Transcript Voltage-Series Feedback

E212 – Analog Electronic II
Chapter 3
Feedback Circuits
1.0 Classification of Amplifiers

Before proceeding with the concept of feedback it is
useful to classify amplifiers into 4 basic categories based
on their input & output signal relationships.




Voltage amplifier
Current amplifier
Transconductance amplifier
Transresistance amplifier
1.1 Voltage amplifier
if
Vi
Vo
Ri  Rs
then
and if
Vi  Vs
Ro  RL
then
Vo  AvVi  AvVs
hence Av 
with
Vo
Vi
RL  
represent the open circuit voltage gain.
1.2 Current amplifier
if
Ii
Io
Ri  Rs
then
and if
Ii  I s
Ro  RL
then
I o  Ai I i  Ai I s
hence
with
Ai 
Io
Ii
RL  0
represent the short circuit current gain.
1.3 Transconductance amplifier
if
Vi
Io
Ri  Rs
then
and if
Vi  Vs
Ro  RL
then
I o  GmVi  GmVs
hence Gm 
with
Io
Vi
RL  0
represent the short circuit mutual or
transfer conductance
1.4 Transresistance amplifier
if
Ii
Vo
Ri  Rs
then
and if
Ii  I s
Ro  RL
then
Vo  Rm I i  Rmis
hence Rm 
Vo
Ii
with RL  
represent the open circuit mutual or
transfer resistance.
2.0 Feedback

Feedback is a technique where a proportion of the output of a
system (amplifier) is fed back and recombined with input.
input
A


There are two types of feedback amplifier.
 Positive feedback
 Negative feedback
output
2.1 Positive Feedback

Positive feedback is the process when the output is added to
the input, amplified again, and this process continues.
input

A
output


Example. In a PA system, you get feedback when you put the
microphone in front of a speaker and the sound gets uncontrollably
loud (you have probably heard this unpleasant effect.
2.2 Negative Feedback

Negative feedback is when the output is subtracted from the
input.
input

A
output



Example. Speed control. If the car starts to speed up above the
desired set-point speed, negative feedback causes the throttle to
close, thereby reducing speed; similarly, if the car slows, negative
feedback acts to open the throttle.
The use of negative feedback reduces the gain. Part of the output
signal is taken back to the input with a negative sign.
3.0 Feedback Concept
Basic structure of a single - loop feedback amplifier
3.1 Feedback Network
• This block is usually a passive two-port network.
• contain resistors, capacitors, and inductors.
• Usually it is simply a resistive network.
3.2 Sampling Network
• The output voltage is sampled by connecting the feedback network in
shunt across the output.
• Type of connection is referred to as voltage or shunt or node sampling.
3.2 Sampling Network
• The output current is sampled by connecting the feedback network in
series with the output
• Type of connection is referred to as current or series or loop sampling.
3.3 Comparator or Mixer Network
• voltage - applied feedback
• identified as voltage or series or loop mixing.
3.3 Comparator or Mixer Network
• current - applied feedback
• identified as current or shunt or node mixing.
4.0 Feedback Amplifier Topologies
Series - shunt
series - series
shunt - series
shunt - shunt
5.0 Feedback Connection Types
There are four basic ways of connecting the feedback
signal:
•
•
•
•
Voltage-series feedback
Voltage-shunt feedback
Current-series feedback
Current-shunt feedback
 Series refers to
connecting the
feedback signal in
series with the
input signal
voltage.
 Shunt refers to
connecting the
feedback signal in
shunt (parallel)
with an input
current source.
Fig. 3-2: Feedback amplifier types: (a) voltage-series feedback; (b)
voltage-shunt feedback; (c) current-series feedback; (d) current-shunt
feedback.
Series feedback connections tend to increase the
input resistance, whereas shunt feedback
connections tend to decrease the input resistance.
Voltage feedback tends to decrease the output
impedance, whereas current feedback tends to
increase the output impedance.
Gain with Feedback
TABLE 3-1: Summary of Gain, Feedback, and Gain with Feedback
from Figure 3-2
VoltageSeries
VoltageShunt
CurrentSeries
CurrentShunt
Gain without
feedback
A
Vo
Vi
Vo
Ii
Io
Vi
Io
Ii
Feedback
β
Vf
If
Vf
If
Vo
Vo
Io
Io
Vo
Vs
Vo
Is
Io
Vs
Io
Is
Gain with
feedback
Af
Voltage-Series Feedback
Figure 3-2 (a) below shows the voltage-series feedback connection
with a part of the output voltage fed back in series with the input
signal.
If there is no feedback (Vf = 0),
the voltage gain of the amplifier
is
Vo Vo
A

Vs Vi
If a feedback signal Vf is
connected with the input in
series, the overall voltage gain
is
Vo
A
Af 

Vs 1  A
(3-1)
Voltage-Shunt Feedback
The gain with feedback for the network of Fig. 3-2 (b) is
A
Af 
1  A
(3-2)
Input Impedance with Feedback
Voltage-Series Feedback
The input impedance
can be determined as
follows:
Vs
Z if   Z i (1   A)
Ii
(3-3)
Fig. 3-3: A more detailed voltage-series
feedback connection
Voltage-Shunt Feedback
The input impedance
can be determined to
be:
Zi
Z if 
1  A
(3-4)
Fig. 3-4: A more detailed voltage-shunt
feedback connection
Output Impedance with Feedback
The output impedance for the connections of Fig. 3-2 is
dependent on whether voltage or current feedback is used.
For voltage feedback, the output impedance is decreased,
whereas current feedback increases the output impedance.
Voltage-Series Feedback
Referring to Fig. 3-3, the output impedance can be
determined by applying a voltage V, resulting in a current I.
Then the output resistance with feedback is
Zo
V
Z of  
I 1  A
(3-5)
Current-Series Feedback
The output impedance
is determined as
V
Z of 
I
Z of  Z o (1   A)
(3-6)
Fig. 3-5: A more detailed current-series feedback
connection
A summary of the effect of feedback on input and output
impedance is provided in Table 3-2:
TABLE 3-2:
VoltageSeries
Zif
Z i (1   A) Z i (1   A)
(increased)
Zof
CurrentSeries
Zo
1  A
(decreased)
(increased)
Z o (1   A)
(increased)
VoltageShunt
CurrentShunt
Zi
1  A
Zi
1  A
(decreased)
(decreased)
Zo
1  A
Z o (1   A)
(decreased)
(increased)
6.0 Negative Feedback Gain
Xi
Xs

Xf
A
Xo

The gain with feedback (or closed-loop gain) Af as follows:
X o  A. X i
Xi  Xs  X f
X f   .X o
Xo
A
Af 

X s 1  A
The quantity A is called the loop gain, and the quantity (1+A)
is called the amount of feedback.
6.0 Advantages of Negative Feedback
1.
Stabilization of gain

2.
Reduce non-linear distortion

3.
make the gain less sensitive to changes in circuit
components e.g. due to changes in temperature.
make the output proportional to the input, keeping the
gain constant, independent of signal level.
Reduce the effect of noise

minimize the contribution to the output of unwanted
signals generated in circuit components or extraneous
interference.
6.0 Advantages of Negative Feedback
4. Extend the bandwidth of the amplifier

Reduce the gain and increase the bandwidth
5. Modification the input and output impedances

raise or lower the input and output impedances by
selection of the appropriate feedback topology.
6.1 Stabilization of Gain
Stabilization of the gain of an amplifier against changes in the
components (e.g., with temperature, frequency)
 If you represent the gain without feedback (the open loop
gain) by Ao, then the system gain with negative feedback is

Af 

Vout
Ao
1


Vin 1  Ao  
where  is the fraction of the output which feeds back as a
negative voltage at the input. The extent of this stabilizing
influence can be illustrated as follows:
6.1 Stabilization of Gain
6.2 Decreasing Distortion/noise with
Feedback

The use of negative feedback can discriminate against sources of
noise or distortion within an amplifier.
6.2 Decreasing Distortion/noise with
Feedback
• showing that distortion within the feedback loop is discriminated
against, with more reduction of distortion which arises near the
output.
6.3 Increasing the Bandwidth
Af 
Ao
1  Ao 
6.4 Modification of input and output
impedance
i)

Input Resistance
The input resistance with negative feedback will be raised for series
or voltage mixing.
Zi 
Vi
Ii
Vi  Vs  V f
Z if 
Vs
 Z i 1  A
Ii
6.4 Modification of input and output
impedance
i)

Input Resistance
The input resistance with negative feedback will be lowered for
shunt or current mixing.
Vi
Zi 
Ii
Ii  I s  I f
Vi
Zi
Z if 

I s 1  A
6.4 Modification of input and output
impedance
ii) Output Resistance
 The output resistance with negative feedback will be lowered
for shunt or voltage sampling.
Let X s  0
replaced load with test voltage
X i   X f   Vt
it 
vt  AX i vt  Avt vt 1  A


Ro
Ro
Ro
Z of 
vt
Ro

it 1  A
6.4 Modification of input and output
impedance
ii) Output Resistance
 The output resistance with negative feedback will be raised
for series or current sampling.
The output resistance with feedback for current
or series sampling to be:
Z of  Ro 1   A
6.4 Modification of input and output
impedance
Summary
 For a series connection at input or output, the resistance is
increased by (1+A) and
 For a shunt connection at input or output, the resistance is
lowered by (1+A).
7.0 Practical Feedback Circuits
Voltage-Series Feedback
The feedback voltage Vf is
connected in series with
the source signal Vs, their
difference being the input
signal Vi.
Without feedback the
amplifier gain is
Vo
A
  g m RL
Vi
Fig. 3-7: FET amplifier with voltageseries feedback.
(3-7)
where,
gm = transconductance
factor
Whereas RL is combination of resistors:
Ro RD
RL  RD Ro ( R1  R2 ) 
Ro  RD
The feedback network provides a feedback factor of
 R2


Vo R1  R2
Vf
Using the values of A and β, we find the gain with negative feedback
to be
 g m RL
Af 

1   A 1  R2 RL g m
R1  R2
A
If βA >>1, we have
R1  R2
Af   

R2
1
(3-7)
Current-Series Feedback
Fig. 3-8: (a) a single transistor amplifier circuit and (b) ac
equivalent circuit without feedback
The feedback voltage VE is resulted in by the current through
resistor RE.
Without Feedback
Referring to the Fig. 3-8 and summarized in Table 3-1, we have
 I b h fe
 h fe
Io
A 

Vi I b hie  I b RE hie  RE
(3-8)
 I o RE


  RE
Io
Io
(3-9)
Vf
The input and output impedances are, respectively,
Z i  RB //( hie  RE )  hie  RE
(3-10)
Z o  RC
(3-11)
With Feedback
Io
A
Af  

Vs 1   A
 h fe / hie
  h fe
1  ( RE )
 hie  RE




 h fe
hie  h fe RE
(3-12)
The input and output impedances are calculated as specified
in Table 3-2,
 h fe RE 
  hie  h fe RE
Z if  Z i (1   A)  hie 1 
hie 

(3-13)
 h fe RE 

Z of  Z o (1   A)  RC 1 
hie 

(3-14)
The voltage gain A with feedback is
 h fe RC
Vo I o RC  I o 
Avf  
   RC  Af RC 
Vs
Vs
hie  h fe RE
 Vs 
(3-15)
Voltage-Shunt Feedback
Fig. 3-9: Voltage-shunt negative
feedback amplifier: (a) constantgain circuit; (b) equivalent circuit.
Referring to Fig. 3-9 and Table
3-1 and the op-amp ideal
characteristics Ii = 0, Vi = 0, and
voltage gain of infinity, for a
constant-gain we have:
Vo
A

Ii
(3-16)
1
 
Vo Ro
(3-17)
If
The gain with feedback is then
Vo Vo
A
1
Af 


   Ro
I s Ii 1   A 
(3-18)
The more usual gain is the voltage gain with feedback,
Vo I s
1  Ro
Avf 
 ( Ro ) 
I s V1
R1
R1
(3-19)
Fig. 3-10: Voltage-shunt feedback amplifier using an FET: (a) circuit;
(b) equivalent circuit.
With no feedback, Vf = 0,
Vo
A
  g m RD RS
Ii
(3-20)
The feedback is,
1
 
Vo RF
If
(3-21)
With feedback, the gain of the circuit is,
Vo
 g m RD RS
A
Af 


I s 1   A 1  (1 / RF )(  g m RD RS )
(3-22)
Or,
 g m RD RS RF
Af 
RF  g m RD RS
(3-23)
The voltage gain of the circuit with feedback is then
Vo I s  g m RD RS RF
Avf 

I s Vs RF  g m RD RS
 g m RD RF
Avf 
RF  g m RD RS
 1

 RS



(3-24)