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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.