GATE Electrical – Analog Electronics

Practice Problems – Page 14

This section contains problems based on Operational Amplifier Applications including summing amplifier and difference amplifier circuits.

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Problem 131

Question:

What is a summing amplifier?

Answer:

A summing amplifier is an op-amp circuit that produces an output voltage proportional to the sum of multiple input voltages.

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Problem 132

Question:

Write the output equation of an inverting summing amplifier.

Answer:

Vo = −Rf (V1/R1 + V2/R2 + V3/R3)

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Problem 133

Question:

If Rf = 10 kΩ, R1 = R2 = 5 kΩ, V1 = 1 V, V2 = 2 V, find output voltage.

Solution:

Vo = −Rf (V1/R1 + V2/R2)

Vo = −10k (1/5k + 2/5k)

Vo = −6 V

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Problem 134

Question:

What is a difference amplifier?

Answer:

A difference amplifier amplifies the difference between two input signals.

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Problem 135

Question:

Write the output voltage equation of a difference amplifier.

Answer:

Vo = (Rf/R1) (V2 − V1)

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Problem 136

Question:

If Rf = R1 and V2 = 4 V, V1 = 1 V, calculate output voltage.

Solution:

Vo = (V2 − V1)

Vo = 4 − 1 = 3 V

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Problem 137

Question:

Which op-amp circuit performs addition of signals?

Answer:

Summing Amplifier

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Problem 138

Question:

Which op-amp circuit is used for signal subtraction?

Answer:

Difference Amplifier

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Problem 139

Question:

Where is summing amplifier commonly used?

Answer:

Audio mixers and signal processing circuits.

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Problem 140

Question:

Which op-amp application is used in digital to analog converters?

Answer:

Summing Amplifier

 

GATE Electrical – Analog Electronics

Practice Problems – Page 13

This section contains problems based on Non-Inverting Operational Amplifier circuits.

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Problem 121

Question:

Write the voltage gain formula of a non-inverting amplifier.

Answer:

Av = 1 + (Rf / R1)

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Problem 122

Question:

If Rf = 10 kΩ and R1 = 2 kΩ, calculate voltage gain.

Solution:

Av = 1 + (Rf / R1)

Av = 1 + (10000 / 2000)

Av = 6

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Problem 123

Question:

If input voltage = 0.5 V and gain = 6, find output voltage.

Solution:

Vo = Av × Vin

Vo = 6 × 0.5 = 3 V

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Problem 124

Question:

What is the phase shift of a non-inverting amplifier?

Answer:

0°

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Problem 125

Question:

What is the input impedance of a non-inverting amplifier?

Answer:

Very high (ideally infinite).

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Problem 126

Question:

If Rf = 20 kΩ and R1 = 10 kΩ, find gain.

Solution:

Av = 1 + (Rf / R1)

Av = 1 + (20k / 10k) = 3

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Problem 127

Question:

Which op-amp configuration is used as voltage follower?

Answer:

Non-Inverting Amplifier

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Problem 128

Question:

What is the gain of a voltage follower?

Answer:

Av = 1

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Problem 129

Question:

Why is voltage follower used?

Answer:

For impedance matching between circuits.

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Problem 130

Question:

Which amplifier configuration has highest input impedance?

Answer:

Non-Inverting Amplifier

 

GATE Electrical – Analog Electronics

Practice Problems – Page 12

This section contains practice problems based on Inverting Operational Amplifier circuits.

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Problem 111

Question:

An inverting amplifier has Rf = 10 kΩ and Rin = 2 kΩ. Find voltage gain.

Solution:

Av = −Rf / Rin

Av = −10000 / 2000

Av = −5

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Problem 112

Question:

If input voltage is 0.5 V and gain is −10, find output voltage.

Solution:

Vo = Av × Vin

Vo = −10 × 0.5 = −5 V

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Problem 113

Question:

What is the input impedance of an inverting amplifier?

Answer:

Input impedance ≈ Rin.

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Problem 114

Question:

If Rin = 5 kΩ and Rf = 25 kΩ, calculate voltage gain.

Solution:

Av = −Rf / Rin

Av = −25k / 5k = −5

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Problem 115

Question:

Why is the inverting input terminal called virtual ground?

Answer:

Because voltage at the inverting terminal is approximately zero due to negative feedback.

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Problem 116

Question:

What is phase shift of an inverting amplifier?

Answer:

180°

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Problem 117

Question:

If Rf = Rin, what is voltage gain?

Answer:

Av = −1

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Problem 118

Question:

Which op-amp circuit performs signal inversion?

Answer:

Inverting amplifier

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Problem 119

Question:

What happens if feedback resistor increases?

Answer:

Voltage gain increases.

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Problem 120

Question:

What is the main advantage of negative feedback in op-amp?

Answer:

It stabilizes gain and reduces distortion.

 

GATE Electrical – Analog Electronics

Practice Problems – Page 10

This section includes practice problems based on Operational Amplifier fundamentals and ideal characteristics.

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Problem 91

Question:

Define an operational amplifier.

Answer:

An operational amplifier is a high-gain differential amplifier used to perform mathematical operations such as addition, subtraction, integration, and differentiation.

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Problem 92

Question:

What are the ideal characteristics of an op-amp?

Answer:

• Infinite open loop gain
• Infinite input impedance
• Zero output impedance
• Infinite bandwidth
• Infinite CMRR
• Infinite slew rate

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Problem 93

Question:

What is the typical open loop gain of an op-amp?

Answer:

≈ 100,000 (10⁵)

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Problem 94

Question:

Define input offset voltage.

Answer:

Input offset voltage is the small differential voltage required between input terminals to make output zero.

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Problem 95

Question:

What is slew rate?

Answer:

Slew rate is the maximum rate of change of output voltage.

Slew Rate = dV/dt

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Problem 96

Question:

What is the ideal input current of an op-amp?

Answer:

Zero

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Problem 97

Question:

Why is input impedance of op-amp very high?

Answer:

To ensure negligible current flows into the input terminals.

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Problem 98

Question:

What is the ideal output impedance of an op-amp?

Answer:

Zero

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Problem 99

Question:

What is the function of feedback in op-amp circuits?

Answer:

Feedback stabilizes gain and improves amplifier performance.

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Problem 100

Question:

Name two basic op-amp configurations.

Answer:

• Inverting amplifier
• Non-inverting amplifier

 

GATE Electrical – Analog Electronics

Practice Problems – Page 9

This section includes numerical problems based on Differential Amplifier Gain, Output Voltage and CMRR.

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Problem 81

Question:

A differential amplifier has differential gain Ad = 150. If V1 = 20 mV and V2 = 5 mV, find output voltage.

Solution:

Vd = V1 − V2

Vd = 20 mV − 5 mV

Vd = 15 mV

Vo = Ad × Vd

Vo = 150 × 15 mV = 2.25 V

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Problem 82

Question:

If common mode gain Ac = 0.2 and common mode voltage is 1 V, find output voltage.

Solution:

Vo = Ac × Vc

Vo = 0.2 × 1 = 0.2 V

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Problem 83

Question:

A differential amplifier has CMRR = 500 and differential gain Ad = 200. Find common mode gain.

Solution:

CMRR = Ad / Ac

Ac = Ad / CMRR

Ac = 200 / 500

Ac = 0.4

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Problem 84

Question:

If differential gain Ad = 300 and input difference voltage = 10 mV, find output voltage.

Solution:

Vo = Ad × Vd

Vo = 300 × 10 mV

Vo = 3 V

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Problem 85

Question:

If differential amplifier output is zero, what can be said about the inputs?

Answer:

Both input voltages are equal.

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Problem 86

Question:

Which type of signal is rejected by differential amplifier?

Answer:

Common Mode Signal

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Problem 87

Question:

What is the purpose of current mirror in differential amplifier?

Answer:

To provide constant bias current.

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Problem 88

Question:

Which amplifier stage in an operational amplifier provides high gain?

Answer:

Differential Amplifier Stage

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Problem 89

Question:

What is the ideal input impedance of differential amplifier?

Answer:

Very high.

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Problem 90

Question:

What is the ideal output impedance of differential amplifier?

Answer:

Very low.

 

GATE Electrical – Analog Electronics

Practice Problems – Page 8

This section contains problems based on Differential Amplifier and Common Mode Analysis.

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Problem 71

Question:

Define differential amplifier.

Answer:

A differential amplifier amplifies the difference between two input signals.

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Problem 72

Question:

Write the formula for differential input voltage.

Answer:

Vd = V1 − V2

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Problem 73

Question:

What is common mode input voltage?

Answer:

Vc = (V1 + V2) / 2

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Problem 74

Question:

Define CMRR.

Answer:

CMRR (Common Mode Rejection Ratio) is the ratio of differential gain to common mode gain.

CMRR = Ad / Ac

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Problem 75

Question:

If differential gain Ad = 200 and common mode gain Ac = 0.5, calculate CMRR.

Solution:

CMRR = Ad / Ac

CMRR = 200 / 0.5

CMRR = 400

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Problem 76

Question:

Express CMRR in decibels if CMRR = 400.

Solution:

CMRR(dB) = 20 log10 (CMRR)

CMRR(dB) = 20 log10 (400)

≈ 52 dB

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Problem 77

Question:

Why is high CMRR desirable in amplifiers?

Answer:

It rejects noise and interference present in common mode signals.

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Problem 78

Question:

Which circuit forms the basic stage of operational amplifier?

Answer:

Differential Amplifier

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Problem 79

Question:

What is the ideal value of common mode gain?

Answer:

Zero

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Problem 80

Question:

What is the ideal value of CMRR?

Answer:

Infinite

 

GATE Electrical – Analog Electronics

Practice Problems – Page 7

This section contains problems based on h-parameter model of transistor amplifiers.

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Problem 61

Question:

Write the four h-parameters of a transistor amplifier.

Answer:

• h_ie – Input impedance
• h_re – Reverse voltage gain
• h_fe – Forward current gain
• h_oe – Output admittance

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Problem 62

Question:

What does h_fe represent in transistor amplifier?

Answer:

Forward current gain in common emitter configuration.

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Problem 63

Question:

If h_fe = 120 and base current = 30 μA, find collector current.

Solution:

Ic = hfe × Ib

Ic = 120 × 30 μA

Ic = 3600 μA = 3.6 mA

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Problem 64

Question:

Which h-parameter represents output conductance?

Answer:

h_oe

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Problem 65

Question:

What is the approximate voltage gain of CE amplifier using h-parameters?

Formula:

Av ≈ − hfe × RL / hie

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Problem 66

Question:

If h_fe = 100, R_L = 2 kΩ and h_ie = 1 kΩ, find voltage gain.

Solution:

Av = − (100 × 2000) / 1000

Av = −200

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Problem 67

Question:

If h_ie increases, what happens to input impedance?

Answer:

Input impedance increases.

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Problem 68

Question:

Why is h_re usually neglected in amplifier analysis?

Answer:

Because its value is extremely small.

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Problem 69

Question:

Which parameter mainly controls current amplification?

Answer:

h_fe

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Problem 70

Question:

What is the main advantage of h-parameter model?

Answer:

It simplifies transistor amplifier analysis using linear equations.