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Oscillators and feedback: board exam questions with solutions

On the ECE exam under Electronics Engineering. Try each question before you open its solution, then practise with fresh numbers below: 2 computed question types on this topic.

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Oscillator criteria (Barkhausen) · Wien-bridge oscillator with lamp stabiliser · RC phase-shift oscillator · Colpitts and Hartley LC oscillators · 555 astable (LED flasher): the same circuits on a live bench, with meters you can move.

Questions

1. What does the Barkhausen criterion require for sustained oscillation?

  1. Loop gain magnitude of 1 with a total loop phase shift of 0° (or 360°)
  2. Loop gain magnitude of 0 with 180° phase shift
  3. Loop gain much less than 1 with 90° phase shift
  4. Infinite open-loop gain with any phase shift
Show the answer and solution

Answer: A. Loop gain magnitude of 1 with a total loop phase shift of 0° (or 360°)

Sustained oscillation requires |Aβ| = 1 and ∠Aβ = 0° or a multiple of 360°, so the fed-back signal exactly reinforces itself.

2. A three-section RC phase-shift oscillator (equal R and C, op-amp inverting amplifier) uses R = 10 kΩ and C = 10 nF. What is its oscillation frequency?

  1. 1592 Hz
  2. 919 Hz
  3. 3898 Hz
  4. 650 Hz
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Answer: D. 650 Hz

f = 1/(2πRC√6) = 1/(2π × 10⁴ × 10⁻⁸ × 2.449) = 650 Hz. The amplifier gain must be at least 29.

3. What minimum non-inverting amplifier gain is needed for a Wien-bridge oscillator to sustain oscillation?

  1. 29
  2. 1
  3. 3
  4. 1/3
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Answer: C. 3

At the Wien network's centre frequency its attenuation is 1/3 with 0° phase, so the amplifier gain must be 3.

4. A Wien-bridge oscillator uses R = 16 kΩ and C = 10 nF in both arms. What is its frequency?

  1. 6250 Hz
  2. 995 Hz
  3. 406 Hz
  4. 332 Hz
Show the answer and solution

Answer: B. 995 Hz

f = 1/(2πRC) = 1/(2π × 16 × 10³ × 10 × 10⁻⁹) = 995 Hz.

5. A Colpitts oscillator has L = 100 µH and C1 = C2 = 2 nF. What is its approximate frequency?

  1. 503 kHz
  2. 252 kHz
  3. 356 kHz
  4. 3162 kHz
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Answer: A. 503 kHz

C1 and C2 act in series: Ceq = 2 × 2/(2 + 2) = 1 nF. f = 1/(2π√(100 × 10⁻⁶ × 10⁻⁹)) = 503.3 kHz.

6. An amplifier with open-loop gain A = 1000 has negative feedback with β = 0.01. What is the closed-loop gain?

  1. 100.0
  2. 1010.0
  3. 10.0
  4. 90.9
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Answer: D. 90.9

Af = A/(1 + Aβ) = 1000/(1 + 10) = 90.9.

7. An amplifier has open-loop gain 1000 and a single-pole bandwidth of 10 kHz. Negative feedback with β = 0.05 is applied. What is the closed-loop bandwidth?

  1. 196 Hz
  2. 500 kHz
  3. 510 kHz
  4. 10 MHz
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Answer: C. 510 kHz

Desensitivity 1 + Aβ = 1 + 1000 × 0.05 = 51. Closed-loop gain = 1000/51 = 19.6; bandwidth increases by the same factor: 10 kHz × 51 = 510 kHz (gain × bandwidth stays ≈ 10 MHz).

8. Which oscillator type offers the best frequency stability, owing to its resonator's extremely high Q?

  1. RC phase-shift oscillator
  2. Crystal oscillator
  3. Wien-bridge oscillator
  4. Hartley LC oscillator
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Answer: B. Crystal oscillator

A quartz crystal has Q in the tens of thousands or more and very stable mechanical resonance, giving far better stability than RC or LC circuits.

Worked examples with computed numbers

These numbers are fixed on this page; in practice they change every time.

9. A 555 astable has R1 = 6.8 kΩ, R2 = 18 kΩ and C = 1 µF. What is its frequency?

  1. 58.1 Hz
  2. 23.4 Hz
  3. 33.6 Hz
  4. 45.6 Hz
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Answer: C. 33.6 Hz

f = 1.44/[(R1 + 2R2)C] = 1.44/[(6.8 kΩ + 2 × 18 kΩ) × 1 µF] = 33.6 Hz.

10. A Wien-bridge oscillator uses R = 8.2 kΩ and C = 100 nF in both arms. At what frequency does it oscillate?

  1. 5.56 Hz
  2. 1.22 kHz
  3. 79.2 Hz
  4. 194 Hz
Show the answer and solution

Answer: D. 194 Hz

A Wien bridge oscillates at f = 1/(2πRC) = 194 Hz, and needs an amplifier gain of 3.

Other topics in the same subjects

DC circuits · AC circuits · Transients (RC, RL, RLC) · Semiconductors and diodes · BJT and FET circuits · Operational amplifiers · Power electronics · Digital electronics · Microprocessors and microcontrollers · Control systems · Instrumentation and measurement

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