A 2 m long center-fed dipole antenna operates in the AM broadcast band at 1 MHz. The dipole is made of copper wire with a radius of 1 mm. (a) Determine the radiation efficiency of the antenna. (b) What is the antenna gain in dB

a) the radiation efficiency of the antenna is 0.3018 ≈ 30%

b) the antenna gain in dB is - 3.4 dB

Explanation:

first we find the type of antenna given the data in the question;

given that, frequency f is 1 MHz

wavelength λ = c / f

c is the speed of light ( 3 × 10⁸), f is frequency 1MHz

so  λ = (3 × 10⁸) / 1000000

λ = 300 m

therefore the length is less than λ/50

l/λ = 1/300 < 1/50      {since l = 1m}

so the antenna is Hertzian Dipole

a)

we find the radiation resistance and loss of resistance to get the radiation efficiency.

the antenna has a radiation α is 1 mm and is made of copper.

therefore its permeable

Цc ≈ Ц0 ≈ 4π × 10⁻⁷ H/m and ∝c= 5.8 × 10⁷ S/m.

R_road = 80π² ( l/λ)²

we substitute 2m for l and 300 for λ

R_road = 80π² ( 2/300)²

R_road = 0.0359 ≈ 3.51 × 10⁻² Ω

Next is resistance loss

R_loss = l/2πa √(πfЦc / ∝c)

we substitute; l = 2, f = 1MHz = 1000000, ∝c = 5.8 × 10⁷,  Цc = 4π × 10⁻⁷, α = 0.001

R_loss = 2/2π(0.001) √((π×1000000×4π × 10⁻⁷) / 5.8 × 10⁷ )

=  318.3098 × 0.00026089

= 0.08304 ≈ 8.3 × 10⁻² Ω

Now to get the radiation efficiency, we say;

E = R_road / ( R_road + R_loss)

we substitute

E = 0.0359 / ( 0.0359 + 0.08304 )

E = 0.0359 / 0.11894

E = 0.3018 ≈ 30%

therefore the radiation efficiency of the antenna is 0.3018 ≈ 30%

b)

to find the antenna gain, we say

G = ED

we know that the directivity of a Hertzian Dipole D = 1.5

so we substitute

G = 0.3028 × 1.5

G = 0.4527

to find the gain in decibels;

G_dB = 10log (0.4527) dB

G_dB  = - 3.4 dB

therefore the antenna gain in dB is - 3.4 dB

hail is a solid form of precipitation composed of large, layered ice particles called pellets that often have spherical shapes. this phenomenon occurs during thunderstorms in the could type known as cumulus

hope this you out ^w^

emily ruth's annual premium is $1058.50

step-by-step explanation:

emily ruth is a female of 27 years age purchasing 20 year endowment insurance with face value $25000.

from the given table,

for females, the age of a male 3 years younger should be used.

so, we have to check for 24 year male for 20 year endowment.

it is 42.34 for every $1000 face value.

for a face value of $25000,

it is 25 * 42.34 = $1058.50

∴ emily ruth's annual premium is $1058.50