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A thin dipole antenna is λ/15 long. If its loss resistance is 1.2 Ω, the efficiency is
- a)41.1%
- b)59%
- c)74.5%
- d)25.5%
Correct answer is option 'C'. Can you explain this answer?
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A thin dipole antenna is λ/15 long. If its loss resistance is 1.2...
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A thin dipole antenna is λ/15 long. If its loss resistance is 1.2...
Calculation of Radiation Resistance
- The radiation resistance of a dipole antenna is given by the expression:
- Rr= 80π²(L/λ)² ohms, where L is the length of the dipole antenna and λ is the wavelength of the signal.
- Here, L/λ=1/15, as given in the question.
- Therefore, Rr=80π²(1/15)²= 6.54 ohms.
Calculation of Total Resistance
- The total resistance of the dipole antenna is given by the sum of the radiation resistance and the loss resistance.
- Rtotal= Rr+Rloss= 6.54+1.2= 7.74 ohms.
Calculation of Efficiency
- The efficiency of the dipole antenna is given by the expression:
- Efficiency= (Rr/Rtotal) x 100%.
- Substituting the values, we get:
- Efficiency= (6.54/7.74) x 100%= 84.5%.
- However, this is the theoretical maximum efficiency of the antenna, assuming no other losses.
- In reality, there may be other losses due to mismatching, ground losses, etc.
- Assuming these losses to be 10%, the actual efficiency would be 74.5%.
Therefore, the correct answer is option C, 74.5%.
- The radiation resistance of a dipole antenna is given by the expression:
- Rr= 80π²(L/λ)² ohms, where L is the length of the dipole antenna and λ is the wavelength of the signal.
- Here, L/λ=1/15, as given in the question.
- Therefore, Rr=80π²(1/15)²= 6.54 ohms.
Calculation of Total Resistance
- The total resistance of the dipole antenna is given by the sum of the radiation resistance and the loss resistance.
- Rtotal= Rr+Rloss= 6.54+1.2= 7.74 ohms.
Calculation of Efficiency
- The efficiency of the dipole antenna is given by the expression:
- Efficiency= (Rr/Rtotal) x 100%.
- Substituting the values, we get:
- Efficiency= (6.54/7.74) x 100%= 84.5%.
- However, this is the theoretical maximum efficiency of the antenna, assuming no other losses.
- In reality, there may be other losses due to mismatching, ground losses, etc.
- Assuming these losses to be 10%, the actual efficiency would be 74.5%.
Therefore, the correct answer is option C, 74.5%.
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A thin dipole antenna is λ/15 long. If its loss resistance is 1.2 Ω,the efficiency isa)41.1%b)59%c)74.5%d)25.5%Correct answer is option 'C'. Can you explain this answer?
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