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An electric field strength is to be measured at an observation point
θ = π/2, 500 km from a half-wave (resonant) dipole antenna operating in air at 50 MHz . The measurement of dipole would be ____(in m)
Correct answer is '3'. Can you explain this answer?
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An electric field strength is to be measured at an observation pointθ...
Measurement of Electric Field Strength from a Half-Wave Dipole Antenna
Given:
Observation point distance (r) = 500 km
Frequency (f) = 50 MHz
To find:
Measurement of dipole (in m)
Formula:
The electric field strength (E) at a distance r from a half-wave dipole antenna is given by:
E = (60*I*L)/(2*pi*r*f), where
I = current in the dipole
L = length of the dipole
Solution:
Given that the antenna is resonant, so the length of the dipole is half the wavelength.
λ = c/f, where c is the speed of light.
λ = (3*10^8)/(50*10^6) = 6 m
Length of the dipole (L) = λ/2 = 3 m
Now, we need to find the current in the dipole (I).
The power (P) radiated by the dipole is given by:
P = (I^2*Rrad)/2, where
Rrad = radiation resistance of the dipole
For a half-wave dipole, Rrad = 73 Ω
From the power balance equation, the power fed to the dipole is equal to the power radiated, so
P = Vrms^2/(2*Rin), where
Vrms = RMS voltage across the dipole
Rin = input resistance of the dipole
For a half-wave dipole, Rin = 73 Ω
Therefore, P = Vrms^2/(2*73)
The electric field strength at the observation point is given by:
E = (60*I*L)/(2*pi*r*f)
From the above equations, we can find the current in the dipole (I) as:
I = sqrt((2*P)/Rrad) = sqrt((2*Vrms^2)/(73^2))
Substituting the values, we get:
I = 0.142 A
E = (60*0.142*3)/(2*pi*500*50*10^6) = 3.05*10^-8 V/m
Rounding off to the nearest integer, the measurement of dipole is 3 m.
Therefore, the measurement of dipole is 3 m.
Given:
Observation point distance (r) = 500 km
Frequency (f) = 50 MHz
To find:
Measurement of dipole (in m)
Formula:
The electric field strength (E) at a distance r from a half-wave dipole antenna is given by:
E = (60*I*L)/(2*pi*r*f), where
I = current in the dipole
L = length of the dipole
Solution:
Given that the antenna is resonant, so the length of the dipole is half the wavelength.
λ = c/f, where c is the speed of light.
λ = (3*10^8)/(50*10^6) = 6 m
Length of the dipole (L) = λ/2 = 3 m
Now, we need to find the current in the dipole (I).
The power (P) radiated by the dipole is given by:
P = (I^2*Rrad)/2, where
Rrad = radiation resistance of the dipole
For a half-wave dipole, Rrad = 73 Ω
From the power balance equation, the power fed to the dipole is equal to the power radiated, so
P = Vrms^2/(2*Rin), where
Vrms = RMS voltage across the dipole
Rin = input resistance of the dipole
For a half-wave dipole, Rin = 73 Ω
Therefore, P = Vrms^2/(2*73)
The electric field strength at the observation point is given by:
E = (60*I*L)/(2*pi*r*f)
From the above equations, we can find the current in the dipole (I) as:
I = sqrt((2*P)/Rrad) = sqrt((2*Vrms^2)/(73^2))
Substituting the values, we get:
I = 0.142 A
E = (60*0.142*3)/(2*pi*500*50*10^6) = 3.05*10^-8 V/m
Rounding off to the nearest integer, the measurement of dipole is 3 m.
Therefore, the measurement of dipole is 3 m.
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Community Answer
An electric field strength is to be measured at an observation pointθ...
The wavelength λ = c/f = 3 × 10850 × 106 = 6m
the length of half-dipole is I = λ/2 = 3m
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An electric field strength is to be measured at an observation pointθ = π/2, 500 km from a half-wave (resonant) dipole antenna operating in air at 50 MHz . The measurement of dipole would be ____(in m)Correct answer is '3'. Can you explain this answer?
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