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Transmission lines: 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. A lossless line has L = 250 nH/m and C = 100 pF/m. What is its characteristic impedance?

  1. 2500 Ω
  2. 25 Ω
  3. 50 Ω
  4. 75 Ω
Show the answer and solution

Answer: C. 50 Ω

Z0 = √(L/C) = √(250 × 10⁻⁹/100 × 10⁻¹²) = √2500 = 50 Ω.

2. A 50 Ω line is terminated in a 100 Ω resistive load. What is the VSWR?

  1. 1.5
  2. 2.0
  3. 3.0
  4. 0.5
Show the answer and solution

Answer: B. 2.0

Γ = (ZL − Z0)/(ZL + Z0) = 50/150 = 0.333; VSWR = (1 + |Γ|)/(1 − |Γ|) = 2.0.

3. What is the return loss at a load with reflection-coefficient magnitude |Γ| = 1/3?

  1. 9.54 dB
  2. 4.77 dB
  3. 3.00 dB
  4. 1.94 dB
Show the answer and solution

Answer: A. 9.54 dB

RL = −20 log|Γ| = 20 log 3 = 9.54 dB.

4. A coaxial cable uses solid polyethylene (εr = 2.25). What is the wavelength of a 100 MHz signal inside the cable?

  1. 3.00 m
  2. 1.33 m
  3. 4.50 m
  4. 2.00 m
Show the answer and solution

Answer: D. 2.00 m

VF = 1/√2.25 = 0.667; λ = VF × c/f = 0.667 × 3 × 10⁸/10⁸ = 2.00 m.

5. What characteristic impedance must a quarter-wave transformer have to match a 100 Ω load to a 50 Ω line?

  1. 75.0 Ω
  2. 150.0 Ω
  3. 70.7 Ω
  4. 25.0 Ω
Show the answer and solution

Answer: C. 70.7 Ω

Z0′ = √(Z0 × ZL) = √(50 × 100) = 70.7 Ω.

6. How does a lossless quarter-wavelength stub with a short-circuited end appear at its input terminals?

  1. As a short circuit
  2. As an open circuit
  3. As a pure resistance equal to Z0
  4. As a pure inductance equal to Z0
Show the answer and solution

Answer: B. As an open circuit

A λ/4 line inverts impedance: Zin = Z0²/ZL; with ZL = 0 the input impedance is infinite.

7. A coaxial line has a ratio of outer-conductor inner diameter to inner-conductor diameter of 3.5 and a polyethylene dielectric (εr = 2.25). Using Z0 = (138/√εr) log(D/d), what is Z0?

  1. 50 Ω
  2. 75 Ω
  3. 33 Ω
  4. 115 Ω
Show the answer and solution

Answer: A. 50 Ω

Z0 = (138/1.5) × log₁₀(3.5) = 92 × 0.5441 = 50.1 Ω.

8. On a normalized Smith chart, what does the exact centre point represent?

  1. A short circuit
  2. An open circuit
  3. A pure reactance equal to Z0
  4. A matched load (Z = Z0, Γ = 0, VSWR = 1)
Show the answer and solution

Answer: D. A matched load (Z = Z0, Γ = 0, VSWR = 1)

The centre is r = 1, x = 0, i.e. the load equals Z0, so there is no reflection.

Worked examples with computed numbers

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

9. A 50 Ω line feeds a purely resistive 30 Ω load. What is the VSWR?

  1. 0.25
  2. 2.27
  3. 1.67
  4. 1.6
Show the answer and solution

Answer: C. 1.67

Γ = |(ZL − Z0)/(ZL + Z0)| = 0.25; VSWR = (1 + Γ)/(1 − Γ) = 1.67 (= 50/30 for resistive loads).

10. A lossless line has 300 nH/m and 67 pF/m. What is its characteristic impedance?

  1. 66.9 Ω
  2. 4480 Ω
  3. 223 Ω
  4. 0.0149 Ω
Show the answer and solution

Answer: A. 66.9 Ω

Z0 = √(L/C) = √(300 nH/67 pF) per metre = 66.9 Ω (velocity factor 0.74).

11. What characteristic impedance must a quarter-wave section have to match a 150 Ω load to a 50 Ω line?

  1. 100 Ω
  2. 86.6 Ω
  3. 130 Ω
  4. 75 Ω
Show the answer and solution

Answer: B. 86.6 Ω

A λ/4 transformer matches when Zq = √(Z0·ZL) = √(50 × 150) = 86.6 Ω.

Other topics in the same subjects

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

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