# What is the directivity of half-wave dipole?

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What is the directivity of half-wave dipole?

(a) 1.64

(b) 1.5

(c) 1.43

(d) 1.44

The question was posed to me during an interview.

This interesting question is from Directivity topic in chapter Antenna Parameters of Antennas

## 1 Answer

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Correct option is (a) 1.64

Easy explanation: Directivity $D=\frac{U_{max}}{U_{av}} = \frac{4\pi U_{max}}{P_{rad}}$

Prad=36.54I0^2 Since the radiation resistance for Half-wave dipole is 36.54Ω.

Maximum radiation intensity is given by $U_{max}=P_{max}.r^2=\frac{\mid E_\theta\mid_{max}^2}{2\eta}.r^2$

Where $E_\theta=\frac{j\eta I_0 e^{-jkr}cos⁡(\frac{\pi cos\theta}{2})}{2\pi rsin\theta}$

⇨ $D=\frac{4\pi}{1}\frac{\eta I_0^2}{8\pi^2} \frac{1}{36.54I_0^2}=1.64.$

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