# Microwave Engineering Questions and Answers – Quarter Wave Transformer

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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

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 Z1=√(ZₒR)L. substituting the given values, we get Z1=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

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 Z1=√(ZₒR)L. substituting the given values,
Z0=100 Ω.

3. Expression for the characteristic impedance of a transmission line(λ/4) used for impedance matching is:
a) Z1=√(ZₒR)L
b) Z1=√(Zₒ/R)L
c) Z1=√(Zₒ+R)L
d) None of the mentioned

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 Z1=√(ZₒR)L.
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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

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

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

Explanation: The expression for reflection co-efficient of a transmission line in terms input and characteristic impedance is (Zin-Zₒ)/(Zin+ 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

Explanation: Substituting the given voltage reflection co-efficient and the characteristic impedance of the transmission line in ┌= (Zin-Zₒ)/(Zin+ 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

Explanation: When a transmission line is matched to a load by using a λ/4 transmission line, the transmission co-efficient T1 of the line is obtained using the expression 2Z1/ (Z1+Z0). Here Z1 is the characteristic impedance of the λ/4 transmission line and Z1 is the characteristic impedance of the transmission line. Substituting the given values, we get T1=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

Explanation: When a transmission line is matched to a load by using a λ/4 transmission line, the transmission co-efficient T2 of the line is obtained using the expression 2Z0/ (Z1+Z0). Here Z1 is the characteristic impedance of the λ/4 transmission line and Z0 is the characteristic impedance of the transmission line. Substituting the given values, we get T2=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