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Antennas and wave propagation: board exam questions with solutions

On the ECE exam under Electronic Systems and Technologies (EST). Try each question before you open its solution, then practise with fresh numbers below: 3 computed question types on this topic.

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Questions

1. Using a 0.95 end-effect factor, what is the practical length of a half-wave dipole for 100 MHz?

  1. 1.43 m
  2. 1.50 m
  3. 2.85 m
  4. 0.71 m
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Answer: A. 1.43 m

λ = 3 × 10⁸/10⁸ = 3 m; λ/2 = 1.5 m; × 0.95 = 1.425 m ≈ 1.43 m.

2. What is the approximate radiation resistance of a thin half-wave dipole in free space?

  1. 36.5 Ω
  2. 300 Ω
  3. 50 Ω
  4. 73 Ω
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Answer: D. 73 Ω

A thin λ/2 dipole has Rrad ≈ 73 Ω (a λ/4 monopole over a ground plane is about half, 36.5 Ω).

3. A 50 W transmitter feeds a 12 dBi antenna through a cable with 2 dB loss. What is the EIRP?

  1. 29.0 dBW
  2. 15.0 dBW
  3. 27.0 dBW
  4. 27.0 dBm
Show the answer and solution

Answer: C. 27.0 dBW

10 log 50 = 16.99 dBW; EIRP = 16.99 − 2 + 12 = 27.0 dBW (about 500 W).

4. What is the free-space path loss over 1 km at 2.4 GHz?

  1. 80.0 dB
  2. 100.1 dB
  3. 120.0 dB
  4. 60.2 dB
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Answer: B. 100.1 dB

FSPL = 32.45 + 20 log f(MHz) + 20 log d(km) = 32.45 + 20 log 2400 + 0 = 100.1 dB.

5. A 5.8 GHz point-to-point link transmits 20 dBm with 15 dBi antennas at both ends over 10 km. Ignoring other losses, what is the received power?

  1. −77.7 dBm
  2. −92.7 dBm
  3. −57.7 dBm
  4. −107.7 dBm
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Answer: A. −77.7 dBm

FSPL = 32.45 + 20 log 5800 + 20 log 10 = 127.7 dB. Pr = 20 + 15 + 15 − 127.7 = −77.7 dBm.

6. What is the gain of a 1.2 m parabolic dish at 12 GHz with 55% aperture efficiency?

  1. 43.6 dBi
  2. 82.0 dBi
  3. 19.2 dBi
  4. 41.0 dBi
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Answer: D. 41.0 dBi

λ = c/f = 2.50 cm; G = η(πD/λ)² = 0.55 × (150.8)² = 12 507 → 41.0 dBi.

7. By which propagation mode do HF signals (3–30 MHz) typically reach receivers thousands of kilometres away?

  1. Ground (surface) wave
  2. Line-of-sight space wave
  3. Sky wave (ionospheric refraction)
  4. Tropospheric ducting only
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Answer: C. Sky wave (ionospheric refraction)

HF waves are refracted back to Earth by the ionosphere, allowing one or more hops far beyond the horizon.

8. Assuming a 4/3 effective Earth radius, what is the approximate maximum line-of-sight radio path between antennas 100 m and 16 m high? (Use d ≈ 4.12(√h1 + √h2) km with h in metres.)

  1. 50.0 km
  2. 57.7 km
  3. 44.4 km
  4. 47.8 km
Show the answer and solution

Answer: B. 57.7 km

d ≈ 4.12(√100 + √16) = 4.12 × 14 = 57.7 km (exact 4/3-Earth geometry gives 57.7 km).

Worked examples with computed numbers

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

9. How long is an electrical half wavelength at 100 MHz in free space?

  1. 2.25 m
  2. 750 mm
  3. 1.5 m
  4. 3 m
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Answer: C. 1.5 m

λ = c/f = 3 m; an electrical half-wave is λ/2 = 1.5 m (cut about 5% shorter in practice).

10. What is the free-space path loss over 20 km at 900 MHz?

  1. 117.5 dB
  2. 177.5 dB
  3. 74.99 dB
  4. 85.11 dB
Show the answer and solution

Answer: A. 117.5 dB

FSPL = 32.44 + 20 log d(km) + 20 log f(MHz) = 32.44 + 26.02 + 59.08 = 117.5 dB.

11. A 5 W transmitter feeds a 9 dBi antenna through 0.5 dB of cable loss. What is the EIRP?

  1. 27.49 dBm
  2. 45.99 dBm
  3. 15.49 dBm
  4. 45.49 dBm
Show the answer and solution

Answer: D. 45.49 dBm

EIRP = P(dBm) + G − L = 36.99 + 9 − 0.5 = 45.49 dBm.

Other topics in the same subjects

Communications fundamentals (dB, noise) · AM, FM and PM · Digital communications · Transmission lines · Microwave, fiber optics and satellite · Data communications and networks · Broadcasting and acoustics

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