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 A
OL
of the basic amplifier is determined without feedback.
3. The calculated gain A
OL is loaded gain : loading of the feedback network,
source and load resistanses are noticed.
4. The feedback network is unilateral.
2
©Loberg University of Jyväskylä
FEEDBACK AMPLIFIERS
Outline of Analysis
Approximate analysis of a feedback amplifier
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.
3. Evaluate :
β = X f Xo
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.
3
©Loberg University of Jyväskylä
FEEDBACK AMPLIFIERS
Topology of a system
Approximate analysis of a feedback amplifier
Input
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.
Topology of input loop Series topology
( Voltage source Vs )
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
X f = Vf
4
©Loberg University of Jyväskylä
FEEDBACK AMPLIFIERS
Approximate analysis of a feedback amplifier
Topology of a system
Input
First step
Identify input loop
Topology of input loop
Shunt topology
( Current source Is )
Define input node
(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 signal
Xf = If
5
©Loberg University of Jyväskylä
FEEDBACK AMPLIFIERS
Approximate analysis of a feedback amplifier
Output
Second step
Topology of a system
Define Output Node
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 output loop Shunt topology
Set Vo = 0 (RL → 0) (short-circuiting the output)
⇒
Xf → 0
⇒
( Voltage sampling )
Topology of output loop Series topology
Set Io = 0 (RL → ∞) (open-circuiting the output)
⇒
Xf → 0
⇒
( Current sampling )
6
©Loberg University of Jyväskylä
FEEDBACK AMPLIFIERS
Amplifier without feedback
Approximate analysis of a feedback amplifier
Third step
AOL and
β
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
Voltage sampling
Output topology is series
Current sampling
Short-circuit output node → V
o
=0
Open-circuit the output loop →
Io = 0
Output circuit :
Input topology is shunt
Input topology is series
Current comparison
Voltage comparison
Short-circuit input node → Vi = 0
Open-circuit the input loop →
(none of the feedback current
enters to the amplifier input)
(none of the feedback voltage
reaches the amplifier input)
Ii = 0
7
©Loberg University of Jyväskylä
FEEDBACK AMPLIFIERS
Approximate analysis of a feedback amplifier
One Stage
Example of analysis of emitter follower.
Input :
Topology of the Emitter follower
Input loop
Serial topology
Voltage comparison
Input loop contains
RE , which is connected to the output.
Vi
Vf
Output :
Shunt topology
Voltage sampling
By setting Vo = 0, the
feedback is eliminated
and Vf = 0. Thus the output is shunt connected.
Series-Shunt topology
8
©Loberg University of Jyväskylä
FEEDBACK AMPLIFIERS
Approximate analysis of a feedback amplifier
Amplifier without feedback
One Stage
Example of analysis of emitter follower.
Modified input circuit
Output has shunt topology
Short-circuit the output node.
Basic amplifier without feedback
Modified output circuit
Input has series topology
Open-circuit the input loop.
Equivalent circuit of modified feedback amplifier
9
©Loberg University of Jyväskylä
FEEDBACK AMPLIFIERS
Approximate analysis of a feedback amplifier
Example of analysis of emitter follower.
From picture (c) we get :
Amplifier without feedback
One Stage
AOL and β
Vf = −Vo
⇒
β ≡ Vf Vo = −1
Vo = gmVπ R'E where R'E = RE ro
and Vπ =
⇒
rπ Vs
Rs + rπ
Vo
AOL =
'
E
gmrπ R
Rs + rπ
+
Equivalent circuit of modified feedback amplifier
10
©Loberg University of Jyväskylä
FEEDBACK AMPLIFIERS
Amplifier with feedback
Approximate analysis of a feedback amplifier
One Stage
Example of analysis of emitter follower.
T and AF
T = − AOL β
β = −1
g m rπ RE'
T=
Rs + rπ
⇒
where
R'E = RE ro
AOL
β0 R'E
AF =
=
1 + T Rs + rπ + β0 R'E
11
©Loberg University of Jyväskylä
FEEDBACK AMPLIFIERS
Amplifier with feedback
Approximate analysis of a feedback amplifier
One Stage
Example of analysis of emitter follower.
AF
If we assumed that
RE << ro
we can write :
β0 RE
AF =
Rs + rπ + β0 RE
when
nonunilateral feedback network
R ≈ RE
'
E
Approximation
unilateral feedback network
(1 + β0 ) → β0
(assumption)
AF =
RE (1 + β0 )
when
Rs + rπ + RE (1 + β0 )
R'E ≈ RE
See Millman,
Grabel table 10-3A
12
©Loberg University of Jyväskylä
FEEDBACK AMPLIFIERS
Amplifier with feedback
Approximate analysis of a feedback amplifier
One Stage
Example of analysis of emitter follower.
RID and RIF
Dead system impedance RID
RID = rπ
13
©Loberg University of Jyväskylä
FEEDBACK AMPLIFIERS
Amplifier with feedback
Approximate analysis of a feedback amplifier
One Stage
Example of analysis of emitter follower.
RID and RIF
Input has Series topology
TOC
Open circuit the input :
T → 0 when Rs → ∞
TOC = T
TSC
Short circuit the input :
(
=0
T → gm R'E when Rs → 0
TSC = T
⇒
Rs = ∞
Rs =0
)
RIF = rπ 1 + gm R'E = rπ + β0 R'E
(1 + β0 ) → β0
RIF = rπ + (1 + β 0 )R'E
= gm R'E
Approximation
unilateral feedback network
See Millman, Grabel table 10-3
14
©Loberg University of Jyväskylä
FEEDBACK AMPLIFIERS
Amplifier with feedback
Approximate analysis of a feedback amplifier
One Stage
Example of analysis of emitter follower.
ROD and ROF
Output has Shunt topology
Dead system impedance ROD
ROD = ro
15
©Loberg University of Jyväskylä
FEEDBACK AMPLIFIERS
Approximate analysis of a feedback amplifier
Amplifier with feedback
Example of analysis of emitter follower.
One Stage
ROD and ROF
Output has Shunt topology
TSC Short circuit the output :
T → 0 when RE → 0
TSC = T
TOC Open circuit the output : T →
β0 ro
Rs + rπ
TOC = T
⇒
ROF =
ro
1 + [β 0 ro (Rs + rπ )]
≈
Rs + rπ
β0
RE = 0
RE = ∞
=0
when RE → ∞
=
β 0 r0
Rs + rπ
when
ro >> (Rs + rπ ) β0
16
©Loberg University of Jyväskylä
FEEDBACK AMPLIFIERS
Example of analysis of amplifier
having several stages
Approximate analysis of a shunt-triple
In general, practical amplifiers have two or more stages.
High closed-loop gain AF
High return ratio T
A bipolar shunt-triple feedback amplifier
Feedback network
RF
Ii
Is
Q1
Rs
Three Common-emitter stages
RC 1
Local feedback
Q3
Q2
RC 2
Vo
RC 3
-
Internal amplifier
Z IF
Global feedback
+
RL
The internal three-stage amplifier can be modeled as
a single equivalent amplifier.
ZOF
Input:
Output:
Current comparison
Voltage sampling
SHUNT topology
SHUNT topology
RF
Ii
Is
ro ≈ RC 3
RS Vi
ro
ri
Zm I i
Vo
RL
ri ≈ rπ 1 + rb1
Zm = ?
17
©Loberg University of Jyväskylä
FEEDBACK AMPLIFIERS
Example of analysis of amplifier
having several stages
Approximate analysis of a shunt-triple
A bipolar shunt-triple feedback amplifier
Voltage gain of the first (input) stage is :
Feedback network
RF
Ii
Is
Av = −
Q3
Q2
Q1
Rs
RC 1
RL
RC 2
RC 3
+
β01 RC1
rπ 1 + rb1
Vo
-
Internal amplifier
Z IF
ZOF
Vi − I i ri = 0
ri = rπ 1 + rb1
RF
Ii
Is
RS Vi
ri
ro
Zm I i
Vo
RL
⇒
Vi = I i (rπ 1 + rb1 )
⇒
The unloaded voltage gain of the input stage (first stage).
Vo1 = Vi Av = − I i (rπ 1 + rb1 )
β01 RC1
rπ 1 + rb1
= − I i β01 RC1
18
©Loberg University of Jyväskylä
FEEDBACK AMPLIFIERS
Example of analysis of amplifier
having several stages
Approximate analysis of a shunt-triple
RF
Ii
Is
RS
Vi
ri
ro
Vo
RL
Zm I i
Total gain (transimpedance)
of controlled source is:
Zm =
Vo
= β01 RC1 Av 2 Av3
Ii
remember load effects
19
©Loberg University of Jyväskylä
FEEDBACK AMPLIFIERS
Example of analysis of amplifier
having several stages
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 Output side:
Modify Input side:
Output has shunt topology
Input has shunt topology
Short circuit output
Short circuit input
RF
RF
Ii
RF
Is
RS
Vi
Ii
ro
ro
Vo
ri
Zm I i
RL
Is
RS
Vi
ri
RF
Zm I i
Vo
RL
20
©Loberg University of Jyväskylä
FEEDBACK AMPLIFIERS
Example of analysis of amplifier
having several stages
Approximate analysis of a shunt-triple
AOL
The approximate model of the basic amplifier (shunt-triple) without feedback
Feedback is removed, but loading effect of RF on the input and output
circuits is included.
Is
Ii
ro
RS
Is
Vi
ri
Vo
RF
Is
RL
Zm I i
RF
I s − I i − I 's = 0
⇒
Vi − I i ri = 0
Ii
I 's
AOL
Vi − I 's R's = 0
'
RS
Vi
ri
ro
I
'
Zm I i
RL
Vo
R's
Vo
R'L
=
= − Zm
ri + R's ro + R'L
Is
Vo − Iro + Z m I i = 0
R's = Rs RF
where
R'L = RL RF
Vo + IR = 0
'
L
21
©Loberg University of Jyväskylä
FEEDBACK AMPLIFIERS
Example of analysis of amplifier
having several stages
Approximate analysis of a shunt-triple
K
X i = t21 X s + t22 X o
K =−
Is
Is
I
Xo
Xs
=−
X i =0
t21
t22
Vi = 0
RS
ri
See a General Analysis
of Feedback Amplifiers
Is + I = 0
RF
Ii = 0
(Millman 12-23)
Vo − IRF = 0
ro
Vo
Zm I i
RL
⇒
K =−
Xo
Xs
=
X i =0
Vo
= − RF
Is
22
©Loberg University of Jyväskylä
FEEDBACK AMPLIFIERS
Example of analysis of amplifier
having several stages
Approximate analysis of a shunt-triple
T
return ratio
AOL
R's
R'L
T=
= − Zm
K
ri + R's ro + R'L
 1 
 −

R
F 

See a General Analysis
of Feedback Amplifiers
Zm
RL
Rs
RF
RL + RF R'L + ro R's + ri RF + Rs
=
⇒
AF =
AOL
A + KT
KT
= D
≈
1+T
1+T
1+T
when dead system gain AD
is very low
23
©Loberg University of Jyväskylä
FEEDBACK AMPLIFIERS
The End of Part 12
24
©Loberg University of Jyväskylä