APPLIED ELECTRONICS II
CHAPTER 1: FEEDBACK AMPLIFIERS
1.
2.
3.
4.
OVERVIEW
Types of Feedback
The Feedback Concept
Feedback Topologies
Advantages of Negative Feedback
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Gain Desensitivity
Noise/ Interference Reduction
Reduction of Nonlinear Distortion
Control of Impedance and Bandwidth Extension
5. Analysis of Feedback Amplifiers
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Voltage-Series (Voltage Amplifier) Feedback
Current-Series (Transconductance Amplifier) Feedback
Current-Shunt (Current Amplifier) Feedback
Voltage-Shunt (Transresistance Amplifier) Feedback
TYPES OF FEEDBACK
• Feedback can either be positive or negative
1. Positive Feedback
•
A portion of the output signal is added to the input. Positive feedback is used in the design of
oscillator and a number of other applications (will be discussed in Chapter 4 and 5).
2. 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, such as to desensitize the gain,
Reduce nonlinear Distortion, Reduce the effect of noise, control input and output impedances and
extend the bandwidth of the amplifiers.
NEGATIVE FEEDBACK
Example
• Introducing resistor at the emitter of BJT common-emitter circuits stabilizes the Q-point
against variation transistor parameters.
THE FEEDBACK CONCEPT
• Signal Source: This block is a voltage source Vs with a series resistor Rs (Thevenin's
equivalent circuit) or a current source Is with a parallel resistor Rs (Norton’s equivalent
circuit).
• Feedback Network: Usually a passive two-port network with reverse transmission β.
THE FEEDBACK CONCEPT
• Sampling Network: Sampling Blocks shown below.
• Voltage or Node Sampling: Output
voltage is sampled by connecting the
feedback network in shunt across the
output.
• Current or loop Sampling: Output
current is sampled by connecting the
feedback network in series with the
output.
THE FEEDBACK CONCEPT
• Comparator or Mixer Network: mixing blocks are shown below
• Series Mixing
• Shunt Mixing
THE FEEDBACK CONCEPT
• Basic Amplifier (A): could be used to represent a Voltage Amplifier, Current Amplifier,
Transconductance Amplifier or a Transresistance Amplifier.
• Thevenin’s equivalent circuit of a Voltage Amplifier. It has ideally infinite input
resistance (Ri), zero output resistance (RO) and a Voltage Gain (𝐴𝑉 = 𝑉𝑜 Τ𝑉𝑠 )
THE FEEDBACK CONCEPT
• Norton’s equivalent circuit of a Current Amplifier. It has ideally zero input
resistance (Ri), infinite output resistance (RO) and a current gain (𝐴𝑖 = 𝐼𝑜 Τ𝐼𝑠 ).
THE FEEDBACK CONCEPT
• Transconductance Amplifier which ideally has infinite input resistance (Ri), infinite
output resistance (RO) and a transconductance gain (𝐺𝑚 = 𝐼𝑜 Τ𝑉𝑠 ). Gm – Short circuit
mutual or transfer conductance.
THE FEEDBACK CONCEPT
• Transresistance Amplifier which ideally has zero input resistance (Ri), zero output
resistance (RO) and a transresistance gain (𝑅𝑚 = 𝑉𝑜 Τ𝐼𝑠 ). Rm – Open circuit mutual or
transfer resistance.
THE TRANSFER GAIN WITH FEEDBACK
• The figure shows the basic structure of a feedback amplifier using a signal flow graph,
where each of the quantities x can represent either a voltage or a current signal.
THE TRANSFER GAIN WITH FEEDBACK
• The open-loop gain, A represents the transfer gain of the basic amplifier without
feedback. Implicit in the description is that the source, the load, and the feedback
network do not load the basic amplifier. That is, the gain A does not depend on any of
these three networks. In practice this will not be the case.
FEEDBACK TOPOLOGIES
• There are four basic feedback topologies, based on the input signal (voltage or
current) and the output signal (voltage or current). They are described by the
type of connection at the input and output of the circuit.
A. Voltage-Series (Series-Shunt) or Voltage Amplifier
B. Current-Shunt (Shunt-Series) or Current Amplifier
C. Current-Series (Series-Series) or Transconductance Amplifier
D. Voltage-Shunt (Shunt-Shunt) or Transeresistance Amplifier
FEEDBACK TOPOLOGIES
GENERAL CHARACTERISTICS OF NEGATIVE FEEDBACK
• Gain Desensitivity: Variation in gain due to temperature, aging or other parameters
is reduced by negative feedback. E.g. Emitter Stabilized Common Emitter Amplifier.
• Assuming β is constant and taking the derivative of Af with respect to A,
GAIN DESENSITIVITY
• Hence the percentage change in Af (due to variations in some circuit parameter) is
•
smaller than the percentage change in A by a factor equal to the amount of feedback.
For this reason, the amount of feedback, 1 + Aβ, is also known as the Desensitivity
Factor.
Example: The open-loop gain of an amplifier is A = 5 × 104V/V exhibits a gain
change of 25% as the operating temperature changes. Calculate the percentage
change if the closed loop gain Af = 50V/V
NOISE/INTERFERENCE REDUCTION
• Under certain condition feedback amplifiers can be used to reduce noise/interference.
• This can be achieved if a preamplifer which is (relatively) noise/interference-free preceded the
noise/interference-prone amplifier.
• Under such conditions the Signal-to-Noise ratio can be improved (compared to noise/interferenceprone amplifier without feedback) by the factor of the preamplifier gain.
REDUCTION OF NONLINEAR DISTORTION
• Distortion in the output is due to application of large amplitude input signal applied
beyond the linear region of operation.
• Negative feedback can be implemented to reduce nonlinear distortion by the
Desensitivity factor.
• Assuming that the open-loop gain
• It implies that Af is independent of the nonlinear properties of the transistors used in
the basic amplifier.
• Since the feedback network usually consists of passive components, which usually can
be chosen to be as accurate as one wishes.
BANDWIDTH EXTENSION AND REDUCTION OF
FREQUENCY DISTORTION
• The amplifier bandwidth is increased by the same factor by which its midband
gain is decreased, maintaining the gain–bandwidth product at a constant value.
CONTROL OF IMPEDANCE
• Input Impedance
• If the feedback signal is returned to the input in series with the
applied voltage (Series mixing), it increases the input resistance.
• If the feedback signal is returned to the input in shunt with the
applied signal (Shunt mixing), it decreases the input resistance
• Output Impedance
• If the feedback samples the output voltage (Voltage sampling), it
tends to decrease the output resistance
• If the feedback samples the output current (Current Sampling), it
tends to increase the output resistance.
VOLTAGE SERIES
• Input Impedance
Applying KVL to the input side,
and
Let
, where Av is the voltage gain
without feedback taking the load resistor into
account. Then,
• Avo represents the open circuit
voltage gain without feedback
taking Rs into account
VOLTAGE SERIES
• Output Impedance: in any circuit to calculate the output impedance we must first
remove the external input source (voltage or current).
• Remove the load resistor and then impress a voltage across the output terminals and
calculate the current in order to obtain 𝑅𝑜𝑓 = 𝑉𝑥 Τ𝐼𝑥
Since,
VOLTAGE SERIES
CURRENT SERIES
• Input Impedance: is calculated in a similar manner to the voltage series topology to
obtain,
• Where,
is the short circuit transconductance, and
is the transconductance without feedback taking the load into account.
CURRENT SERIES
• Applying KCL at the output
• The input voltage is given by,
• Substituting,
• Rearranging for the output impedance,
CURRENT SERIES
• The output impedance with feedback taking the load resistor into consideration will be,
• Dividing both the numerator and denominator by RO + RL we get,
CURRENT SHUNT
• Input Impedance:
• Applying KCL at the input and current
division at the output,
• Taking
,
• Ai is the short-circuit current gain taking
Rs into account, and AI is the current gain
taking the load into account.
• Output Impedance: is calculated in the same manner to the current series topology,
VOLTAGE SHUNT
• Input Impedance: is calculated in a similar manner to the current shunt topology,
• Output Impedance: is calculated in a similar manner to the voltage series topology,
•
Rm is the open circuit transresistance
gain taking Rs into account and
Is the transresistance gain without
feedback taking the load into account.
FUNDAMENTAL ASSUMPTIONS
• Some fundamental assumptions are taken in order to analyze the four feedback
configurations.
• The basic amplifier (A) is unilateral, transmitting signal from input to output.
• The feedback network (β) is unilateral, transmitting signal from output to input.
• β is independent of the source and load resistors (RS and RL)
• In practical case,
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•
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feedback network will not be ideal, 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
The feedback network should be expressed as a two port network
METHOD OF ANALYSIS OF FEEDBACK AMPLIFIERS
• First identify the feedback component then proceed with the following steps:
METHOD OF ANALYSIS OF FEEDBACK AMPLIFIERS
EXAMPLE
• Assume RS = 0, hfe = 50, hie = 1.1kΩ , hre = hoe = 0 and identical transistors