## Total Radiated Power in Free Space Solution

STEP 0: Pre-Calculation Summary
Formula Used
Total Radiated Power in Free Space = 30*Amplitude of Oscillating Current^2*int((Dipole Antenna Pattern Function)^2*sin(Theta)*x,x,0,pi)
PR = 30*Io^2*int((F)^2*sin(θem)*x,x,0,pi)
This formula uses 1 Constants, 2 Functions, 4 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Functions Used
sin - Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse., sin(Angle)
int - The definite integral can be used to calculate net signed area, which is the area above the x -axis minus the area below the x -axis., int(expr, arg, from, to)
Variables Used
Total Radiated Power in Free Space - (Measured in Watt) - Total Radiated Power in Free Space is the total amount of electromagnetic wave power emitted by an antenna.
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.
Dipole Antenna Pattern Function - Dipole Antenna Pattern Function describes the electric field strength variation in the plane containing its electric field and maximum radiation direction in E-plane.
Theta - (Measured in Radian) - Theta is an angle that can be defined as the figure formed by two rays meeting at a common endpoint.
STEP 1: Convert Input(s) to Base Unit
Amplitude of Oscillating Current: 5 Ampere --> 5 Ampere No Conversion Required
Dipole Antenna Pattern Function: 0.2128 --> No Conversion Required
Theta: 30 Degree --> 0.5235987755982 Radian (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
PR = 30*Io^2*int((F)^2*sin(θem)*x,x,0,pi) --> 30*5^2*int((0.2128)^2*sin(0.5235987755982)*x,x,0,pi)
Evaluating ... ...
PR = 83.8000474804174
STEP 3: Convert Result to Output's Unit
83.8000474804174 Watt --> No Conversion Required
83.8000474804174 83.80005 Watt <-- Total Radiated Power in Free Space
(Calculation completed in 00.004 seconds)
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## Credits

Created by Vignesh Naidu
Vellore Institute of Technology (VIT), Vellore,Tamil Nadu
Vignesh Naidu has created this Calculator and 25+ more calculators!
Verified by Dipanjona Mallick
Heritage Insitute of technology (HITK), Kolkata
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## < 17 Electromagnetic Radiation and Antennas Calculators

Average Power Density of Half-Wave Dipole
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
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
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 = ((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
Power that Crosses Surface of Sphere
Power Crossed at Sphere Surface = pi*((Amplitude of Oscillating Current*Wavenumber*Short Antenna Length)/(4*pi))^2*Intrinsic Impedance of Medium*(int(sin(Theta)^3*x,x,0,pi))
Electric Field due to N Point Charges
Electric Field due to N Point Charges = sum(x,1,Number of Point Charges,(Charge)/(4*pi*[Permitivity-vacuum]*(Distance from Electric Field-Charge Distance)^2))
Poynting Vector Magnitude
Poynting Vector = 1/2*((Dipole Current*Wavenumber*Source Distance)/(4*pi))^2*Intrinsic Impedance*(sin(Polar Angle))^2
Total Radiated Power in Free Space
Total Radiated Power in Free Space = 30*Amplitude of Oscillating Current^2*int((Dipole Antenna Pattern Function)^2*sin(Theta)*x,x,0,pi)
Radiation Resistance = 60*(int((Dipole Antenna Pattern Function)^2*sin(Theta)*x,x,0,pi))
Time Average Radiated Power of Half-Wave Dipole
Time Average Radiated Power = (((Amplitude of Oscillating Current)^2)/2)*((0.609*Intrinsic Impedance of Medium)/pi)
Polarization
Polarization = Electric Susceptibility*[Permitivity-vacuum]*Electric Field Strength
Radiation Resistance of Half-wave Dipole = (0.609*Intrinsic Impedance of Medium)/pi
Directivity of Half-Wave Dipole
Directivity of Half Wave Dipole = Maximum Power Density/Average Power Density
Electric Field for Hertzian Dipole
Electric Field Component = Intrinsic Impedance*Magnetic Field Component
Radiation Efficiency of Antenna = Maximum Gain/Maximum Directivity
Average Power
Average Power = 1/2*Sinusoidal Current^2*Radiation Resistance
Radiation Resistance = 2*Average Power/Sinusoidal Current^2

## Total Radiated Power in Free Space Formula

Total Radiated Power in Free Space = 30*Amplitude of Oscillating Current^2*int((Dipole Antenna Pattern Function)^2*sin(Theta)*x,x,0,pi)
PR = 30*Io^2*int((F)^2*sin(θem)*x,x,0,pi)

## What are the Applications of Total Radiated Power in Free Space ?

1. Antenna Design and Optimization: Knowing the total radiated power allows engineers to assess the efficiency of an antenna in converting electrical power into electromagnetic waves. This helps optimize antenna design for specific applications where maximizing radiated power is crucial.
2. Link Budget Calculations: In wireless communication systems, link budget analysis determines the received signal strength at the receiver. Prad is a critical parameter in this calculation, as it represents the total power available at the source (antenna) for transmission.

## How to Calculate Total Radiated Power in Free Space?

Total Radiated Power in Free Space calculator uses Total Radiated Power in Free Space = 30*Amplitude of Oscillating Current^2*int((Dipole Antenna Pattern Function)^2*sin(Theta)*x,x,0,pi) to calculate the Total Radiated Power in Free Space, The Total Radiated Power in Free Space formula is defined as the total amount of electromagnetic wave power emitted by an antenna and requires knowledge of the Poynting vector distribution around the antenna. Total Radiated Power in Free Space is denoted by PR symbol.

How to calculate Total Radiated Power in Free Space using this online calculator? To use this online calculator for Total Radiated Power in Free Space, enter Amplitude of Oscillating Current (Io), Dipole Antenna Pattern Function (F) & Theta em) and hit the calculate button. Here is how the Total Radiated Power in Free Space calculation can be explained with given input values -> 83.80005 = 30*5^2*int((0.2128)^2*sin(0.5235987755982)*x,x,0,pi).

### FAQ

What is Total Radiated Power in Free Space?
The Total Radiated Power in Free Space formula is defined as the total amount of electromagnetic wave power emitted by an antenna and requires knowledge of the Poynting vector distribution around the antenna and is represented as PR = 30*Io^2*int((F)^2*sin(θem)*x,x,0,pi) or Total Radiated Power in Free Space = 30*Amplitude of Oscillating Current^2*int((Dipole Antenna Pattern Function)^2*sin(Theta)*x,x,0,pi). The Amplitude of Oscillating Current refers to the maximum magnitude or strength of the alternating electric current as it varies over time, Dipole Antenna Pattern Function describes the electric field strength variation in the plane containing its electric field and maximum radiation direction in E-plane & Theta is an angle that can be defined as the figure formed by two rays meeting at a common endpoint.
How to calculate Total Radiated Power in Free Space?
The Total Radiated Power in Free Space formula is defined as the total amount of electromagnetic wave power emitted by an antenna and requires knowledge of the Poynting vector distribution around the antenna is calculated using Total Radiated Power in Free Space = 30*Amplitude of Oscillating Current^2*int((Dipole Antenna Pattern Function)^2*sin(Theta)*x,x,0,pi). To calculate Total Radiated Power in Free Space, you need Amplitude of Oscillating Current (Io), Dipole Antenna Pattern Function (F) & Theta em). With our tool, you need to enter the respective value for Amplitude of Oscillating Current, Dipole Antenna Pattern Function & Theta 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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