This set of Microwave Engineering Multiple Choice Questions & Answers (MCQs) focuses on “Quarter Wave Transformer”.

1. If a transmission line of characteristic impedance 50 Ω is to be matched to a load of 100Ω, then the characteristic impedance of the ƛ/4 transmission line to be used is:

a) 70.71 Ω

b) 50 Ω

c) 100 Ω

d) 75 Ω

View Answer

Explanation: When a transmission line is not terminated with a matched load, it leads to losses and reflections. In order to avoid this, a λ/4 transmission line can be used for matching purpose. The characteristic impedance of the λ/4 transmission line is given by Z

_{1}=√(ZₒR)L. substituting the given values, we get Z

_{1}=70.71 Ω.

2. If a λ/4 transmission line is 100Ω is used to match a transmission line to a load of 100Ω, then the characteristic impedance of the transmission line is:

a) 100 Ω

b) 50 Ω

c) 70.71 Ω

d) 200 Ω

View Answer

Explanation: When a transmission line is not terminated with a matched load, it leads to losses and reflections. In order to avoid this, a λ/4 transmission line can be used for matching purpose. The characteristic impedance of the λ/4 transmission line is given by Z

_{1}=√(ZₒR)L. substituting the given values,

Z

_{0}=100 Ω.

3. Expression for the characteristic impedance of a transmission line(λ/4) used for impedance matching is:

a) Z_{1}=√(ZₒR)L

b) Z_{1}=√(Zₒ/R)L

c) Z_{1}=√(Zₒ+R)L

d) None of the mentioned

View Answer

Explanation: When a transmission line is not terminated with a matched load, it leads to losses and reflections. In order to avoid this, a λ/4 transmission line can be used for matching purpose. Hence the expression used to find the characteristic impedance of the λ/4 transmission line is Z

_{1}=√(ZₒR)L.

4. If there is no standing wave on a transmission line, then the value of SWR is:

a) 1

b) 0

c) Infinity

d) Insufficient data

View Answer

Explanation: When there are no standing waves in the transmission line, the reflection co-efficient is zero and hence input impedance of the transmission line is equal to the characteristic impedance of the line. Hence the relation between SWR and reflection co-efficient yields SWR as 1.

5. When a λ/4 transmission line is used for impedance matching, then which of the following is valid?

a) Standing waves are present on the λ/4 transmission line

b) No standing waves on the λ/4 transmission line

c) Standing waves are not present both on the feed line and the matching λ/4 line

d) Standing waves are present on both the feed line and the matching λ/4 line

View Answer

Explanation: λ/4 transmission line is used to match the load impedance to the characteristic impedance of the transmission line. Hence, standing waves are present on the λ/4 transmission line, but not on the transmission line since it is matched

6. For a transmission line , if the input impedance of the transmission line is 100Ω with a characteristic impedance of 150Ω, then the magnitude of the reflection co efficient:

a) 0.5

b) 1

c) 0.2

d) 0

View Answer

Explanation: The expression for reflection co-efficient of a transmission line in terms input and characteristic impedance is (Z

_{in}-Zₒ)/(Z

_{in}+ Zₒ). Substituting the given values in the above expression, reflection co-efficient is 0.2.

7. If the reflection co-efficient of a transmission line is 0.334 with a characteristic impedance of 50Ω then the input impedance of the transmission line is:

a) 100 Ω

b) 50 Ω

c) 150 Ω

d) None of the mentioned

View Answer

Explanation: Substituting the given voltage reflection co-efficient and the characteristic impedance of the transmission line in ┌= (Z

_{in}-Zₒ)/(Z

_{in}+ Zₒ). The input impedance of the transmission line is 100Ω

8. When a transmission line of characteristic impedance(50Ω) zₒ is matched to a load by a λ/4 transmission line of characteristic impedance 100Ω, then the transmission co efficient is:

a) 1.5

b) 0.5

c) 1.333

d) 2

View Answer

Explanation: When a transmission line is matched to a load by using a λ/4 transmission line, the transmission co-efficient T

_{1}of the line is obtained using the expression 2Z

_{1}/ (Z

_{1}+Z

_{0}). Here Z

_{1}is the characteristic impedance of the λ/4 transmission line and Z

_{1}is the characteristic impedance of the transmission line. Substituting the given values, we get T

_{1}=1.3333.

9. If a transmission line of zₒ=50Ω is matched using λ/4 transmission line of z₁=100Ω, then the transmission co efficient T₂ is:

a) 1

b) 0.6667

c) 1.3333

d) 2

View Answer

Explanation: When a transmission line is matched to a load by using a λ/4 transmission line, the transmission co-efficient T

_{2}of the line is obtained using the expression 2Z

_{0}/ (Z

_{1}+Z

_{0}). Here Z

_{1}is the characteristic impedance of the λ/4 transmission line and Z

_{0}is the characteristic impedance of the transmission line. Substituting the given values, we get T

_{2}=0.6667.

10. If the transmission co-efficient T₁ of a transmission line is 1.333 and the characteristic impedance of the λ/4 transmission line used is 100Ω, then the characteristic impedance of the transmission line is:

a) 50Ω

b) 100Ω

c) 70.71Ω

d) None of the mentioned

View Answer

Explanation: Expression for transmission co-efficient of a transmission line matched using a λ/4 transmission line is 2Z

_{1}/ (Z

_{1}+Z

_{0}). Substituting the known values, the characteristic impedance of the transmission line is 50Ω.

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