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

 

Analog Electronics – Page 31

Comparison of BJT Amplifier Configurations

There are three basic transistor amplifier configurations:

• Common Emitter (CE)
• Common Base (CB)
• Common Collector (CC)

Each configuration has different gain and impedance characteristics.

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1️⃣ Common Emitter Amplifier

• High voltage gain
• High current gain
• Moderate input impedance
• Moderate output impedance
• Phase shift = 180°

Voltage gain: Av ≈ − (hfe RL) / hie

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2️⃣ Common Base Amplifier

• High voltage gain
• Current gain ≈ 1
• Low input impedance
• High output impedance
• No phase shift

Current gain: α ≈ Ic / Ie

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3️⃣ Common Collector Amplifier (Emitter Follower)

• Voltage gain ≈ 1
• High current gain
• Very high input impedance
• Low output impedance
• No phase shift

Voltage gain ≈ 1

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Important Comparison Table

Parameter	CE	CB	CC
Voltage Gain	High	High	≈1
Current Gain	High (β)	≈1 (α)	High
Input Impedance	Medium	Low	High
Output Impedance	Medium	High	Low
Phase Shift	180°	0°	0°

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GATE Important Points

• CE is most widely used amplifier
• CB used for high-frequency applications
• CC used as buffer amplifier

 

Analog Electronics – Page 30

Common Emitter Amplifier Gain using h-Parameters

The hybrid h-parameter model is widely used for analyzing transistor amplifiers. It simplifies the transistor into a linear two-port network.

                                      

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CE h-Parameter Model

The equations for h-parameter model are:

V1 = h11 I1 + h12 V2

I2 = h21 I1 + h22 V2

For Common Emitter configuration:

• h11 = hie (Input resistance)
• h21 = hfe (Current gain)
• h12 = hre (Reverse voltage gain)
• h22 = hoe (Output admittance)

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Voltage Gain Derivation

Output voltage:

Vo = − Ic RL

Collector current:

Ic = hfe Ib

Input voltage:

Vi = Ib hie

Therefore voltage gain:

Av = Vo / Vi

Av = − (hfe RL) / hie

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Current Gain

Current gain of CE amplifier:

Ai = Ic / Ib = hfe

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Power Gain

Power gain is:

Ap = Av × Ai

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Example Problem

Given:

• hfe = 120
• hie = 1.2 kΩ
• RL = 3 kΩ

Find Voltage Gain

Av = − (hfe RL) / hie

Av = − (120 × 3000) / 1200

Av = −300

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Key Observations

• Voltage gain increases with higher hfe
• Voltage gain increases with larger load resistance
• Higher hie reduces voltage gain