Analog Electronics – Page 41

Voltage Shunt Feedback Amplifier – Complete Derivation

                    

Voltage shunt feedback is a feedback configuration in which:

• Output voltage is sampled
• Feedback signal is applied in parallel (shunt) with the input

This configuration is commonly used in transresistance amplifiers.

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Closed Loop Gain Derivation

Let

• A = Open loop gain
• β = Feedback factor
• Af = Closed loop gain

Feedback voltage:

Vf = βVo

Input signal current becomes:

Ii = Is − If

Output voltage:

Vo = A Ii

Substituting feedback:

Vo = A(Is − βVo)

Rearranging:

Vo + AβVo = AIs

Vo(1 + Aβ) = AIs

Closed loop gain:

Af = A / (1 + Aβ)

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Input Resistance with Feedback

Shunt mixing reduces input resistance.

Rif = Ri / (1 + Aβ)

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Output Resistance with Feedback

Voltage sampling reduces output resistance.

Rof = Ro / (1 + Aβ)

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Key Characteristics

• Input resistance decreases
• Output resistance decreases
• Gain becomes stable
• Bandwidth increases

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Important GATE Points

• Voltage shunt feedback → Transresistance amplifier
• Closed loop gain = A / (1 + Aβ)
• Input resistance decreases
• Output resistance decreases
•         
  
  
  

 

Analog Electronics – Page 40

Voltage Series Feedback Amplifier – Complete Derivation

                                              

Voltage series feedback is one of the most widely used feedback configurations in amplifiers.

In this method:

• Output voltage is sampled
• Feedback signal is applied in series with input

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Closed Loop Gain Derivation

Let

• A = Open loop gain
• β = Feedback factor
• Af = Closed loop gain

Feedback voltage:

Vf = βVo

Input to amplifier:

Vi = Vs − Vf

Substitute feedback:

Vi = Vs − βVo

Output voltage:

Vo = AVi

Substitute Vi:

Vo = A(Vs − βVo)

Expand equation:

Vo = AVs − AβVo

Rearranging:

Vo + AβVo = AVs

Vo(1 + Aβ) = AVs

Closed loop gain:

Af = Vo / Vs = A / (1 + Aβ)

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Input Resistance with Feedback

Voltage series feedback increases input resistance.

Rif = Ri (1 + Aβ)

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Output Resistance with Feedback

Voltage sampling reduces output resistance.

Rof = Ro / (1 + Aβ)

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Key Characteristics

• Input resistance increases
• Output resistance decreases
• Gain becomes stable
• Bandwidth increases

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Important GATE Points

• Voltage series feedback → Voltage amplifier
• Closed loop gain = A / (1 + Aβ)
• Input resistance increases
• Output resistance decreases

 

Analog Electronics – Page 39

Four Types of Feedback Amplifiers

Feedback amplifiers are classified based on:

• How the feedback signal is taken from output
• How the feedback signal is applied to input

                                                 

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Types of Feedback Amplifiers

Feedback Type	Output Sampling	Input Mixing	Amplifier Type
Voltage Series	Voltage	Series	Voltage Amplifier
Voltage Shunt	Voltage	Parallel	Transresistance Amplifier
Current Series	Current	Series	Transconductance Amplifier
Current Shunt	Current	Parallel	Current Amplifier

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1. Voltage Series Feedback

• Output voltage sampled
• Feedback applied in series with input
• Increases input impedance
• Decreases output impedance

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2. Voltage Shunt Feedback

• Output voltage sampled
• Feedback applied in parallel
• Reduces input impedance
• Reduces output impedance

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3. Current Series Feedback

• Output current sampled
• Feedback applied in series
• Increases input impedance
• Increases output impedance

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4. Current Shunt Feedback

• Output current sampled
• Feedback applied in parallel
• Reduces input impedance
• Increases output impedance

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Important GATE Points

• Feedback classification depends on input mixing and output sampling
• Series mixing increases input resistance
• Shunt mixing decreases input resistance
• Voltage sampling reduces output resistance
• Current sampling increases output resistance

 

Analog Electronics – Page 38

Bandwidth Improvement Using Negative Feedback

One of the major advantages of negative feedback in amplifiers is the increase in bandwidth.

Although feedback reduces gain, it significantly increases the frequency range over which the amplifier operates.

                               

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Gain with Negative Feedback

The closed-loop gain of a feedback amplifier is given by:

Af = A / (1 + Aβ)

Where

• A = Open loop gain
• β = Feedback factor
• Af = Closed loop gain

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Bandwidth Relation

For an amplifier without feedback:

BW = fH − fL

When negative feedback is applied:

BWf = BW (1 + Aβ)

This means bandwidth increases by the same factor by which gain decreases.

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Gain-Bandwidth Product

The gain-bandwidth product of an amplifier remains approximately constant.

A × BW = Constant

After feedback:

Af × BWf = A × BW

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Example Problem

If an amplifier has:

• Open loop gain A = 100
• Bandwidth = 10 kHz
• Feedback factor β = 0.04

Find new bandwidth.

1 + Aβ = 1 + (100 × 0.04)

1 + Aβ = 5

BWf = 10 kHz × 5 = 50 kHz

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Important GATE Points

• Negative feedback increases bandwidth
• Gain reduces but stability improves
• Gain × Bandwidth remains constant
• Used in most practical amplifier circuits

 

Analog Electronics – Page 37

Feedback Amplifiers – Concept and Types

Feedback is the process of taking a portion of the output signal and returning it to the input of the amplifier.

Feedback is widely used in electronic circuits to control gain, improve stability, and reduce distortion.

                                   

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Basic Feedback System

A feedback amplifier consists of three main parts:

• Input Signal
• Amplifier (Gain Block)
• Feedback Network

Output → Feedback Network → Returned to Input

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Types of Feedback

1. Positive Feedback

• Feedback signal is in phase with input
• Used in oscillators
• Increases gain

Positive feedback can cause instability.

2. Negative Feedback

• Feedback signal is opposite phase
• Used in amplifiers
• Improves stability
• Reduces distortion

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Advantages of Negative Feedback

• Stabilizes amplifier gain
• Reduces noise
• Improves bandwidth
• Reduces distortion

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Types of Feedback Amplifiers

• Voltage Series Feedback
• Voltage Shunt Feedback
• Current Series Feedback
• Current Shunt Feedback

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Important GATE Points

• Negative feedback improves bandwidth
• Gain becomes more stable
• Distortion reduces significantly
• Used in most practical amplifiers

 

Analog Electronics – Page 36

Bode Plot and Bandwidth of Amplifiers

A Bode plot is a graphical representation of amplifier gain versus frequency on a logarithmic scale.

It helps engineers understand how amplifier gain changes over different frequencies.

                                       

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What is a Bode Plot?

• Frequency is plotted on logarithmic scale
• Gain is plotted in decibels (dB)
• Shows amplifier frequency response clearly

Gain(dB) = 20 log₁₀(Av)

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Important Frequency Points

• Lower cutoff frequency → fL
• Upper cutoff frequency → fH
• Midband region → constant gain

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Bandwidth

Bandwidth is the frequency range where the amplifier gain remains approximately constant.

Bandwidth (BW) = fH − fL

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Slope of Bode Plot

At cutoff frequencies, gain begins to decrease.

• Single pole system → −20 dB/decade
• Two pole system → −40 dB/decade

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Example Problem

If an amplifier has:

• Lower cutoff frequency fL = 200 Hz
• Upper cutoff frequency fH = 200 kHz

Find bandwidth.

BW = fH − fL

BW = 200000 − 200

BW ≈ 199.8 kHz

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Important GATE Points

• Bode plot uses logarithmic frequency scale
• Gain expressed in decibels
• Cutoff occurs at 0.707 of midband gain
• Slope is −20 dB/decade for single pole systems

 

Analog Electronics – Page 35

High Frequency Analysis of Amplifiers

       

At high frequencies, the gain of an amplifier decreases due to internal capacitances of the transistor.

The main capacitances affecting high frequency response are:

• Base–Emitter Capacitance (Cπ)
• Collector–Base Capacitance (Cμ)

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Transistor Internal Capacitances

These capacitances form RC networks which limit amplifier bandwidth.

• Cπ → between base and emitter
• Cμ → between collector and base

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Miller Effect

The collector-base capacitance appears multiplied at the input due to voltage gain.

This phenomenon is called Miller Effect.

CM = Cμ (1 − Av)

Where:

• CM = Miller capacitance
• Cμ = Collector-base capacitance
• Av = Voltage gain

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Effect of Miller Capacitance

• Increases input capacitance
• Reduces bandwidth
• Limits high frequency operation

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Upper Cutoff Frequency

The upper cutoff frequency occurs when gain drops to 0.707 of midband gain.

fH = 1 / (2πRC)

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Example Problem

If:

• Cμ = 2 pF
• Voltage gain Av = −100

Find Miller capacitance.

CM = Cμ (1 − Av)

CM = 2 pF (1 − (−100))

CM = 2 × 101 = 202 pF

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Important GATE Points

• Miller effect increases input capacitance
• High voltage gain increases Miller capacitance
• Bandwidth decreases due to Miller effect
• Common base amplifier avoids Miller effect