The radiation intensity of the antenna is given by -U- - - 1 0- 20 - 0-342 cosec- 20- 60 - 0 60- - 180 0- 2 -then the directivity in dB is

D = 4 πU(θ, ϕ )P_rad P_rad = ∮ _s U(θ , ϕ)sinθ d θ dϕ = ∫_θ = 0^2 π∫_20^2 πsinθ dθ dϕ+∫_θ = 0^2 π∫_60^2 π0.342 cosecθsinθ dθ nbsp;d ϕ = 1.88 D= 4π11.88 = 6.68 ...

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Antenna Characteristics Parameters (Part 2)

The radiation...

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The radiation intensity of the antenna is given by
$\begin{matrix} U (θ, ϕ) = 1 & 0 \leq θ \leq 20 = 0.342 c o s e c θ & 20 \leq θ \leq 60 = 0 & 60 < θ < 180 \end{matrix} ⎫ ⎪ ⎬ ⎪ ⎭ 0 \leq ϕ \leq 2 π$
then the directivity (in dB) is

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Solution

$D = 4 π \frac{U (θ, ϕ)}{P_{r a d}}$
$P_{r a d} = \oint_{s} U (θ, ϕ) sin θ d θ d ϕ$
$= \int_{θ = 0}^{2 π} \int_{20}^{2 π} sin θ d θ d ϕ + \int_{θ = 0}^{2 π} \int_{60}^{2 π} 0.342 c o s e c θ sin θ d θ d ϕ = 1.88$
$D = 4 π \frac{1}{1.88} = 6.68$
$D = 8.25 d B$

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The radiation intensity of the antenna is given by U(θ,ϕ)=10≤θ≤20=0.342cosecθ20≤θ≤60=060<θ<180⎫⎪⎬⎪⎭0≤ϕ≤2π then the directivity (in dB) is

D=4πU(θ,ϕ)Prad Prad=∮sU(θ,ϕ)sinθdθdϕ =∫2πθ=0∫2π20sinθdθdϕ+∫2πθ=0∫2π600.342cosecθsinθdθdϕ=1.88 D=4π11.88=6.68 D=8.25 dB

The radiation intensity of the antenna is given by
$\begin{matrix} U (θ, ϕ) = 1 & 0 \leq θ \leq 20 = 0.342 c o s e c θ & 20 \leq θ \leq 60 = 0 & 60 < θ < 180 \end{matrix} ⎫ ⎪ ⎬ ⎪ ⎭ 0 \leq ϕ \leq 2 π$
then the directivity (in dB) is

$D = 4 π \frac{U (θ, ϕ)}{P_{r a d}}$
$P_{r a d} = \oint_{s} U (θ, ϕ) sin θ d θ d ϕ$
$= \int_{θ = 0}^{2 π} \int_{20}^{2 π} sin θ d θ d ϕ + \int_{θ = 0}^{2 π} \int_{60}^{2 π} 0.342 c o s e c θ sin θ d θ d ϕ = 1.88$
$D = 4 π \frac{1}{1.88} = 6.68$
$D = 8.25 d B$