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

 

Analog Electronics – Page 34

Low Frequency Analysis of Amplifiers

At low frequencies, the gain of an amplifier decreases due to the effect of capacitors present in the circuit.

The capacitors responsible for low frequency behavior are:

                                          

• Input Coupling Capacitor
• Emitter Bypass Capacitor
• Output Coupling Capacitor

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1️⃣ Input Coupling Capacitor

The input capacitor blocks DC and allows AC signals to pass to the amplifier.

At low frequencies:

• Capacitive reactance increases
• Signal attenuation occurs
• Amplifier gain decreases

XC = 1 / (2πfC)

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2️⃣ Emitter Bypass Capacitor

The emitter bypass capacitor provides AC ground for the emitter resistor.

At low frequencies:

• Capacitor reactance becomes large
• Emitter degeneration increases
• Voltage gain reduces

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3️⃣ Output Coupling Capacitor

This capacitor transfers AC output to the load while blocking DC.

At low frequencies:

• Capacitive reactance increases
• Output signal reduces

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Lower Cutoff Frequency

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

fL = 1 / (2πRC)

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Example Problem

If coupling capacitor C = 10 µF and resistance R = 1 kΩ.

Find lower cutoff frequency.

fL = 1 / (2πRC)

fL = 1 / (2π × 1000 × 10×10⁻⁶)

fL ≈ 15.9 Hz

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Important GATE Points

• Low frequency roll-off caused by capacitors
• Three capacitors control low-frequency response
• Coupling capacitors block DC components
• Bypass capacitor increases voltage gain

 

Analog Electronics – Page 33

Frequency Response of Amplifiers

The frequency response of an amplifier describes how the gain of the amplifier varies with signal frequency.

It shows the relationship between amplifier gain and input signal frequency.

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Three Frequency Regions

• Low Frequency Region
• Mid Frequency Region
• High Frequency Region

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Low Frequency Region

• Gain decreases at low frequencies
• Due to coupling capacitors and bypass capacitors
• Capacitive reactance becomes large

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Mid Frequency Region

• Gain remains constant
• Amplifier operates normally
• This region is called midband gain

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High Frequency Region

• Gain decreases at high frequencies
• Due to internal transistor capacitances
• Parasitic capacitances affect performance

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Cutoff Frequencies

The frequencies at which the gain drops to 70.7% of maximum gain are called cutoff frequencies.

• Lower cutoff frequency = fL
• Upper cutoff frequency = fH

Gain at cutoff = 0.707 × Maximum Gain

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Bandwidth

The bandwidth of an amplifier is the difference between upper and lower cutoff frequencies.

Bandwidth = fH − fL

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Example Problem

If an amplifier has:

• Lower cutoff frequency = 100 Hz
• Upper cutoff frequency = 100 kHz

Find bandwidth.

BW = fH − fL

BW = 100000 − 100

BW = 99.9 kHz

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Important GATE Points

• Midband gain is constant
• Cutoff occurs at 70.7% gain
• Bandwidth determines amplifier performance
• Higher bandwidth means better amplifier

 

Analog Electronics – Page 32

Multistage Amplifiers

A multistage amplifier consists of two or more amplifier stages connected in cascade to increase overall gain.

Each stage amplifies the signal and passes it to the next stage.

                                               

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Why Multistage Amplifiers are Used

• To obtain very high voltage gain
• To improve power amplification
• To drive heavy loads
• To increase signal strength

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Types of Coupling

• RC Coupling
• Transformer Coupling
• Direct Coupling

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Overall Voltage Gain

The total gain of a multistage amplifier is the product of gains of individual stages.

Av = Av1 × Av2 × Av3 × ... × Avn

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Gain in Decibels

Gain is often expressed in decibels.

Gain(dB) = 20 log10(Av)

For multistage amplifier:

Total Gain(dB) = Gain1 + Gain2 + Gain3

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Example Problem

A two-stage amplifier has gains:

• First stage gain = 50
• Second stage gain = 20

Find total voltage gain.

Av = Av1 × Av2

Av = 50 × 20

Av = 1000

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Gain in dB

Gain(dB) = 20 log10(1000)

Gain = 60 dB

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Key Points for GATE

• Overall gain is multiplication of stage gains
• In decibel scale gains are added
• RC coupling is most common in voltage amplifiers
• Transformer coupling used for power amplification