GATE Electrical – Analog Electronics

Page 18 : Miller Effect in Amplifiers

The Miller Effect explains how a small capacitance between the input and output terminals of an amplifier appears as a much larger capacitance at the input.

This effect significantly reduces the high-frequency performance of amplifiers.

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Origin of Miller Effect

In transistor amplifiers, there is a small internal capacitance between:

• Base and Collector in BJT
• Gate and Drain in MOSFET

This capacitance is called the feedback capacitance.

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Miller Capacitance Formula

If a capacitance C exists between input and output, the effective input capacitance becomes:

C_in = C (1 − Av)

Where:

• C = feedback capacitance
• Av = voltage gain of amplifier

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Example

If:

• Feedback capacitance = 2 pF
• Voltage gain Av = −100

Then:

C_in = 2 (1 − (-100)) C_in = 202 pF

Thus a very small capacitor appears very large at the input.

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Effect on Amplifier

• Reduces bandwidth
• Limits high frequency response
• Introduces unwanted feedback

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How to Reduce Miller Effect

• Use Cascade Amplifier
• Use Common Base configuration
• Use Cascode amplifier

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Important GATE Points

• Miller effect increases effective input capacitance.
• It reduces amplifier bandwidth.
• Occurs due to feedback capacitance.
• Cascode amplifier reduces Miller effect.

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Next Page → Differential Amplifier

 

GATE Electrical – Analog Electronics

Page 17 : Bode Plot of Amplifiers

A Bode Plot is a graphical method used to represent the frequency response of an amplifier using a logarithmic frequency scale.

It shows how amplifier gain varies with frequency.

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What is a Bode Plot?

A Bode plot consists of two graphs:

• Magnitude plot (Gain vs Frequency)
• Phase plot (Phase vs Frequency)

For most GATE questions, the magnitude plot is mainly used.

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Gain in Decibels

In Bode plots, amplifier gain is expressed in decibels (dB).

Gain (dB) = 20 log10 (Av)

Where:

• Av = Voltage gain

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Frequency Scale

Frequency is plotted on a logarithmic scale.

Example frequency values:

• 10 Hz
• 100 Hz
• 1 kHz
• 10 kHz
• 100 kHz

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Slope of Bode Plot

The gain decreases with frequency at a certain rate.

Typical slopes are:

• -20 dB / decade
• -40 dB / decade
• -60 dB / decade

Each pole introduces a slope of -20 dB/decade.

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Corner Frequency

The frequency at which gain starts decreasing is called the corner frequency.

At this point gain drops by:

3 dB

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Important GATE Points

• Bode plot uses logarithmic frequency scale.
• Gain is expressed in decibels.
• Each pole contributes -20 dB/decade slope.
• Cut-off frequency corresponds to -3 dB point.

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Next Page → Miller Effect in Amplifiers

 

GATE Electrical – Analog Electronics

Page 17: Frequency Response of Amplifiers

Frequency response describes how the gain of an amplifier changes with the frequency of the input signal. In practical amplifiers, gain is not constant for all frequencies.

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Frequency Response Curve

The frequency response is usually represented by a graph of Voltage Gain (Av) versus Frequency (f).

The amplifier operates in three regions:

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

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1. Low Frequency Region

At low frequencies, the gain decreases due to the effect of coupling capacitors and bypass capacitors.

Capacitive reactance becomes large, reducing signal transfer.

XC = 1 / (2πfC)

Thus low-frequency gain drops.

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2. Mid Frequency Region

In the mid-frequency range, capacitors behave like short circuits and the amplifier gain becomes approximately constant.

This region provides the maximum and stable gain.

Av ≈ Constant

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3. High Frequency Region

At high frequencies, internal transistor capacitances affect the amplifier operation.

• Base-emitter capacitance
• Base-collector capacitance

These capacitances reduce gain at high frequencies.

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Cut-off Frequencies

Two important frequencies define amplifier bandwidth:

• Lower Cut-off Frequency (fL)
• Upper Cut-off Frequency (fH)

At these frequencies, gain becomes:

Av = 0.707 × Av(max)

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Bandwidth

Bandwidth is the range of frequencies where amplifier gain remains nearly constant.

Bandwidth = fH − fL

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Important GATE Points

• Gain drops at both low and high frequencies.
• Mid-band gain is maximum and constant.
• Cut-off gain = 0.707 × maximum gain.
• Bandwidth = fH − fL.

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Next Page → Bode Plot of Amplifiers

 

GATE Electrical – Analog Electronics

Page 15: Emitter Follower (Common Collector Amplifier)

The Emitter Follower amplifier is also called the Common Collector (CC) amplifier. In this configuration, the collector terminal is common to both input and output circuits.

                                            

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Circuit Configuration

In the emitter follower configuration:

• Input signal is applied between base and collector
• Output signal is taken from the emitter terminal
• The collector is connected to the supply voltage

Since the output voltage follows the input voltage, this amplifier is called an Emitter Follower.

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Working Principle

When an input signal is applied to the base, the emitter voltage changes accordingly.

The emitter voltage is approximately:

VE ≈ VB − VBE

Where:

• VB = Base voltage
• VBE ≈ 0.7 V (for silicon transistor)

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Voltage Gain

Voltage gain of emitter follower is approximately:

Av ≈ 1

Thus the output voltage nearly follows the input voltage.

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Input Resistance

Input resistance is very high:

Rin ≈ β RE

Typical value ranges from:

100 kΩ – 1 MΩ

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Output Resistance

Output resistance is very low:

Rout ≈ RE / β

Typical value ranges from:

10 Ω – 100 Ω

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Applications

• Impedance matching
• Buffer amplifier
• Voltage follower circuits
• Signal isolation

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Important GATE Points

• Voltage gain ≈ 1
• Very high input resistance
• Very low output resistance
• No phase inversion
• Used as buffer amplifier

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Next Page → Multistage Amplifiers

 

GATE Electrical – Analog Electronics

Page 14: Common Emitter (CE) Amplifier

The Common Emitter amplifier is the most widely used transistor amplifier configuration because it provides high voltage gain and moderate input and output resistance.

                                       

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CE Amplifier Circuit

In the CE amplifier configuration:

• Input signal is applied between base and emitter
• Output is taken between collector and emitter
• The emitter terminal is common for both input and output

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Working Principle

A small change in base current produces a large change in collector current. This results in amplification of the input signal.

Collector current relationship:

IC = β IB

Since the collector resistor converts current variation into voltage variation, a large output voltage appears across the load.

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Voltage Gain

Using the small signal model, voltage gain of CE amplifier is:

Av = -gm RC

Where:

• gm = transconductance
• RC = collector resistance

Negative sign indicates phase inversion.

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Input Resistance

Input resistance of CE amplifier is approximately:

Rin = rπ

Typical value ranges from:

1 kΩ – 10 kΩ

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Output Resistance

Output resistance of CE amplifier is approximately:

Rout ≈ RC

Typical value ranges from:

10 kΩ – 50 kΩ

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Phase Inversion

One important feature of the CE amplifier is that the output signal is 180° out of phase with the input signal.

This means when the input signal increases, the output voltage decreases.

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Important GATE Points

• CE amplifier provides high voltage gain.
• Output signal is inverted (180° phase shift).
• Moderate input resistance.
• Moderate output resistance.
• Most widely used transistor amplifier.

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Next Page → Emitter Follower (Common Collector Amplifier)

 

GATE Electrical – Analog Electronics

Page 13: Small Signal Model of BJT

In amplifier analysis, signals are usually small compared to the DC bias values. To analyze such circuits easily, the transistor is replaced with a simplified equivalent circuit called the Small Signal Model.

This model helps determine voltage gain, input resistance and output resistance of transistor amplifiers.

                                              

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Why Small Signal Model is Needed

• Simplifies transistor analysis
• Helps calculate amplifier gain
• Used in AC analysis of amplifier circuits

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Hybrid-π Model

The most widely used small signal model is the Hybrid-π Model.

It consists of the following elements:

• rπ → Base-emitter resistance
• gm vπ → Controlled current source
• ro → Output resistance

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Important Small Signal Parameters

1. Transconductance (gm)

Transconductance represents the relationship between collector current and base-emitter voltage.

gm = IC / VT

Where:

• IC = Collector current
• VT ≈ 25 mV at room temperature

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2. Input Resistance (rπ)

Input resistance between base and emitter is:

rπ = β / gm

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3. Output Resistance (ro)

Output resistance is caused by Early effect.

ro = VA / IC

Where:

• VA = Early voltage

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Voltage Gain of CE Amplifier

Using the small signal model, the voltage gain becomes:

Av = -gm RC

Negative sign indicates phase inversion.

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Important GATE Points

• Small signal model is used for AC analysis.
• Hybrid-π model is most commonly used.
• gm increases with collector current.
• Voltage gain of CE amplifier is negative.

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Next Page → CE Amplifier Analysis

 

GATE Electrical – Analog Electronics

Page 12: BJT Biasing Techniques

Biasing is the process of establishing the correct operating point (Q-point) of a transistor so that it can work properly as an amplifier.

Proper biasing ensures:

                                 

• Stable operation
• Linear amplification
• Minimum signal distortion

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1. Fixed Bias (Base Bias)

This is the simplest biasing method where a resistor is connected between the base and the supply voltage.

Base current is determined by:

IB = (VCC − VBE) / RB

Collector current becomes:

IC = β IB

Advantages

• Simple circuit
• Easy to design

Disadvantages

• Very poor stability
• Q-point changes with temperature

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2. Collector-to-Base Bias

In this method the base resistor is connected to the collector instead of the supply voltage.

This provides a small negative feedback which improves stability.

Advantages

• Better stability than fixed bias
• Provides negative feedback

Disadvantages

• Still not very stable
• Limited practical use

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3. Voltage Divider Bias

Voltage divider bias is the most widely used biasing method.

Two resistors form a voltage divider network to set the base voltage.

VB = VCC × R2 / (R1 + R2)

Emitter resistor improves thermal stability.

Advantages

• Excellent stability
• Q-point remains nearly constant
• Widely used in amplifier circuits

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Comparison of Biasing Methods

Bias Method	Stability	Complexity
Fixed Bias	Poor	Simple
Collector Bias	Moderate	Medium
Voltage Divider Bias	Excellent	Most Used

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Important GATE Points

• Voltage divider bias is the most stable method.
• Emitter resistor improves thermal stability.
• Biasing ensures correct Q-point.
• Without proper biasing, amplifier distortion occurs.

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Next Page → Small Signal Model of BJT