
• Darlington Amplifier
• Bootstrap Technique
• cascaded Stages,Cascode stage
Linear analog amplifier
Notation
Basic characteristics of an amplifier
Basic BJT amplifier
Analysis of BJT amplifiers
Dc analysis and equivalent circuit
Ac analysis and equivalent circuit
BJT Small-Signal Models
• h-parameter model
– More complex
– Better for ac operation
– Common Emitter model
• hie = input impedance (Ω)
• hre = reverse voltage transfer ratio (unitless)
• hfe = forward current transfer ratio (unitless)
• hoe = output admittance (S)
hfeib
B
E
hie
iC
ie
ib
hreVce
1/hoe
Calculating Av, zin, zout, and Ai of a Transistor Amplifier
• Voltage Gain, Av
– Output voltage divided by input voltage
• Input Impedance, zin
– Input voltage divided by input current
in
inin
in
outv
i
vz
v
vA
Calculating Av, zin, zout, and Ai of a Transistor Amplifier
• Output Impedance, zout
• Current Gain, Ai
• Power Gain, Ap
out(SC)
out(OC)out i
vz
in
outi i
iA
in
outp P
PA
The Hybrid Equivalent Model
Hybrid parameters are developed and used for modeling the transistor. These parameters can be found on a transistor’s specification sheet:
hi = input resistancehr = reverse transfer voltage ratio (Vi/Vo) 0 hf = forward transfer current ratio (Io/Ii)ho = output conductance
Simplified General h-Parameter Model
hi = input resistancehf = forward transfer current ratio (Io/Ii)
Common-Emitter
• General BJT circuit analysis– Find operating point
– Determine ac parameters (T- or h- models)
– Remove dc Voltage sources & replace with short circuits
– Replace coupling & bypass capacitors with short circuits
– Replace BJT with circuit model
– Solve resulting circuit
Common-Emitter Amplifier
• ac equivalent of fixed-bias CE amplifier using h-parameter model
Common-Emitter Amplifier-contd…
• Equations for h-parameter model for fixed-bias CE amplifier– Circuit voltage gain a function of• Model forward current transfer ratio, hfe
• Model input impedance, hie
• Circuit collector resistance, RC
• Circuit load resistance, RL ie
LCfev h
RRhA
Common-Emitter Amplifier-contd…
• Circuit current gain a function of– Same parameters, plus Fixed bias resistance, RB
ieBLC
CBfei hRRR
RRhA
Common-Emitter Amplifier-contd…
• Equations for h-parameter model for fixed-bias CE amplifier
– Circuit input impedance a function of
• Model forward current transfer ratio, hfe
• Model input impedance, hie
ieBin hRz
Common-Emitter Amplifier-contd…
• Circuit output impedance a function of
– Collector resistance (model output admittance), hoe very low
Cout Rz
Common-Emitter Fixed-Bias Configuration
The input is applied to the baseThe output is taken from the collector
High input impedanceLow output impedance
High voltage and current gain
Phase shift between input and output is 180
Fixed-Bias-contd…
ieBi hRZ ||
oeCo hRZ /1||
ie
oCfe
i
ov h
ehRh
V
VA
/1||
fei
oi h
I
IA
Input impedance:
Output impedance:
Voltage gain:
Current gain:
Emitter-Follower Configuration
boi
Efeb
Z||RZ
RhZ
boi
Efeb
ZRZ
RhZ
||
Input impedance:
Output impedance:
Voltage gain:
Current gain:
fe
ieEo h
hRZ ||
feieE
E
i
ov hhR
R
V
VA
/
E
ivi
bB
Bfei
R
ZAA
ZR
RhA
Common Base Configuration
Common-Base Configuration
ibEi h||RZ
Co RZ
ib
Cfb
i
ov h
Rh
V
VA
1hI
IA fb
i
oi
Input impedance:
Output impedance:
Voltage gain:
Current gain:
Hybrid pi model
• The hybrid pi model is most useful for analysis of high-frequency transistor applications.
• At lower frequencies the hybrid pi model closely approximate the re parameters, and can be replaced by them.
Small-signal hybrid-π equivalent circuit
Small-signal hybrid-π equivalent circuit (Cont’d)
Small-signal voltage gain
Input and output resistances
Common-emitter amplifiers (with voltage-divider biasing & coupling capacitor)
Common-emitter amplifiers (with voltage-divider biasing & coupling capacitor)-
Cont’d
Common-emitter amplifiers (with voltage-divider biasing & coupling capacitor &
emitter resistor)
Dc & Ac load lines
• Dc load line is used to find Q-point
• Ac load line is used to determine graphically the operation of a BJT amplifier
• Dc and ac load lines are essentially different since capacitors appear as an open circuit for a de operation but a short circuit for an ac operation
Ac load line
35
Maximum output symmetrical swing
36
Common-Collector Amplifier
• Circuit gains and impedances– Av ≈ 1
– zin = RB||zin(Q)
– close to hfe
– very small( )
||
1
V ini
L
S Bout Q e
fe
A zA
R
R Rz r
h
BJT Transistor Modeling
A model is an equivalent circuit that represents the AC characteristics of the transistor.
A model uses circuit elements that approximate the behavior of the transistor.
There are two models commonly used in small signal AC analysis of a transistor:
re model
Hybrid equivalent model
The re Transistor Model
BJTs are basically current-controlled devices.The re model uses a diode and a current source to duplicate the behavior of the transistor.
One disadvantage to this model is its sensitivity to the DC level. This model is designed for specific circuit conditions.
Common-Emitter Configuration-re model
bbe II I 1
ee I
mV26 r
The diode re model can be replaced by the resistor re.
Input and Output Impedances
An equivalent small signal circuit of a differential amplifier can be drawn as
Input Impedance
During the small signal analysis, it was shown that:
m
C
m
CCC
mBB g
igi
iig
vv 212121
221
BxCx ii But,
m
BBB g
ivv 1
21
2
mB
BBin gi
vvr
2
1
21
Output Impedance
00Set CIN iv
Applying Kirchoff’s current law:
RCOUTOUTRCC iiiii 0
RC
OUTC
RC
CCRCC i
vR
i
vRIV 15
By Ohm’s law:
CCRC
OUT
OUT
OUTOUT RR
i
v
i
vr
Coupling and Biasing
• Input and output coupling capacitors may be required to remove d.c. bias voltages
• If input coupling capacitors are used, a d.c. bias current path to the transistors’ bases must be established
• Extra base resistors accomplish this
• These will appear in parallel with the input impedance
Non-Ideal D.C. Effects
• If operation down to d.c is required, the coupling components are omitted
• This leads to some effects that are peculiar to d.c. operation:– Offset Voltage– Bias Current
Offset Voltage
• With zero differential input, the collector currents and, therefore, the collector voltages should be identical
• This assumes that:– The transistors are identical– The loads are also identical
• In practice, loads will vary and the quiescent conditions will not be perfectly symmetrical
• There will be an offset voltage between the actual output and the ideal assumption
Bias Current
• In order to bring the transistors into the active region, a small d.c. base bias current is required
• This d.c. current must be supplied by the signal source
• This is a separate issue to the current drawn by the input impedance
• Note that bias current and offset voltage effects are identical to those observed with op-amps
/CxBx II
Differential Amplifier-Common mode
Differential Amplifier-Differential mode
Differential Amplifier-Transfer Characteristics
Differential Amplifier-Emitter Resistor
Differential Amplifier-one half Equivalent Circuit
Differential Amplifier –active loaded
Differential Amplifier –active loadedsmall signal equivalent
Applications
• Differential inputs and outputs– Useful when negative feedback is required in a multi-stage
amplifier– Also useful for balanced signals
Transmitter
Noisy Channel
Noisy received signals
Difference Amp
Output
Bootsrap Technique
• The field of electronic a bootstrap circuit is one where part of the output of an amplifier stage is applied to the input, so as to alter the input impedance of the amplifier.
• When applied deliberately, the intention is usually to increase rather than decrease the impedance.
Bootsrap Technique
• The effect of a high input impedance is to reduce the input current to the amplifier.
• If the input current for a given input voltage is reduced by whatever method, the effect is to increase the input impedance.
• The emitter follower has a high input impedance, but this may be reduced to an unacceptable level by the presence of the base bias resistor.
Boosted Output Impedances
SOSmout
EOEmout
RrRgR
rRrrRgR
1
||||1
2
1
Darlington Amplifier
• One emitter follower (Tr1) to drive another (Tr2) the overall current gain becomes the product of the individual gains, hfe1 x hfe2 and can be typically 1000 or more.
• This greatly reduces the signal current required by the base of Tr1 and thereby dramatically increases the input impedance.
Darlington Amplifier(cont)
The Darlington circuit provides very high current gain, equal to the product of the individual current gains:
D = 1 2
The practical significance is that the circuit provides a very high input impedance.
DC Bias of Darlington Circuits
BDBDE III )1(
EEE RIV
EDB
BECCB RR
VVI
Base current:
Emitter current:
Emitter voltage:
Base voltage:
BEEB VVV
Feedback Pair
This is a two-transistor circuit that operates like a Darlington pair, but it is not a Darlington pair.
It has similar characteristics: • High current gain• Voltage gain near unity• Low output impedance• High input impedance
The difference is that a Darlington uses a pair of like transistors, whereas the feedback-pair configuration uses complementary transistors.
Cascaded Systems
• The output of one amplifier is the input to the next amplifier
• The overall voltage gain is determined by the product of gains of the individual stages
• The DC bias circuits are isolated from each other by the coupling capacitors
• The DC calculations are independent of the cascading
• The AC calculations for gain and impedance are interdependent
Cascaded SystemsCE-CC
• The cascade of a Common Emitter amplifier stage followed by a Common Collector amplifier stage can provide a good overall voltage amplifier
Cascaded SystemsCE-CC
• The Common Emitter input resistance is relatively high and Common Collector output resistance is relatively low.
• The voltage follower second stage, Q2, contributes no increase in voltage gain but provides a near voltage-source (low resistance) output so that the gain is nearly independent of load resistance.
Cascaded SystemsCE-CC
• The high input resistance of the Common Emitter stage, Q1, makes the input voltage nearly independent of input-source resistance.
• Multiple Common Emitter stages can be cascaded with emitter follower stages inserted between them to reduce the attenuation due to inter-stage loading.
Cascaded SystemsCE-CE
•Each stage is separately biased and coupled to adjacent stages via DC blocking capacitors.
•Inserting coupling capacitors between stages blocks the DC operating bias level of one stage from affecting the DC operating point of the next.
Cascaded SystemsR-C Coupled BJT Amplifiers
Co RZ
Input impedance, first stage:
Output impedance, second stage:
Voltage gain:
ei RRRZ |||| 21
21
2
211
||||||
vvv
e
Cv
e
eCv
AAA
r
RA
r
RRRRA
Bipolar Cascode Stage
1211
12112
||
||)]||(1[
rrrgR
rrrrrgR
OOmout
OOOmout
Maximum Bipolar Cascode Output Impedance
• The maximum output impedance of a bipolar cascode is bounded by the ever-present r between emitter and ground of Q1.
11max,
11max, 1
Oout
Omout
rR
rrgR
Example: Output Impedance
• Typically r is smaller than rO, so in general it is impossible to double the output impedance by degenerating Q2 with a resistor.
21
122
O
OoutA rr
rrR
PNP Cascode Stage
1211
12112
||
||)]||(1[
rrrgR
rrrrrgR
OOmout
OOOmout
Improved Cascode Stage
• In order to preserve the high output impedance, a cascode PNP current source is used.
)||(||)||( 21223433 rrrgrrrgR OOmOOmout
Cascode Connection
This example is a CE–CB combination. This arrangement provides high input impedance but a low voltage gain.
The low voltage gain of the input stage reduces the Miller input capacitance, making this combination suitable for high-frequency applications.
MOS Cascode Stage
211
21211
OOmout
OOOmout
rrgR
rrrgR
Improved MOS Cascode Amplifier
• Similar to its bipolar counterpart, the output impedance of a MOS cascode amplifier can be improved by using a PMOS cascode current source.
oponout
OOmop
OOmon
RRR
rrgR
rrgR
||
433
122
