ECE 2133
Electronic Circuits
Dept. of Electrical and Computer Engineering
International Islamic University Malaysia
Chapter 12
Feedback and Stability
Introduction to Feedback
Introduction to Feedback



1-4
Harold Black, an electronics engineer from Western Electric
Company, invented the feedback amplifier in 1928 while searching
for methods to stabilize the gain of amplifiers for use in telephone
repeaters.
In a feedback system, a signal that is proportional to the output is
fed back to the input and combined with the input signal to produce
a desired system response.
Feedback can be either negative or positive.

In negative feedback, a portion of the output signal is subtracted from
the input signal.


Tends to maintain a constant value of amplifier voltage gain against
variations in transistor parameters, supply voltages, and temperature.
In positive feedback, a portion of the output signal is added to the input
signal.

Used in the design of oscillators and other applications.
© Electronic Circuits
Advantages of Negative
Feedback

Gain sensitivity


Increase the signal-to-noise ration if noise is generated within the
feedback loop
Reduction of nonlinear distortion


The bandwidth of a circuit that incorporates negative feedback is
larger than that of the basic amplifier
Noise sensitivity


Variations in the circuit transfer (gain) as a result of changes in
transistor parameters are reduced by feedback
Bandwidth extension


1-5
At large signal levels, distortion may appear in the transistor output
signal due to its nonlinear characteristics. Negative feedback reduces
this distortion
Control of impedance levels

The input and output impedances can be increased or decreased with
the proper type of negative feedback circuit
© Electronic Circuits
Disadvantages of Negative
Feedback

Circuit Gain


1-6
The overall amplifier gain, with negative feedback, is
reduced compared to the basic amplifier used in the
circuit
Stability

The feedback circuit may become unstable (oscillate) at
high frequencies
© Electronic Circuits
Basic Concepts of Feedback
Basic Feedback Circuit





1-8
S  current or voltage.
A  open loop gain of a basic amplifier
Sfb  feedback signal by sampling the output signal
Sɛ  error signal by subtracting the feedback signal from the
input source signal
Error signal is the input to the basic amplifier and amplified
to produce the output signal
© Electronic Circuits
Assumptions





1-9
The input signal is transmitted through the amplifier only, none
through the feedback network
The output signal is transmitted back through the feedback network
only, none through the amplifier
There are no loading effects in the ideal feedback system
The feedback network does not load down the output of the basic
amplifier
The basic amplifier and feedback network do not produce a loading
effect on the input signal source
© Electronic Circuits
1-10
Ideal Closed-Loop
Signal Gain

A  amplification factor

  feedback transfer function

Af  closed-loop transfer function



© Electronic Circuits
T  loop gain
S*  can be either voltage or
currents or a combination of
both
T is (+) for negative feedback
but can be a complex
number also
1-11
Ideal Closed-Loop
Signal Gain

If the loop gain is large so that A >> 1, the overall gain of
the feedback is a function of the feedback network only

© Electronic Circuits
For a large loop gain
Gain Sensitivity
1-12
Consider the feedback transfer function  is a constant

The percent change in the closed-loop gain Af is less than the corresponding
percent change in the open-loop gain A by the factor (1+ A)
© Electronic Circuits
Ideal Feedback Topologies
Preview

1-14
There are four feedback topologies, based on the
parameter to be amplified (voltage or current) and the
output parameter (voltage or current).




Series-Shunt (voltage amplifier).
Shunt-Series (current amplifier)
Series-Series (transconductance amplifier)
Shunt-Shunt (transresistance amplifier)
© Electronic Circuits
Preview
© Electronic Circuits
1-15
Series-Shunt Configuration





1-16
The circuit is a voltage-controlled voltage source and is an ideal voltage
amplifier.
The feedback circuit samples the output voltage and provides a feedback
voltage in series with the source voltage.
An increase in the output voltage produces an increase in the feedback
voltage, which in turn decreases the error voltage due to the negative
feedback.
The smaller error voltage is amplified producing a smaller output voltage.
Which means that the output signal tends to be stabilized.
© Electronic Circuits
Series-Shunt Configuration

The output of the feedback network is an open circuit


Vfb  feedback voltage, v (= Vfb/Vo)  voltage
feedback transfer function
Source resistance RS is negligible


1-17
Avf  closed-loop voltage transfer function
The magnitude of Avf is less than that of Av, the advantage is that Avf becomes
independent of the individual transistor parameters
© Electronic Circuits
Series-Shunt Configuration

1-18
A series input connection results in an increased input
resistance compared to that of the basic voltage
amplifier. This eliminates loading effects on the input
signal source due to the amplifier
© Electronic Circuits
Series-Shunt Configuration

1-19
A shunt output connection results in a decreased output
resistance compared to that of the basic voltage
amplifier. This eliminates loading effects on the output
signal when an output load is connected
© Electronic Circuits
Series-Shunt Configuration
© Electronic Circuits
1-20
Shunt-Series Configuration





1-21
The circuit is a current-controlled current source and is an ideal current
amplifier.
The feedback circuit samples the output current and provides a feedback
signal in shunt with the signal current.
An increase in the output current produces an increase in the feedback
current, which in turn decreases the error current due to the negative
feedback.
The smaller error current is amplified producing a smaller output current.
Which means that the output signal tends to be stabilized.
© Electronic Circuits
Shunt-Series Configuration

The output of the feedback network is a short circuit


Ifb  feedback current, i (= Ifb/Io)  feedback
current transfer function
Source resistance RS is large


1-22
Aif  closed-loop current transfer function
The magnitude of Aif is less than that of Ai, the
advantage is that Aif becomes independent of the
individual transistor parameters
© Electronic Circuits
Shunt-Series Configuration

1-23
A shunt input connection decreases the input resistance compared
to that of the basic amplifier. This eliminates loading effects on the
input signal current source due to the amplifier
© Electronic Circuits
Shunt-Series Configuration

1-24
A series output connection increases the output
resistance compared to that of the basic voltage
amplifier. This eliminates loading effects on the output
signal when an output load is connected
© Electronic Circuits
Shunt-Series Configuration
© Electronic Circuits
1-25
Series-Series Configuration


1-26
The feedback circuit samples a portion of the output
current and converts it to a voltage.
This feedback circuit is a voltage-to-current amplifier.
© Electronic Circuits
Series-Series Configuration


The output of the feedback network is a short circuit
Vfb  feedback voltage, z (= Vfb/Io)  resistance
feedback transfer function

Neglecting the affect of Source resistance RS

© Electronic Circuits
1-27
Agf  closed-loop current-to-voltage
transfer function or transconductance gain
Series-Series Configuration
1-28
Vi  V  V fb
 V   z I o
 V   z ( AgV )
 V 1   z Ag 
V 
Vi
1   z Ag
V
Vi
Ii   
Ri Ri 1   z Ag 
V
Rif  i  Ri 1   z Ag 
Ii

Input resistance increases compared to that of the basic amplifier.
© Electronic Circuits
Series-Series Configuration

1-29

Vx  I x  AgV Ro  I x  Ag   z I x  Ro
 I x 1   z Ag Ro
V
Rof  x  1   z Ag Ro
Ix

The output resistance increases compared to that of the
basic amplifier.
© Electronic Circuits
Series-Series Configuration
© Electronic Circuits
1-30
Shunt-Shunt Configuration


1-31
The feedback circuit samples a portion of the output
voltage and converts it to a current.
This feedback circuit is a current-to-voltage amplifier.
© Electronic Circuits
Shunt-Shunt Configuration


The output of the feedback network is an open circuit
Ifb  feedback current, g (= Ifb/Vo)  conductance
feedback transfer function

Source resistance RS is very large

© Electronic Circuits
1-32
Azf  closed-loop voltage-to-current
transfer function or transresistance gain
Shunt-Shunt Configuration
1-33
I i  I   I fb  I    gVo  I    g  Az I  
Ii
I 
1   g Az 
Vi  I  Ri 
I i Ri
1   g Az 
V
Ri
Rif  i 
I i 1   g Az 

Input resistance decreases compared to that of the
basic amplifier.
© Electronic Circuits
Shunt-Shunt Configuration
1-34
Vx  Az I  Vx  Az   gVx  Vx 1   g Az 
Ix 


Ro
Ro
Ro
V
Ro
Rof  x 
I x 1   g Az 

The output resistance decreases compared to that of
the basic amplifier.
© Electronic Circuits
Shunt-Shunt Configuration
© Electronic Circuits
1-35
Feedback Networks
1-37
Voltage Amplifiers

Av is very large
i1  
i2 

.

© Electronic Circuits
R1

v fb  vo
R2
vi
R1

vi  vo
R2
vi vi  vo

R1
R2
Av 

v fb
vo
R
 1 2
vi
R1
v is feedback transfer function
Voltage Amplifiers

Av is the open-loop voltage gain of the basic
amplifier. For Ro  0

© Electronic Circuits
1-38
Ri is very large
1-39
Voltage Amplifiers

.
Av is positive and v is also positive, thus the loop gain is positive for negative feedback
T   v Av
V  I i Ri , Vo  AvV , Vi  V  V fb
=
© Electronic Circuits
Current Amplifiers


Ai is open-loop current gain and very large
if RS >> Rif, then Ii’  Ii and I is negligible,

© Electronic Circuits
1-40
Assuming V1 is at virtual ground
1-41
Current Amplifiers


© Electronic Circuits
Ai is very large
Assuming V1 is at virtual ground
1-42
Current Amplifiers

.Solving for Ifb and substitute
to
and rearranging to find the
closed-loop current gain
© Electronic Circuits
Transconductance Amplifiers

Ag is open-loop transconductance gain and very
large
Ag is very large


© Electronic Circuits
1-43
Neglecting base current
Transconductance Amplifiers

© Electronic Circuits
1-44
Assume Ic  Ie ad Ri is very large
1-45
Transresistance Amplifiers

Az is open-loop transresistance gain and very
large
Az is very large


Assuming V1 is at virtual ground

© Electronic Circuits
Ifb = Ii
Transresistance Amplifiers


© Electronic Circuits
Vo = -AzI, I = Ii – Ifb, and Vo = -Az(Ii – Ifb)
Assuming V1 is at virtual ground
1-46