Radiated Resistance Calculator

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Electromagnetic Radiation and Antennas

Guided Waves in Field Theory

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✖Dipole Antenna Pattern Function describes the electric field strength variation in the plane containing its electric field and maximum radiation direction in E-plane.ⓘ Dipole Antenna Pattern Function [F]			+10% -10%
✖Theta is an angle that can be defined as the figure formed by two rays meeting at a common endpoint.ⓘ Theta [θ_em]			+10% -10%

✖Radiation Resistance is the effective resistance of antenna.ⓘ Radiated Resistance [R_rad]

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Formula

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Radiated Resistance

Formula

`"R"_{"rad"} = 60*(int(("F")^2*sin("θ"_{"em"})*x,x,0,pi))`

Example

`"6.704004Ω"=60*(int(("0.2128")^2*sin("30°")*x,x,0,pi))`

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Radiated Resistance Solution

STEP 0: Pre-Calculation Summary

Formula Used

Radiation Resistance = 60*(int((Dipole Antenna Pattern Function)^2*sin(Theta)*x,x,0,pi))
R_rad = 60*(int((F)^2*sin(θ_em)*x,x,0,pi))
This formula uses 1 Constants, 2 Functions, 3 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

Radiation Resistance - (Measured in Ohm) - Radiation Resistance is the effective resistance of antenna.
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

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

R_rad = 60*(int((F)^2*sin(θ_em)*x,x,0,pi)) --> 60*(int((0.2128)^2*sin(0.5235987755982)*x,x,0,pi))

Evaluating ... ...

R_rad = 6.7040037984334

STEP 3: Convert Result to Output's Unit

6.7040037984334 Ohm --> No Conversion Required

FINAL ANSWER

6.7040037984334 ≈ 6.704004 Ohm <-- Radiation Resistance

(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

Dipanjona Mallick has verified this Calculator and 50+ more calculators!

< 17 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

Power that Crosses Surface of Sphere

Go 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

Go 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

Go Poynting Vector = 1/2*((Dipole Current*Wavenumber*Source Distance)/(4*pi))^2*Intrinsic Impedance*(sin(Polar Angle))^2

Total Radiated Power in Free Space

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

Radiated Resistance

Go Radiation Resistance = 60*(int((Dipole Antenna Pattern Function)^2*sin(Theta)*x,x,0,pi))

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

Radiated Resistance Formula

Radiation Resistance = 60*(int((Dipole Antenna Pattern Function)^2*sin(Theta)*x,x,0,pi))
R_rad = 60*(int((F)^2*sin(θ_em)*x,x,0,pi))

What are the Applications of Radiated Resistance ?

1. Matching Networks: An antenna and its transmission line need to be impedance matched for efficient power transfer. The radiated resistance helps determine the impedance transformation required in the matching network to achieve optimal power transfer between the antenna and the feeding circuit.
2. Antenna Efficiency: The efficiency of an antenna is the ratio between the radiated power (P_rad ) and the total input power (P_in). Radiated resistance is directly related to P_rad through the formula R_rad = P_rad / (Irms^2). Knowing the radiated resistance allows us to calculate the efficiency and assess how well the antenna converts electrical power into radiated electromagnetic waves.

How to Calculate Radiated Resistance?

Radiated Resistance calculator uses Radiation Resistance = 60*(int((Dipole Antenna Pattern Function)^2*sin(Theta)*x,x,0,pi)) to calculate the Radiation Resistance, The Radiated Resistance formula represents the equivalent resistance that would dissipate the same amount of power as the antenna radiates. Radiation Resistance is denoted by R_rad symbol.

How to calculate Radiated Resistance using this online calculator? To use this online calculator for Radiated Resistance, enter Dipole Antenna Pattern Function (F) & Theta (θ_em) and hit the calculate button. Here is how the Radiated Resistance calculation can be explained with given input values -> 6.704004 = 60*(int((0.2128)^2*sin(0.5235987755982)*x,x,0,pi)).

FAQ

What is Radiated Resistance?

The Radiated Resistance formula represents the equivalent resistance that would dissipate the same amount of power as the antenna radiates and is represented as R_rad = 60*(int((F)^2*sin(θ_em)*x,x,0,pi)) or Radiation Resistance = 60*(int((Dipole Antenna Pattern Function)^2*sin(Theta)*x,x,0,pi)). 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 Radiated Resistance?

The Radiated Resistance formula represents the equivalent resistance that would dissipate the same amount of power as the antenna radiates is calculated using Radiation Resistance = 60*(int((Dipole Antenna Pattern Function)^2*sin(Theta)*x,x,0,pi)). To calculate Radiated Resistance, you need Dipole Antenna Pattern Function (F) & Theta (θ_em). With our tool, you need to enter the respective value for 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.

How many ways are there to calculate Radiation Resistance?

In this formula, Radiation Resistance uses Dipole Antenna Pattern Function & Theta. We can use 1 other way(s) to calculate the same, which is/are as follows -

Radiation Resistance = 2*Average Power/Sinusoidal Current^2

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