FYSE400 ANALOG ELECTRONICS
LECTURE 12
Feedback Amplifiers
1
FEEDBACK AMPLIFIERS
Approximate analysis of a feedback amplifier Assumptions
1. The basic amplifier is unilateral.
2. The gain AOL of the basic amplifier is determined without feedback.
2
3. The calculated gain AOL is loaded gain : loading of the feedback network,
source and load resistanses are noticed.
4. The feedback network is unilateral.
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Outline of Analysis
1. Identify the topology → Xf is current or voltage.
2. Draw the basic amplifier circuit without feedback
Replace each active device by its proper model.
Identify Xf and Xo on the circuit obtained.
FEEDBACK AMPLIFIERS
Approximate analysis of a feedback amplifier
3
Identify Xf and Xo on the circuit obtained.
3. Evaluate : of XX====β
Evaluate AOL by applying KVL and KCL to the equivalent circuit obtained.
4. From AOL and β, find T and AF
5. From the equivalent circuit find RID and ROD. Apply the Backman's
impedance formula to obtain RIF and ROF.
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Topology of a system
First step Identify input loop
It contains Vs , and (a) base-to-emitter region of the bipolar transistor.
(b) gate-to-source region of the first FET in the amplifier
(c) the section between the two inputs of a differential or
operational amplifier.
FEEDBACK AMPLIFIERS
Approximate analysis of a feedback amplifier
Input
4
Topology of input loop Series topology
In the input circuit, there is a circuit component W in series
with Vs .
And W is connected to the output (portion of the system
containing the load).
Voltage across W is feedback signal ff VX ====⇒⇒⇒⇒
( Voltage source Vs )
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Topology of input loop Shunt topology
Define input node
( Current source Is )
Topology of a system
FEEDBACK AMPLIFIERS
Approximate analysis of a feedback amplifier
First step Identify input loopInput
5
(a) The base of the first BJT
(b) The gate of the first FET
(c) The inverting terminal of a differential
or operational amplifier.
Shunt topology if there is a connection between the input
node and the output circuit.
The current in this connection is the feedback signalff IX ====
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The voltage Vo (with respect to ground) at the output node appears
across the load resistor (RL) and output current Io is the current in RL.
Topology of a system
Topology of output loop Shunt topology
FEEDBACK AMPLIFIERS
Approximate analysis of a feedback amplifier
Second step Define Output NodeOutput
6
( Voltage sampling )
Set Vo = 0 (RL → 0) (short-circuiting the output)
0X f →→→→⇒⇒⇒⇒ ⇒⇒⇒⇒
( Current sampling )
Set Io = 0 (RL → ∞) (open-circuiting the output)
0X f →→→→⇒⇒⇒⇒
Topology of output loop Series topology
⇒⇒⇒⇒
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Amplifier without feedback
AOL
Calculate the gain of the basic amplifier without feedback but taking the
loading of the β network into account.
Modify circuit first
Input circuit :
Output topology is shunt Output topology is series
βand
FEEDBACK AMPLIFIERS
Approximate analysis of a feedback amplifier
Third step
7
0=oV
Output topology is shunt
Short-circuit output node →
Voltage sampling
Output topology is series
0=oIOpen-circuit the output loop →
Current sampling
Output circuit :
0Vi ====Short-circuit input node →
Input topology is shunt
Current comparison
(none of the feedback current
enters to the amplifier input)
0Ii ====Open-circuit the input loop →
Input topology is series
Voltage comparison
(none of the feedback voltage
reaches the amplifier input)
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Topology of the Emitter follower
Example of analysis of emitter follower.
Input :
Input loop contains
RE , which is connec-
ted to the output.
Serial topology
Voltage comparison
One Stage
Vf
Vi
Input loop
FEEDBACK AMPLIFIERS
Approximate analysis of a feedback amplifier
8
Output :
Shunt topology
Voltage sampling
By setting Vo = 0, the
feedback is eliminated
and Vf = 0. Thus the out-
put is shunt connected.
Series-Shunt topology
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Amplifier without feedback
Modified input circuit
Output has shunt topology
Short-circuit the output node.
One Stage
FEEDBACK AMPLIFIERS
Approximate analysis of a feedback amplifier
Example of analysis of emitter follower.
9
Modified output circuit
Open-circuit the input loop.
Input has series topology
Basic amplifier without feedback
Equivalent circuit of modified feedback amplifier
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of VV −−−−====From picture (c) we get :
1VV of −−−−====≡≡≡≡β⇒⇒⇒⇒
βandAOL
Amplifier without feedback
One Stage
FEEDBACK AMPLIFIERS
Approximate analysis of a feedback amplifier
Example of analysis of emitter follower.
10
Equivalent circuit of modified feedback amplifier
+
-
Vo
oE
'
E
'
Emo rRRwhereRVgV ======== π
π
ππ
rR
VrVand
s
s
++++====
⇒
π
π
rR
RrgA
s
'
EmOL ++++
====
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FAandT
βOLAT −−−−====
1−−−−====β ⇒⇒⇒⇒ π
rR
RrgT Em
+=
'
whereoE
'
E rRR ====
One Stage
Amplifier with feedback
FEEDBACK AMPLIFIERS
Approximate analysis of a feedback amplifier
Example of analysis of emitter follower.
11
πrRT
s +=
'
E0s
'
E0OLF
RrR
R
T1
AA
ββ
π ++++++++====
++++====
oEE rRR ====
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E
'
E
E0s
E0F RRwhen
RrR
RA ≈≈≈≈
++++++++====
ββ
π
oE rR <<If we assumed that we can write :
Approximation
FA
Amplifier with feedback
One Stage
FEEDBACK AMPLIFIERS
Approximate analysis of a feedback amplifier
Example of analysis of emitter follower.
12
E0s π
(((( ))))(((( )))) E
'
E
0Es
0EF RRwhen
1RrR
1RA ≈≈≈≈
++++++++++++++++====
ββ
π
(((( )))) 001 ββ →→→→++++
unilateral feedback networknonunilateral feedback network
See Millman,
Grabel table 10-3A
(assumption)
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IFID RandR
Dead system impedance RID
πrRID ====
Amplifier with feedback
One Stage
FEEDBACK AMPLIFIERS
Approximate analysis of a feedback amplifier
Example of analysis of emitter follower.
13©Loberg University of Jyväskylä
Amplifier with feedback
One Stage
IFID RandRInput has Series topology
TOC Open circuit the input : ∞∞∞∞→→→→→→→→ sRwhen0T
0TTsR
OC ======== ∞∞∞∞====
TSC 0RwhenRgT s
'
Em →→→→→→→→Short circuit the input :
FEEDBACK AMPLIFIERS
Approximate analysis of a feedback amplifier
Example of analysis of emitter follower.
14
(((( )))) '
E0IF R1rR βπ ++++++++==== See Millman, Grabel table 10-3
(((( )))) 001 ββ →→→→++++unilateral feedback network
sEm
'
Em0RSC RgTTs
======== ====
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(((( )))) '
E0
'
EmIF RrRg1rR βππ ++++====++++==== Approximation⇒⇒⇒⇒
Output has Shunt topology
oOD rR ====
Dead system impedance ROD
Amplifier with feedback
One Stage
OFOD RandR
FEEDBACK AMPLIFIERS
Approximate analysis of a feedback amplifier
Example of analysis of emitter follower.
15©Loberg University of Jyväskylä
OFOD RandR
Amplifier with feedback
TSC Short circuit the output : 0Rwhen0T E →→→→→→→→
00
===ERSC TT
One Stage
Output has Shunt topology
FEEDBACK AMPLIFIERS
Approximate analysis of a feedback amplifier
Example of analysis of emitter follower.
16
Open circuit the output : ∞∞∞∞→→→→++++
→→→→ E
s
o0 RwhenrR
rT
π
β
π
βrR
rTT
sROC
E +==
∞=00
( )[ ] 001 ββπ
π
rR
rRr
rR s
so
oOF
+≈
++=
(((( )))) 0so rRr βπ++++>>>>>>>>
when
⇒
TOC
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Approximate analysis of a shunt-triple
In general, practical amplifiers have two or more stages. High closed-loop gain AF
High return ratio T
Local feedback
Global feedback
Three Common-emitter stages
sI sR
FR
LR
oV
+
R R
1Q 2Q3Q
iI
Feedback network
A bipolar shunt-triple feedback amplifier
Example of analysis of amplifier
having several stages
FEEDBACK AMPLIFIERS
17
The internal three-stage amplifier can be modeled as
a single equivalent amplifier.
sI sR oV
-1CR 2CR
3CR
IFZOFZ
Internal amplifier
Input:
Current comparison
SHUNT topology
Output:
Voltage sampling
SHUNT topology
SRsI oViV
imIZ
iror
FR
iI
LR
?Z
rrr
Rr
m
1b1i
3Co
====++++≈≈≈≈
≈≈≈≈
π
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sI sR
FR
LR
oV
+
-1CR 2CR
3CR
1Q 2Q3Q
iI
Feedback network
A bipolar shunt-triple feedback amplifier
Voltage gain of the first (input) stage is :
1b1
1C01v
rr
RA
++++−−−−====
π
β
Approximate analysis of a shunt-triple
FEEDBACK AMPLIFIERS
Example of analysis of amplifier
having several stages
SRsI oViV
imIZ
iror
FR
iI
LR
18
-
IFZOFZ
Internal amplifier
1b1i
iii
rrr
0rIV
++++========−−−−
π(((( ))))1b1ii rrIV ++++==== π⇒⇒⇒⇒
⇒⇒⇒⇒The unloaded voltage gain of the input stage (first stage).
(((( )))) 1C01i
1b1
1C011b1ivi1o RI
rr
RrrIAVV ββ
ππ −−−−====
++++++++−−−−========
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Approximate analysis of a shunt-triple
SRsI oViV
imIZ
iror
FR
iI
LR
FEEDBACK AMPLIFIERS
Example of analysis of amplifier
having several stages
19
Total gain (transimpedance)
of controlled source is:
3v2v1C01
i
om AAR
I
VZ β========
remember load effects
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Approximate analysis of a shunt-triple
The approximate model of the basic amplifier (shunt-triple) without feedback
Feedback is removed, but not loading
effect of RF .
Modify Input side:
Output has shunt topology
Modify Output side:
Input has shunt topology
FEEDBACK AMPLIFIERS
Example of analysis of amplifier
having several stages
20
SRsI oViV
imIZ
ir
or
FR
iI
LR
SRsI oViV
imIZ
ir
orFRiI
LR
Short circuit output Short circuit input
SRsI oViV
imIZ
ir
or
FR
iI
LR
SRsI oViV
imIZ
ir
or
FR
iI
LR
SRsI oViV
imIZ
ir
or
FR
iI
LR
SRsI oViV
imIZ
ir
or
FR
iI
LR
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Approximate analysis of a shunt-triple
Vor
iI
Feedback is removed, but loading effect of RF on the input and output
circuits is included.
oriI'
sI
sI
I
OLAThe approximate model of the basic amplifier (shunt-triple) without feedback
FEEDBACK AMPLIFIERS
Example of analysis of amplifier
having several stages
21
SRsI oViV
imIZir
or
FR
LRFR'
SRsI oViV
imIZir
or
'
LR
sI I
0IRV
0IZIrV
0RIV
0rIV
0III
'
Lo
imoo
'
s
'
si
iii
'
sis
====++++
====++++−−−−====−−−−
====−−−−====−−−−−−−−
⇒⇒⇒⇒'
Lo
'
L
'
si
'
sm
s
oOL
Rr
R
Rr
RZ
I
VA
++++++++−−−−========
FL
'
L
Fs
'
s
RRR
RRR
====
====where
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Approximate analysis of a shunt-triple
K
o22s21i XtXtX ++++==== (Millman 12-23)
22
21
0Xs
o
t
t
X
XK
i
−−−−====−−−−========
See a General Analysis
of Feedback Amplifiers
FEEDBACK AMPLIFIERS
Example of analysis of amplifier
having several stages
22
220Xs tXi ====
SR
sI oV0Vi ====imIZ
iror
FR
0I i ====
LR
IsI 0IRV
0II
Fo
s
====−−−−====++++
⇒⇒⇒⇒ F
s
o
0Xs
o RI
V
X
XK
i
−−−−========−−−−========
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Approximate analysis of a shunt-triple
Treturn ratio
sF
F
i
'
s
s
o
'
L
L
FL
m
F
'
Lo
'
L
'
si
'
sm
OL
RR
R
rR
R
rR
R
RR
Z
R
1
Rr
R
Rr
RZ
K
AT
++++++++++++++++====
−−−−
++++++++−−−−======== See a General Analysis
of Feedback Amplifiers
FEEDBACK AMPLIFIERS
Example of analysis of amplifier
having several stages
23
T1
KT
T1
KTA
T1
AA DOL
F ++++≈≈≈≈
++++++++====
++++==== when dead system gain AD
is very low
⇒⇒⇒⇒
sFisoLFL
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The End of Part 12
FEEDBACK AMPLIFIERS
24
The End of Part 12
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