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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