Transcript unit2 class

Unit II
BJT Amplifiers
Outline
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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)
ib
iC
B
hie
hfeib
hreVce
ie
E
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
vout
Av 
vin
vin
zin 
iin
Calculating Av, zin, zout, and Ai of a Transistor
Amplifier
vout(OC)
• Output Impedance, zout
z out 
• Current Gain, Ai
iout
Ai 
iin
• Power Gain, Ap
iout(SC)
Pout
Ap 
Pin
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 resistance
hr = reverse transfer voltage ratio (Vi/Vo)  0
hf = forward transfer current ratio (Io/Ii)
ho = output conductance
Simplified General h-Parameter Model
hi = input resistance
hf = 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 hparameter 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
Av  
hfe RC RL 
hie
Common-Emitter Amplifier-contd…
• Circuit current gain a function of
– Same parameters, plus Fixed bias resistance, RB
hfe RB RC
Ai 
RC  RL RB  hie 
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
zin  RB hie
Common-Emitter Amplifier-contd…
• Circuit output impedance a function of
– Collector resistance (model output admittance),
hoe very low
zout  RC
Common-Emitter Fixed-Bias Configuration
The input is applied to the base
The output is taken from the
collector
High input impedance
Low output impedance
High voltage and current gain
Phase shift between input and output
is 180
Fixed-Bias-contd…
Input impedance:
Zi  RB || hie
Output impedance:
Zo  RC || 1/ hoe
Voltage gain:
Av 
Vo
h R || 1/ ho e 
  fe C
Vi
hie
Current gain:
Ai 
Io
 hfe
Ii
Emitter-Follower Configuration
Input impedance:
Zb  hfeRE
Zi  Ro || Zb
Z b  h fe R E
Z i  R o || Z b
Output impedance:
Zo  RE ||
hie
hfe
Voltage gain:
Av 
Vo
RE

Vi RE  hie / hfe
Ai 
Current gain:
h fe RB
RB  Z b
Ai   Av
Zi
RE
Common Base Configuration
Common-Base Configuration
Input impedance:
Zi  RE || hib
Output impedance:
Zo  RC
Voltage gain:
Av 
Vo
h R
  fb C
Vi
hib
Current gain:
Ai 
Io
 hfb  1
Ii
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 voltagedivider biasing & coupling capacitor)
Common-emitter amplifiers (with voltagedivider biasing & coupling capacitor)Cont’d
Common-emitter amplifiers (with voltagedivider 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)
– A z
close to hfe
Ai  
V in
RL
RS || RB
zout (Q ) 
 re
h fe  1
–
very small
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
The diode re model
can be replaced by
the resistor re.
Ie    1 Ib  Ib
re 
26 mV
Ie
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:
vB1  vB 2
But,
2iC1
2iC 2
1

iC1  iC 2  

gm
gm
gm
iCx  iBx
 vB1  vB 2 
rin 
2 iB1
gm
vB1  vB 2 2 

iB1
gm
Output Impedance
Set vIN  0  iC  0
Applying Kirchoff’s current law:
iC  iRC  iOUT  0  iOUT  iRC
By Ohm’s law:
vC
vOUT
VC  15  I RC RC 
  RC 
iRC
iRC
rOUT
vOUT
vOUT


  RC   RC
iOUT
iRC
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
I Bx  I Cx / 
• 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
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 loaded
small signal equivalent
Applications
• Differential inputs and outputs
– Useful when negative feedback is required in a multi-stage
amplifier
– Also useful for balanced signals
Noisy Channel
Transmitter
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
Rout1  1  g m RE || r rO  RE || r
Rout 2  1  g m RS rO  RS
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
Base current:
IB 
VCC  VBE
RB   D R E
Emitter current:
IE  (D  1)IB  DIB
Emitter voltage:
VE  IE RE
Base voltage:
VB  VE  VBE
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 Systems
CE-CC
• The cascade of a Common Emitter amplifier
stage followed by a Common Collector
amplifier stage can provide a good overall
voltage amplifier
Cascaded Systems
CE-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 Systems
CE-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 Systems
CE-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 Systems
R-C Coupled BJT Amplifiers
Voltage gain:
Av 1 
RC || R1 || R2 ||  Re
re
Av 2 
RC
re
Av  Av 1Av 2
Input impedance,
first stage:
Zi  R1 || R2 || Re
Output impedance,
second stage:
Zo  RC
Bipolar Cascode Stage
Rout  [1  g m (rO 2 || r 1 )]rO1  rO 2 || r 1
Rout  g m1rO1 rO 2 || r 1 
Maximum Bipolar Cascode Output Impedance
Rout , max  g m1rO1r 1
Rout , max  1rO1
• The maximum output impedance of a bipolar cascode is
bounded by the ever-present r between emitter and
ground of Q1.
Example: Output Impedance
RoutA
2rO 2 r 1

r 1  rO 2
• Typically r is smaller than rO, so in general it is
impossible to double the output impedance by
degenerating Q2 with a resistor.
PNP Cascode Stage
Rout  [1  g m (rO 2 || r 1 )]rO1  rO 2 || r 1
Rout  g m1rO1 rO 2 || r 1 
Improved Cascode Stage
Rout  g m3 rO3 (rO 4 || r 3 ) || g m2 rO 2 (rO1 || r 2 )
• In order to preserve the high output impedance, a
cascode PNP current source is used.
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 highfrequency applications.
MOS Cascode Stage
Rout  1  g m1rO 2 rO1  rO 2
Rout  g m1rO1rO 2
Improved MOS Cascode Amplifier
Ron  g m 2 rO 2 rO1
Rop  g m 3 rO 3 rO 4
Rout  Ron || Rop
• Similar to its bipolar counterpart, the output
impedance of a MOS cascode amplifier can be
improved by using a PMOS cascode current source.