Addis Ababa Science and Technology University
College of Mechanical and Electrical Engineering
Department of Electrical and Computer Engineering
Applied Electronics II
ECEg3102
Lecture I
Feedback Amplifiers
Contents
• Basic Feedback Amplifier
• Properties of Negative Feedback
• Feedback Topologies
• Analysis of Feedback Amplifiers
Basic concepts of Feedback…
• 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.
• Most physical systems incorporate some form of feedback.
• Fig 1.1. Closed loop configuration
Basic concepts of Feedback…
• Feedback can be broadly classified as:
• Positive Feedback
• A portion of the output signal is added to the input. Positive feedback is
used in the design of oscillator, signal generators and a number of other
applications (will be discussed in later chapters).
• Negative Feedback
• A portion of the output signal is subtracted from the input signal. The
basic idea of negative feedback is to trade off gain for other desirable
properties. It is used for amplifiers
Basic concepts of Feedback…
Mathematical Relationship for open and closed loop gain
For open loop configuration

𝑉0 𝜃0
Voltage gain , 𝐴 = =
𝑉𝑖 𝜃𝑒
For closed loop configuration (with feedback network)
 Voltage gain , 𝛽 =
𝑉𝑓
𝑉0𝑢𝑡
=
𝑉𝑓
𝜃0
𝑉𝑖𝑛 − 𝑉𝑓 =𝜃𝑒 for negative feed back.
But 𝑉𝑓 = 𝛽𝑉0𝑢𝑡 and 𝜃𝑒 = 𝜃𝐴0 , substituting these expression in above equation
𝑉𝑖𝑛 − 𝛽𝑉0𝑢𝑡 =

𝜃0
𝐴
and 𝜃0= 𝑉0𝑢𝑡
𝑉
𝑉𝑖𝑛 − 𝛽𝑉0𝑢𝑡 = 0𝑢𝑡
𝐴
Basic concepts of Feedback…
Rearranging the above expression , we have
𝑉
𝐴
𝐴𝑓 = 0𝑢𝑡 =
closed loop gain (negative feedback amplifier gain)
𝑉𝑖𝑛
𝐴𝛽+1
 As 𝛽 increases the overall gain(𝐴𝑓 ) decreases ,
 Negative feedback leads to reducing the gain of the amplifier .
Example : For ideal closed loop case
Calculate the feedback transfer function β, given 𝐴 and 𝐴𝑓 .
 CASE A. Assume that the open-loop gain of a system is A = 105 and the closed-loop gain is
𝐴𝑓 = 50.
 CASE B. Assume that the open-loop gain is A = −105 and the closed-loop gain is 𝐴𝑓 = 50.
`
Negative Feedback…
Advantages of Negative feedback
Gain Sensitivity
 Variations in the circuit transfer function (gain) as a result of changes in transistor parameter
are reduced by feedback.
If the output voltage Varies in open loop configuration the gain factor may
vary , this variation leads very small change (negative feedback) configuration
. This is important that even if there is a reduction in open loop gain there
will not be much change in overall gain . This is called desensistivity of gain
𝑑𝐴𝑓
1
= (1+β𝐴)2
𝑑𝐴
KEY:
𝑑𝐴𝑓
→
𝑑𝐴𝑓
𝐴𝑓
1
𝑑𝐴
= (1+β𝐴) 𝐴
 percent change in the closed-loop gain
𝐴𝑓
𝑑𝐴
 percent change in the open-loop gain
𝐴
The above shows that 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 of (1 + β𝐴).
The term (1 + β𝐴) is called desensitivity factor.
Negative Feedback
Advantages of Negative feedback
Bandwidth Extension
The bandwidth of a circuit that incorporates negative feedback is larger than the
basic amplifier.
 Since,𝐵𝑊 = 𝑓2 − 𝑓1,the gain bandwidth product is given
by 𝐴 × 𝐵𝑊.
Now, when negative feedback is applied , the amplifier gain
is reduced .since the gain Bandwidth product has to remain
the same in both cases , the bandwidth has to be increased to
compensate the reduction in gain. Hence, the lower
frequency decrease by 1 + 𝛽𝐴 and the higher frequency
increase by 1 + 𝛽𝐴. i.e
𝐵𝑊 × 𝐴 = 𝐵𝑊 " × 𝐴𝑓
Rearranging the expression we have 𝑓2 " =𝑓2 1 + 𝛽𝐴
𝑓1 " =𝑓1
and
1 + 𝛽𝐴
Example: An RC-coupled amplifier has a mid-frequency gain of 200 for frequency response of
100Hz to 20kHz.If the negative feedback amplifier has β=0.02 what are the new parameters .
Negative Feedback
Advantages of Negative feedback
Noise Sensitivity
Negative feedback may increase the Signal-to-noise ratio if noise
generated within the feedback loop.
Negative feedback may reduce the noise level in amplifiers; more accurately, it
may increase the signal-to-noise ratio (SNR).
i.e. 𝑵𝒇 = 𝑵 𝟏+𝑨𝜷
The input SNR is defined as
𝑠𝑖
𝑣𝑖
• (𝑆𝑁𝑅)𝑖 = =
𝑁𝑖
𝑣𝑛
The output SNR is
𝑠
𝑁𝑜
• (𝑆𝑁𝑅)𝑜 = 𝑜 =
𝐴𝑇𝑖 𝑠𝑖
𝐴𝑇𝑛 𝑁𝑖
Negative Feedback
Advantages of Negative feedback
Reduction of nonlinear and harmonic distortion
′ when
 Let the harmonic distortion voltage generated
within
the
amplifier
change
from
D
to
𝐷
negative feedback is applied to the amplifier 𝐷 ′ = α𝐷
The fraction of the output distortion voltage which is feedback to the input voltage is β𝐷 ′ = βα𝐷
After amplification it becomes βα𝐷𝐴 and it is anti-phase with original distortion voltage (D)
The new distortion voltage becomes → 𝐷 ′ = 𝐷 − βα𝐷𝐴
Rearranging the expression we
1
α = 1+𝛽𝐴
This shows that negative feedback reduces the amplifier distortion by closed loop gain,
this true when distortion is created by amplifier itself .
Example : An amplifier has a gain of 100 and 5 percent distortion with input
signal of 1V. Calculate
a)Output signal voltage
b)distortion voltage
C) Output voltage
Reduction of Nonlinear Distortion
• Distortion in an output signal is caused by a change in the basic
amplifier gain or a change in the slope of the basic amplifier transfer
function.
• The change in gain is a function of the nonlinear properties of bipolar
and MOS transistors used in the basic amplifier.
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Reduction of Nonlinear Distortion - Example
Given β=0.099
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Negative Feedback
Advantages of Negative feedback
Control of impedance levels
• Input and output impedance
The output and input impedance will also improved by the factor of
1 + 𝛽𝐴 ,based on feedback connection type. The different types of
feedback connection is called circuit topology which we will discusses
next slides
Negative Feedback
Disadvantages of Negative feedback
• Circuit Gain
• The overall amplifier gain, with the negative feedback, is reduced
compared to the basic amplifier used in the circuit.
• Stability
• There is a possibility that the feedback circuit may become unstable
(oscillate) at high frequencies.
Ideal Feedback Topologies
Input terminal
Output terminal
Circuit name
Current
Parallel (shunt)
Current
series
Current amplifier (A/A)
Shunt-series (if the name of the
circuit start with the connection
of input terminal )
Voltage
series
Voltage
Parallel
Voltage amplify (V/V)
Series-shunt
Current
shunt
Voltage
Shunt
Trans-resistance (V/A)
Shunt-shunt
Voltage
Series
Current
series
Trans-conductance (A/V)
Series-series
Ideal Feedback Topologies
• There are four basic feedback topologies, based on the parameter to be amplified
(voltage or current) and the output parameter (voltage or current).
Monday, April 22, 2024
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Analysis of Feedback Amplifiers
Fundamental Assumptions
• Some fundamental
assumptions are taken in order
to analyze the four feedback
configurations.
• Input is transmitted through the
amplifier only, not through the
feedback.
• The feedback signal
transmitted feedback network
only, not through the amplifier.
• ß is independent of the load
and source impedance.
Ideal structure of a Voltage-Series feedback amplifier
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Analysis of Feedback Amplifiers
Voltage-Series (Voltage Amplifier) Feedback
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Analysis of Feedback Amplifiers
Voltage-Series (Voltage Amplifier) Feedback
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Analysis of Feedback Amplifiers
Voltage-Series (Voltage Amplifier) Feedback
From equation ..(1)
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Analysis of Feedback Amplifiers
Voltage-Series (Voltage Amplifier) Feedback
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Analysis of Feedback Amplifiers
Voltage-Series (Voltage Amplifier) Feedback
Practical case
• In practical case, feedback network will not be ideal.
• Actually, it is resistive and will load the amplifier.
• Source and load resistances will affect A, Ri, and Ro.
• Source and load resistances should be lumped with basic amplifier.
• Expressed as two-port network.
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Analysis of Feedback Amplifiers
Method of Analysis of Feedback Amplifiers
Steps
1. Identify if the mixing or comparison is series or shunt
a) Series mixing : If the feedback signal subtracts from the externally applied
signal as a voltage
b) Shunt mixing : If the feedback signal subtracts from the applied excitation
signal as a current.
2. Identify the sampled signal as series or shunt
a) Voltage sampling : Set Vo = 0 (RL= 0). If Xf becomes zero, we have voltage
sampling.
b) Current sampling : Set Io = 0(RL = 1). If Xf becomes zero, we have current
sampling.
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Analysis of Feedback Amplifiers
3. The amplifier without feedback but taking the feedback network
loading into account
1. Find the input circuit.
a)
b)
Set Vo = 0 for voltage sampling.
Set Io = 0 for current sampling.
2. Find the output circuit.
a)
b)
Set Vi = 0 for shunt comparison so that no feedback current enters the amplifier input.
Set Io = 0 for series comparison so that no feedback voltage reaches the amplifier
input.
4. Find the feedback network.
5. Calculate ß, A, Ri and Ro.
6. Calculate the closed loop Af, Rif, Rof.
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Analysis of Feedback Amplifiers
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 voltage-series feedback.
where,
gm = transconductance
factor
(3-7)
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)
Analysis of Feedback Amplifiers
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Analysis of Feedback Amplifiers
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Analysis of Feedback Amplifiers
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Analysis of Feedback Amplifiers
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Analysis of Feedback Amplifiers
Current-Shunt (Current Amplifier) Feedback
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Analysis of Feedback Amplifiers
Current-Shunt (Current Amplifier) Feedback
Note: The effect of current-shunt
Feedback in an amplifier is to decrease
the Input resistance and increase the
output resistance.
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Analysis of Feedback Amplifiers
Current-Series (Transconductance Amplifier) Feedback
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Analysis of Feedback Amplifiers
Current-Series (Transconductance Amplifier) Feedback
Since Ix= I0
Note: The effect of current-series
Feedback in an amplifier is
to increase both the output and
input resistance .
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Analysis of Feedback Amplifiers
Current-Series (Transconductance Amplifier) Feedback
35
Analysis of Feedback Amplifiers
Current-Series (Transconductance Amplifier) Feedback
36
Analysis of Feedback Amplifiers
Current-Series (Transconductance Amplifier) Feedback
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Analysis of Feedback Amplifiers
Current-Series (Transconductance Amplifier) Feedback
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Analysis of Feedback Amplifiers
Current-Series (Transconductance Amplifier) Feedback
39
Analysis of Feedback Amplifiers
Voltage-Shunt (Transresistance Amplifier) Feedback
40
Analysis of Feedback Amplifiers
Voltage-Shunt (Transresistance Amplifier) Feedback
41
Summary
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