Analog Electronics – Problems Page 27

Ultra Hard Multi-Concept Problems (GATE Level)

This section contains multi-concept problems combining diode circuits, transistor amplifiers, op-amp circuits and oscillators.

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Problem 1

A silicon diode conducts 2 mA current when forward voltage is 0.7 V. Find the dynamic resistance at this operating point.

Solution

rd = VT / I

VT = 25 mV

rd = 0.025 / 0.002

rd = 12.5 Ω

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Problem 2

A BJT transistor has β = 100 and collector current IC = 2 mA. Find the transconductance gm.

Solution

gm = IC / VT

gm = 0.002 / 0.025

gm = 0.08 S

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Problem 3

An op-amp inverting amplifier has Rin = 2 kΩ and Rf = 20 kΩ. If Vin = 0.2 V, calculate output voltage.

Solution

Av = −Rf / Rin

Av = −20k / 2k = −10

Vo = Av × Vin

Vo = −10 × 0.2 = −2 V

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Problem 4

A Hartley oscillator uses L1 = 3 mH, L2 = 7 mH and C = 150 pF. Find oscillation frequency.

Solution

Total inductance

L = L1 + L2 = 10 mH

f = 1 / (2π√LC)

f ≈ 130 kHz

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Problem 5

An op-amp differential amplifier has Ad = 3000 and Ac = 0.3. Find CMRR in dB.

Solution

CMRR = Ad / Ac

CMRR = 3000 / 0.3 = 10000

CMRR(dB) = 20 log (10000)

CMRR = 80 dB

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Problem 6

An RC oscillator uses R = 8 kΩ and C = 0.02 μF. Find oscillation frequency.

Solution

f = 1 / (2πRC)

f ≈ 995 Hz

 

Analog Electronics – Problems Page 26

GATE Previous Year Type Questions

This section contains important conceptual and numerical questions inspired by previous GATE examinations.

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Problem 1

A silicon diode is forward biased with voltage 0.7 V. The thermal voltage is 25 mV. Calculate exponential factor V/VT.

Solution

V / VT = 0.7 / 0.025

V/VT = 28

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Problem 2

A transistor has β = 150 and emitter current IE = 3 mA. Find collector current IC.

Solution

Relation:

IC ≈ α IE

Where

α = β / (1 + β)

α = 150 / 151 ≈ 0.993

IC ≈ 2.98 mA

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Problem 3

An op-amp has open loop gain 10⁵. If feedback factor β = 0.01, find closed loop gain.

Solution

Acl = A / (1 + Aβ)

Acl = 10⁵ / (1 + 10⁵ × 0.01)

Acl ≈ 100

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Problem 4

A low pass filter has R = 1 kΩ and C = 0.1 μF. Find cutoff frequency.

Solution

fc = 1 / (2πRC)

fc ≈ 1591 Hz

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Problem 5

In an RC phase shift oscillator, how many RC sections are used?

3 RC sections

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Problem 6

A Wien bridge oscillator has R = 20 kΩ and C = 0.005 μF. Calculate oscillation frequency.

Solution

f = 1 / (2πRC)

f ≈ 1592 Hz

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Problem 7

What is the ideal value of CMRR for an op-amp?

Infinite

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Problem 8

Which oscillator is commonly used in RF circuits?

Hartley or Colpitts oscillator

 

Analog Electronics – Problems Page 25

Very Hard Numerical Problems (GATE Level)

This section contains advanced numerical problems combining diode circuits, BJT amplifiers, operational amplifiers and oscillators.

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Problem 1

A silicon diode has reverse saturation current Is = 10⁻¹² A. Calculate diode current when forward voltage is 0.7 V at room temperature.

Solution

Diode equation: I = Is (e^(V/VT) − 1)

At room temperature:

VT ≈ 25 mV

Substitute values:

I = 10⁻¹² (e^(0.7/0.025) − 1)

I ≈ 1.2 mA

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Problem 2

A BJT amplifier has Rc = 4 kΩ and re = 25 Ω. Find the voltage gain of the CE amplifier.

Solution

Av = −Rc / re

Av = −4000 / 25 Av = −160

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Problem 3

An inverting op-amp has Rin = 5 kΩ and Rf = 50 kΩ. If input voltage is 0.1 V, calculate output voltage.

Solution

Av = −Rf / Rin

Av = −50k / 5k = −10

Vo = Av × Vin Vo = −10 × 0.1 = −1 V

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Problem 4

An LC oscillator uses L = 2 mH and C = 200 pF. Find oscillation frequency.

Solution

f = 1 / (2π√LC)

f ≈ 251 kHz

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Problem 5

An op-amp differential amplifier has Ad = 2000 and Ac = 0.5. Calculate CMRR in dB.

Solution

CMRR = Ad / Ac

CMRR = 2000 / 0.5 = 4000

CMRR(dB) = 20 log(4000)

CMRR ≈ 72 dB

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Problem 6

A Wien bridge oscillator uses R = 10 kΩ and C = 0.01 μF. Find oscillation frequency.

Solution

f = 1 / (2πRC)

f ≈ 1591 Hz

 

Analog Electronics – Problems Page 24

Mixed Concept & Numerical Problems

This section includes mixed questions from diode circuits, BJT amplifiers, operational amplifiers and oscillators for GATE preparation.

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Problem 1

Find the thermal voltage at room temperature (300 K).

Solution

VT = kT / q

VT ≈ 25 mV

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Problem 2

A BJT has β = 120 and base current 20 μA. Find collector current.

Solution

Ic = β × Ib

Ic = 120 × 20 μA Ic = 2.4 mA

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Problem 3

Calculate the voltage gain of an inverting op-amp with Rf = 100 kΩ and Rin = 10 kΩ.

Solution

Av = −Rf / Rin

Av = −100k / 10k Av = −10

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Problem 4

An LC oscillator has L = 5 mH and C = 100 pF. Find oscillation frequency.

Solution

f = 1 / (2π√LC)

f ≈ 225 kHz

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Problem 5

What is the ripple factor of a full wave rectifier?

Ripple Factor = 0.482

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Problem 6

What is the ideal input impedance of an operational amplifier?

Infinite

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Problem 7

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

Zero

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Problem 8

For oscillations to occur, what should be the loop gain?

Aβ = 1

This is the Barkhausen criterion.

 

Analog Electronics – Problems Page 23

Oscillator Advanced Numerical Problems

This section contains advanced numerical problems on oscillator circuits useful for GATE and PSU examinations.

                                     

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Problem 1

An RC phase shift oscillator uses R = 5 kΩ and C = 0.02 μF. Find the oscillation frequency.

Solution

Formula:

f = 1 / (2πRC√6)

Substitute values:

f = 1 / (2π × 5000 × 0.02×10⁻⁶ × √6)

Result:

f ≈ 650 Hz

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Problem 2

A Hartley oscillator has inductors L1 = 4 mH and L2 = 6 mH with capacitor C = 200 pF. Calculate the oscillation frequency.

Solution

Total inductance:

L = L1 + L2 = 10 mH

Formula:

f = 1 / (2π√LC)

Substitute:

f = 1 / (2π √(10×10⁻³ × 200×10⁻¹²))

Result:

f ≈ 112 kHz

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Problem 3

A Colpitts oscillator has capacitors C1 = 100 pF, C2 = 400 pF and inductor L = 2 mH. Find the oscillation frequency.

Solution

Equivalent capacitance:

Ceq = (C1C2)/(C1 + C2)

Substitute:

Ceq = (100×400)/(500)

Ceq = 80 pF

Frequency:

f = 1/(2π√LC)

Result:

f ≈ 125 kHz

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Problem 4

A crystal oscillator has inductance L = 0.5 H and capacitance C = 0.02 pF. Calculate the series resonant frequency.

Solution

Formula:

f = 1/(2π√LC)

Substitute values:

f = 1/(2π √(0.5 × 0.02×10⁻¹²))

Result:

f ≈ 1.59 MHz

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Problem 5

An oscillator has amplifier gain A = 10 and feedback factor β = 0.1. Check whether oscillations will occur.

Solution

Loop gain:

Aβ = 10 × 0.1

Aβ = 1

Since loop gain equals 1,

Oscillations will occur.

 

Analog Electronics – Problems Page 22

Oscillator Conceptual & GATE Level Problems

This section includes conceptual questions and solved problems on oscillator circuits useful for GATE and PSU examinations.

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Problem 1

State the Barkhausen criterion for sustained oscillations.

Solution

The Barkhausen criterion states that for sustained oscillations:

|Aβ| = 1

and the total phase shift around the loop must be:

360° (or 0°)

This ensures that the feedback signal reinforces the input signal.

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Problem 2

Why are LC oscillators used for high frequency applications?

Solution

• LC circuits have very low losses
• They provide high Q factor
• They can operate efficiently at radio frequencies

Hence LC oscillators are used in RF transmitters and communication systems.

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Problem 3

Calculate the oscillation frequency of an LC oscillator if L = 2 mH and C = 50 pF.

Solution

Formula:

f = 1 / (2π√LC)

Substitute values:

f = 1 / (2π √(2×10⁻³ × 50×10⁻¹²))

Result:

f ≈ 503 kHz

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Problem 4

What is the advantage of crystal oscillators compared to RC oscillators?

Solution

Crystal oscillators provide:

• Very high frequency stability
• Very high Q factor
• Low frequency drift

Hence they are used in digital clocks, microprocessors and communication systems.

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Problem 5

Which oscillator is commonly used in audio frequency applications?

Solution

RC Phase Shift Oscillator

Because RC networks are suitable for low frequency ranges.

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Problem 6

What happens if the loop gain Aβ is greater than 1?

Solution

• Oscillations grow in amplitude
• Signal distortion occurs
• The amplifier eventually saturates

Therefore practical circuits stabilize the gain.

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Problem 7

What is the main function of the feedback network in an oscillator?

Solution

The feedback network:

• Provides the required phase shift
• Controls the oscillation frequency
• Maintains the feedback ratio β

 

Analog Electronics – Problems Page 21

Oscillators Numerical Problems (GATE Level)

This page contains solved problems from oscillator circuits including RC phase shift, Wien bridge, Hartley and Colpitts oscillators.

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Problem 1

An RC phase shift oscillator uses R = 10 kΩ and C = 0.01 μF. Find the frequency of oscillation.

Solution

Formula:

f = 1 / (2πRC√6)

Given:

R = 10 × 10³ Ω
C = 0.01 × 10⁻⁶ F

Substitute values:

f = 1 / (2π × 10⁴ × 0.01×10⁻⁶ × √6)

Result:

f ≈ 650 Hz

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Problem 2

In a Wien bridge oscillator R = 5 kΩ and C = 0.02 μF. Calculate the oscillation frequency.

Solution

Formula:

f = 1 / (2πRC)

Substitute values:

f = 1 / (2π × 5000 × 0.02×10⁻⁶)

Result:

f ≈ 1590 Hz

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Problem 3

A Hartley oscillator has L1 = 2 mH, L2 = 8 mH and C = 100 pF. Find the frequency.

Solution

Total inductance:

L = L1 + L2 = 10 mH

Formula:

f = 1 / (2π√LC)

Substitute values:

f = 1 / (2π √(10×10⁻³ × 100×10⁻¹²))

Result:

f ≈ 159 kHz

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Problem 4

A Colpitts oscillator uses C1 = 200 pF, C2 = 300 pF and L = 1 mH. Calculate the frequency.

Solution

Equivalent capacitance:

Ceq = (C1C2)/(C1 + C2)

Substitute values:

Ceq = (200×300)/(500)

Ceq = 120 pF

Frequency:

f = 1/(2π√LC)

Result:

f ≈ 145 kHz

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Problem 5

For a Wien bridge oscillator, what minimum gain is required for oscillations?

Solution

From Barkhausen criterion:

Aβ = 1

For Wien bridge network:

β = 1/3

Therefore

A = 3

Minimum amplifier gain required is:

A = 3