Power Radiated by Half-Wave Dipole Solution

STEP 0: Pre-Calculation Summary
Formula Used
Power Radiated by Half-wave Dipole = ((0.609*Intrinsic Impedance of Medium*(Amplitude of Oscillating Current)^2)/pi)*sin(((Angular Frequency of Half Wave Dipole*Time)-((pi/Length of Antenna)*Radial Distance From Antenna))*pi/180)^2
prad = ((0.609*ηhwd*(Io)^2)/pi)*sin(((Whwd*t)-((pi/Lhwd)*rhwd))*pi/180)^2
This formula uses 1 Constants, 1 Functions, 7 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Functions Used
sin - Trigonometric sine function, sin(Angle)
Variables Used
Power Radiated by Half-wave Dipole - (Measured in Watt) - Power Radiated by Half-wave Dipole refers to the amount of electromagnetic energy that the antenna emits into space in the form of radio waves.
Intrinsic Impedance of Medium - (Measured in Ohm) - The Intrinsic Impedance of Medium, refers to the characteristic impedance of a material through which electromagnetic waves propagate.
Amplitude of Oscillating Current - (Measured in Ampere) - The Amplitude of Oscillating Current refers to the maximum magnitude or strength of the alternating electric current as it varies over time.
Angular Frequency of Half Wave Dipole - (Measured in Radian per Second) - The Angular Frequency of Half Wave Dipole refers to the rate at which the dipole oscillates back and forth in an electromagnetic field.
Time - (Measured in Second) - Time is a dimension in which events occur in succession, allowing for the measurement of durations between those events.
Length of Antenna - (Measured in Meter) - The Length of Antenna refers to the physical size of the conductive element that make up the antenna structure.
Radial Distance From Antenna - (Measured in Meter) - The Radial Distance From Antenna refers to the distance measured radially outward from the center of the antenna structure.
STEP 1: Convert Input(s) to Base Unit
Intrinsic Impedance of Medium: 377 Ohm --> 377 Ohm No Conversion Required
Amplitude of Oscillating Current: 5 Ampere --> 5 Ampere No Conversion Required
Angular Frequency of Half Wave Dipole: 62800000 Radian per Second --> 62800000 Radian per Second No Conversion Required
Time: 0.001 Second --> 0.001 Second No Conversion Required
Length of Antenna: 2 Meter --> 2 Meter No Conversion Required
Radial Distance From Antenna: 0.5 Meter --> 0.5 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
prad = ((0.609*ηhwd*(Io)^2)/pi)*sin(((Whwd*t)-((pi/Lhwd)*rhwd))*pi/180)^2 --> ((0.609*377*(5)^2)/pi)*sin(((62800000*0.001)-((pi/2)*0.5))*pi/180)^2
Evaluating ... ...
prad = 230.08282202564
STEP 3: Convert Result to Output's Unit
230.08282202564 Watt --> No Conversion Required
FINAL ANSWER
230.08282202564 230.0828 Watt <-- Power Radiated by Half-wave Dipole
(Calculation completed in 00.020 seconds)

Credits

Created by Souradeep Dey
National Institute of Technology Agartala (NITA), Agartala, Tripura
Souradeep Dey has created this Calculator and 25+ more calculators!
Verified by Santhosh Yadav
Dayananda Sagar College Of Engineering (DSCE), Banglore
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13 Electromagnetic Radiation and Antennas Calculators

Average Power Density of Half-Wave Dipole
Go Average Power Density = (0.609*Intrinsic Impedance of Medium*Amplitude of Oscillating Current^2)/(4*pi^2*Radial Distance From Antenna^2)*sin((((Angular Frequency of Half Wave Dipole*Time)-(pi/Length of Antenna)*Radial Distance From Antenna))*pi/180)^2
Magnetic Field for Hertzian Dipole
Go Magnetic Field Component = (1/Dipole Distance)^2*(cos(2*pi*Dipole Distance/Wavelength of Dipole)+2*pi*Dipole Distance/Wavelength of Dipole*sin(2*pi*Dipole Distance/Wavelength of Dipole))
Maximum Power Density of Half-Wave Dipole
Go Maximum Power Density = (Intrinsic Impedance of Medium*Amplitude of Oscillating Current^2)/(4*pi^2*Radial Distance From Antenna^2)*sin((((Angular Frequency of Half Wave Dipole*Time)-(pi/Length of Antenna)*Radial Distance From Antenna))*pi/180)^2
Power Radiated by Half-Wave Dipole
Go Power Radiated by Half-wave Dipole = ((0.609*Intrinsic Impedance of Medium*(Amplitude of Oscillating Current)^2)/pi)*sin(((Angular Frequency of Half Wave Dipole*Time)-((pi/Length of Antenna)*Radial Distance From Antenna))*pi/180)^2
Poynting Vector Magnitude
Go Poynting Vector = 1/2*((Dipole Current*Wavenumber*Source Distance)/ (4*pi))^2*Intrinsic Impedance*(sin(Polar Angle))^2
Time Average Radiated Power of Half-Wave Dipole
Go Time Average Radiated Power = (((Amplitude of Oscillating Current)^2)/2)*((0.609*Intrinsic Impedance of Medium)/pi)
Polarization
Go Polarization = Electric Susceptibility*[Permitivity-vacuum]*Electric Field Strength
Radiation Resistance of Half-Wave Dipole
Go Radiation Resistance of Half-wave Dipole = (0.609*Intrinsic Impedance of Medium)/pi
Directivity of Half-Wave Dipole
Go Directivity of Half Wave Dipole = Maximum Power Density/Average Power Density
Electric Field for Hertzian Dipole
Go Electric Field Component = Intrinsic Impedance*Magnetic Field Component
Radiation Efficiency of Antenna
Go Radiation Efficiency of Antenna = Maximum Gain/Maximum Directivity
Average Power
Go Average Power = 1/2*Sinusoidal Current^2*Radiation Resistance
Radiation Resistance of Antenna
Go Radiation Resistance = 2*Average Power/Sinusoidal Current^2

Power Radiated by Half-Wave Dipole Formula

Power Radiated by Half-wave Dipole = ((0.609*Intrinsic Impedance of Medium*(Amplitude of Oscillating Current)^2)/pi)*sin(((Angular Frequency of Half Wave Dipole*Time)-((pi/Length of Antenna)*Radial Distance From Antenna))*pi/180)^2
prad = ((0.609*ηhwd*(Io)^2)/pi)*sin(((Whwd*t)-((pi/Lhwd)*rhwd))*pi/180)^2

What is the significance of Power radiated by half wave dipole?

For a wide range of applications, the power that a half-wave dipole antenna radiates is quite important. This power emission, which serves as a channel for electromagnetic energy, has a direct impact on the dependability, strength, and range of communication lines. The antenna system guarantees effective transmission, improving performance and cutting down on operating expenses by optimizing radiated power while minimizing losses. Furthermore, sufficient radiated power reduces interference problems and improves signal dependability and clarity in busy radio frequency situations. Additionally, compliance with regulatory standards and limitations is made easier, guaranteeing interoperability and reducing interference with other communication systems. Comprehending the subtleties of radiating power facilitates the methodical configuration of antenna systems, taking into account elements like positioning, alignment, and the properties of signal propagation.

How to Calculate Power Radiated by Half-Wave Dipole?

Power Radiated by Half-Wave Dipole calculator uses Power Radiated by Half-wave Dipole = ((0.609*Intrinsic Impedance of Medium*(Amplitude of Oscillating Current)^2)/pi)*sin(((Angular Frequency of Half Wave Dipole*Time)-((pi/Length of Antenna)*Radial Distance From Antenna))*pi/180)^2 to calculate the Power Radiated by Half-wave Dipole, The Power Radiated by Half-Wave Dipole antenna is the electromagnetic energy emitted into space as radio waves. It's determined by the RMS current and the radiation resistance of the antenna. Power Radiated by Half-wave Dipole is denoted by prad symbol.

How to calculate Power Radiated by Half-Wave Dipole using this online calculator? To use this online calculator for Power Radiated by Half-Wave Dipole, enter Intrinsic Impedance of Medium hwd), Amplitude of Oscillating Current (Io), Angular Frequency of Half Wave Dipole (Whwd), Time (t), Length of Antenna (Lhwd) & Radial Distance From Antenna (rhwd) and hit the calculate button. Here is how the Power Radiated by Half-Wave Dipole calculation can be explained with given input values -> 230.0828 = ((0.609*377*(5)^2)/pi)*sin(((62800000*0.001)-((pi/2)*0.5))*pi/180)^2.

FAQ

What is Power Radiated by Half-Wave Dipole?
The Power Radiated by Half-Wave Dipole antenna is the electromagnetic energy emitted into space as radio waves. It's determined by the RMS current and the radiation resistance of the antenna and is represented as prad = ((0.609*ηhwd*(Io)^2)/pi)*sin(((Whwd*t)-((pi/Lhwd)*rhwd))*pi/180)^2 or Power Radiated by Half-wave Dipole = ((0.609*Intrinsic Impedance of Medium*(Amplitude of Oscillating Current)^2)/pi)*sin(((Angular Frequency of Half Wave Dipole*Time)-((pi/Length of Antenna)*Radial Distance From Antenna))*pi/180)^2. The Intrinsic Impedance of Medium, refers to the characteristic impedance of a material through which electromagnetic waves propagate, The Amplitude of Oscillating Current refers to the maximum magnitude or strength of the alternating electric current as it varies over time, The Angular Frequency of Half Wave Dipole refers to the rate at which the dipole oscillates back and forth in an electromagnetic field, Time is a dimension in which events occur in succession, allowing for the measurement of durations between those events, The Length of Antenna refers to the physical size of the conductive element that make up the antenna structure & The Radial Distance From Antenna refers to the distance measured radially outward from the center of the antenna structure.
How to calculate Power Radiated by Half-Wave Dipole?
The Power Radiated by Half-Wave Dipole antenna is the electromagnetic energy emitted into space as radio waves. It's determined by the RMS current and the radiation resistance of the antenna is calculated using Power Radiated by Half-wave Dipole = ((0.609*Intrinsic Impedance of Medium*(Amplitude of Oscillating Current)^2)/pi)*sin(((Angular Frequency of Half Wave Dipole*Time)-((pi/Length of Antenna)*Radial Distance From Antenna))*pi/180)^2. To calculate Power Radiated by Half-Wave Dipole, you need Intrinsic Impedance of Medium hwd), Amplitude of Oscillating Current (Io), Angular Frequency of Half Wave Dipole (Whwd), Time (t), Length of Antenna (Lhwd) & Radial Distance From Antenna (rhwd). With our tool, you need to enter the respective value for Intrinsic Impedance of Medium, Amplitude of Oscillating Current, Angular Frequency of Half Wave Dipole, Time, Length of Antenna & Radial Distance From Antenna and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
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