University of Gondar
Institute of Technology
Department of Electrical Engineering
Applied Electronics II (EEng3082)
Chapter One:
By:
Mersha K.
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Chapter One: Feedback in Amplifiers
By the end of this chapter, students will be able to:
Describe the basic feedback concepts
Perform the representation of feedback in amplifiers
Identify the topologies of feedback amplifiers
Construct & analyze each feedback topology
Explain the effect of feedback on different parameters
Applied Electronics II By Mersha K. 2
Chapter One: Feedback in Amplifiers
What is feedback?
In the process of feedback, a part of output is sampled and fed back to the
input of an electronic circuit (the amplifier).
It adjusts the amplification process based on the comparison between the
output and input signals.
There are two types of feedback in amplifiers.
1. Positive (regenerative) feedback
2. Negative (degenerative) feedback
Applied Electronics II By Mersha K. 3
Chapter One: Feedback in Amplifiers
1. Positive feedback
It is called regenerative or direct feedback.
If the feedback signal is in phase with i/p, then it is called positive feedback.
Positive feedback is used in oscillator, Schmitt trigger and comparator circuits.
2. Negative feedback
Other name of negative feedback is called degenerative feedback.
If the feedback signal is 180° out of phase with it, then it is called negative FD.
Negative feedback is frequently used in amplifier circuits and control systems.
Applied Electronics II By Mersha K. 4
Chapter One: Feedback in Amplifiers
Representation of feedback in amplifiers:
Fig1.1: Basic configuration of Positive and Negative feedback Amplifiers
Applied Electronics II By Mersha K. 5
Chapter One: Feedback in Amplifiers
Principle of Feedback Amplifiers
For an ordinary amplifier (without
feedback), the voltage gain is given by the
ratio of the output voltage by input voltage.
The input voltage 𝑉𝑖𝑛 is amplified by a
Fig1.2: Basic configuration of an open loop amplifier
factor of A to the value 𝑉𝑜𝑢𝑡 of the output
voltage.
The amplifier gain without feedback
is given by:
𝑜/𝑝 𝑠𝑖𝑔𝑛𝑎𝑙 𝑉𝑜𝑢𝑡
𝐴= =
𝑖/𝑝 𝑠𝑖𝑔𝑛𝑎𝑙 𝑉𝑖𝑛
Applied Electronics II By Mersha K. 6
Chapter One: Feedback in Amplifiers
Principle of Feedback Amplifiers
For a closed loop amplifier a feedback loop
is added to the amplifier, see Fig1.3.
The output signal is: 𝑆𝑜 = 𝐴𝑆ε
The feedback signal is: 𝑆𝑓 = β𝑆𝑜 , i. e f = "β"
At the summing node, we have: 𝑆ε = 𝑆𝑖 − 𝑆𝑓 Fig1.3: Basic configuration of a feedback amplifier
Then output signal becomes: • As mentioned, signals 𝑆𝑖 , 𝑆𝑜 , 𝑆𝑓 and 𝑆ε can
𝑆𝑜 = 𝐴(𝑆𝑖 − β𝑆𝑜 ) be either currents or voltages signal.
The amplifier gain with feedback is given by: • The sacrifice factor is defined as:
𝑆𝑜 𝐴 𝐴
𝐴𝑣𝑓 = = 𝑆=
𝑆𝑖 1 + βA 𝐴𝑣
Applied Electronics II By Mersha K. 7
Chapter One: Feedback in Amplifiers
Example 1.1:
1. The voltage gain of a certain amplifier without feedback is 400. If the
feedback ratio is equal to 0.1. Find the voltage gain with feedback amplifier.
2. A negative-feedback amplifier has a closed-loop gain of 𝐴𝑓 = 100 and an open-
loop gain of 𝐴 = 5×104 . Determine the feedback transfer function β.
3. When negative voltage feedback is applied to an amplifier of gain 100, the
overall gain falls to 50.
i. Calculate the fraction of the feedback factor.
ii. If this fraction is maintained, calculate the value of the amplifier gain required if the
overall stage gain is to be 75.
Applied Electronics II By Mersha K. 8
Chapter One: Feedback in Amplifiers
Gain Sensitivity
We can quantify the characteristic of an amplifier without feedback and with feedback
as follows.
𝐴
The gain of an amplifier with negative feedback is: 𝐴𝑓 = , the feedback gain β is a
1+βA
constant, then taking the derivative of 𝐴𝑓 with respect to A, and have:
𝑑𝐴𝑓 1 𝑑𝐴
= → 𝑑𝐴𝑓 =
𝑑𝐴 (1+βA)2 (1+βA)2
Dividing both sides by the closed-loop gain yields
𝑑𝐴𝑓 1 𝑑𝐴
= ∗
𝐴𝑓 1 + βA 𝐴
Applied Electronics II By Mersha K. 9
Chapter One: Feedback in Amplifiers
Example 1.2: An amplifier has an open-loop gain of 400 and a feedback of 0.1. If
open loop gain changes by 20% due to temperature, find the percentage change in
closed-loop gain.
Exercise 1.1:
1. If an amplifier with open loop gain of 1000 and feedback of “β” = 0.1 has a
gain change of 20% due to temperature, calculate the change in gain of the
feedback amplifier.
2. The closed-loop gain of a feedback amplifier using an ideal feedback
amplifier (A → ∞) is 𝐴𝑓 = 125. What is the value of β?
Applied Electronics II By Mersha K. 10
Chapter One: Feedback in Amplifiers
Quiz-1: An amplifier has an open-loop gain of A= 5000 and a feedback factor 𝛽 =
0.05. The open-loop gain decreases by 10% due to temperature changes.
I. Calculate the new closed-loop gain with the changed open-loop gain.
II. How does the closed-loop gain change as a result?
Applied Electronics II By Mersha K. 11
Chapter One: Feedback in Amplifiers
Feedback Topology:
There are four basic feedback topologies, based on the parameter to be
amplified and the output parameter.
The four feedback circuit categories can be described by the types of
connections at the input and output of circuit.
The four connections are referred to as:
i. Series–shunt (voltage amplifier) topologies
ii. Shunt–series (current amplifier) topologies
iii. Series–series (transconductance amplifier) topologies
iv. Shunt–shunt (transresistance amplifier) topologies
Applied Electronics II By Mersha K. 12
Chapter One: Feedback in Amplifiers
I. The Series–shunt (voltage amplifier) topologies:
Referred to as shunt-derived series-fed feedback.
Voltage source at the input side and output
voltage drop at the load.
Output voltage proportional to input voltage.
The closed-loop voltage gain is given by:
𝐴 Fig1.4: Configuration of voltage amplifiers
𝐴𝑣𝑓 =
1 + βA
High input impedance and low output impedance is
desirable.
𝑅𝑜
𝑅𝑖𝑓 = 𝑅𝑖 (1 + βA) 𝑅𝑜𝑓 =
1 + βA
Applied Electronics II By Mersha K. 13
Chapter One: Feedback in Amplifiers
II. Shunt–series (current amplifier) topologies
Referred to as series-derived shunt-fed feedback.
Current source at the input side and output
current passing through the load.
Output current proportional to input current.
The closed-loop current gain is given by:
Fig1.5: Configuration of Current amplifiers
𝐴
𝐴𝑖𝑓 =
1 + βA
Low input impedance and High output impedance is
desirable.
𝑅𝑖
𝑅𝑖𝑓 = 𝑅𝑜𝑓 = 𝑅𝑜 (1 + βA)
1 + βA
Applied Electronics II By Mersha K. 14
Chapter One: Feedback in Amplifiers
III. Séries - Séries (transconductance amplifier) topologies:
Known as series-derived series-fed feedback.
Voltage source at the input side and output
current passing through the load.
Output current proportional to input voltage.
The closed-loop transconductance gain is:
Fig1.6: Configuration of trans conductance
𝐴 amplifier
𝐴𝑔𝑓 =
1 + βA
High input impedance and high output impedance
is desirable.
𝑅𝑖𝑓 = 𝑅𝑖 (1 + βA) 𝑅𝑜𝑓 = 𝑅𝑜 (1 + βA)
Applied Electronics II By Mersha K. 15
Chapter One: Feedback in Amplifiers
IV. Shunt–shunt (transresistance amplifier) topologies:
Referred to as shunt-derived shunt-fed feedback.
Current source pass through the input side and
output voltage drop at the load.
Output voltage proportional to input current.
The closed-loop transresistance gain is given by: Fig1.7: Configuration of transresistance
𝐴 amplifier
𝐴𝑟𝑓 =
1 + βA
Low input impedance and low output impedance is
desirable.
𝑅𝑖 𝑅𝑜
𝑅𝑖𝑓 = 𝑅𝑜𝑓 =
1 + βA 1 + βA
Applied Electronics II By Mersha K. 16
Chapter One: Feedback in Amplifiers
Summary
Summary results of feedback amplifier functions for the ideal feedback circuit.
Applied Electronics II By Mersha K. 17
Chapter One: Feedback in Amplifiers
Example 1.3: In the series-parallel feedback amplifier of Fig1.8, calculate;
a) Open-loop gain of the amplifier
b) Gain of the feedback network
c) Closed-loop gain of the amplifier
d) Sacrifice factor, S
Fig1.8: Series-parallel (SP) feedback amplifier
Example 1.4: Design an ideal series–series feedback amplifier to meet the following
specifications, assume 𝑅𝑠 is negligibly small. If 𝑉𝑖 = 100 mV, 𝑉𝑓𝑏 = 99 mV, and 𝐼𝑜 = 5 mA.
a. Determine A, β, and 𝐴𝑔𝑓 , including units. (if exist).
b. Determine 𝑅𝑖𝑓 and 𝑅𝑜𝑓 , for 𝑅𝑖 = 5𝑘Ω and 𝑅𝑜 = 4𝑘Ω.
Applied Electronics II By Mersha K. 18
Chapter One: Feedback in Amplifiers
The effect of feedback on different parameters:
Feedback can affect many parameters in an electronics circuit, including:
Gain stability: Positive feedback decreases the gain stability, while negative feedback
increases it.
Gain: Negative feedback reduces the gain of an amplifier while positive feedback
increases it.
Noise and distortion: Positive feedback increases noise and distortion, while negative
feedback decreases it.
Bandwidth: Positive feedback decreases bandwidth, while negative feedback
increases it.
Impedance: Negative feedback improves input and output impedances.
Applied Electronics II By Mersha K. 19
Chapter One: Feedback in Amplifiers
The effect of feedback on different parameters:
Frequency response: Negative feedback can smooths frequency response.
Manufacturing variations: Negative feedback minimizes the effect of manufacturing
variations in component parameters.
Temperature changes: Negative feedback compensates for changes in characteristics
due to temperature change.
System performance: Negative feedback reduces the effect of noise and disturbance on
the system performance.
System accuracy: Negative feedback makes the system more accurate.
System sensitivity: Negative feedback improves the sensitivity of the system..
Applied Electronics II By Mersha K. 20
Chapter One: Feedback in Amplifiers
Steps to analyse feedback amplifier:
Step 1: Identify the topology and calculate the feedback gain
Step 2: Draw equivalent circuit; removing the feedback and taking the load of
feedback in to account.
Step 3: Draw AC model.
Step 4: Calculating gain, Input and Output Impedance.
Applied Electronics II By Mersha K. 21
Chapter One: Feedback in Amplifiers
Exercise 1.2: A series-shunt feedback amplifier employ a basic amplifier with
input and output resistance each of 1kΩ and gain 𝐴 = 200. The feedback factor
β = 1/15. Determine:
a. The closed loop gain
b. The input resistance for the closed loop amplifier
c. The output resistance for the closed loop amplifier
d. If a manufacture error results in a change of 𝐴 = 1800, what is the new
value for the closed loop gain and what is your conclusion?
Applied Electronics II By Mersha K. 22
circuits
End of Chapter One:
Feedback in Amplifiers
