Correct Answer - Option 1 : 73 Ω
Concept:
The radiation resistance of a dipole antenna is given as:
\(R_{Rad}=\frac{80\pi^2L_{ef}^2}{\lambda^2}\) ----(1)
Where Lef= Effective Length of antenna
For Half-wave dipole,
Lef = 2Lphy
Where Lphy = Physical length of the antenna
\(L_{phy}=\frac{\lambda}{2} \ (given)\)
Calculation:
From equation (1):
\(R_{Rad}=\frac{80\pi^2{(2\frac{\lambda}{2}})^2}{\lambda^2}=80\pi^2\)
RRad = 73 Ω
Hence option (1) is the correct answer.
λ/2 Dipole or Half-wave dipole:
- Length of dipole = λ/2
- Directivity = 1.64 or 2.15 dBi
- Impedance for half-wave dipole antenna in free space is 73 Ω
- Half power beamwidth = 78°
- The frequency is related to the wavelength by the relation c = νλ
λ/4 Monopole or Quarter wave monopole:
- It’s length = λ/4
- Impedance of λ/4 monopole = 1/2 (Impedance of λ/2 dipole)
- Impedance of λ/4 monopole = 36.5 Ω
- Directivity of λ/4 monopole = 2 × (Directivity of λ/2 dipole)
= 2 × 1.64 = 3.286
Short dipole:
- Length of dipole < λ/10
- Radiation resistance \(= 20{\left( {\frac{{\pi L}}{\lambda }} \right)^2}\)
- Directivity = 1.5 or 1.76 dB
- λ = wavelength
- L = length of dipole
