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Power Radiated by Half-Wave Dipole Formula

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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. Check FAQs

p rad = (\frac{0.609 \cdot η hwd \cdot {(I o)}^{2}}{π}) \cdot {\sin (((W hwd \cdot t) - ((\frac{π}{L hwd}) \cdot r hwd)) \cdot \frac{π}{180})}^{2}

p_rad - Power Radiated by Half-wave Dipole?η_hwd - Intrinsic Impedance of Medium?I_o - Amplitude of Oscillating Current?W_hwd - Angular Frequency of Half Wave Dipole?t - Time?L_hwd - Length of Antenna?r_hwd - Radial Distance from Antenna?π - Archimedes' constant?

Power Radiated by Half-Wave Dipole Example

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Here is how the Power Radiated by Half-Wave Dipole equation looks like with Values.

Here is how the Power Radiated by Half-Wave Dipole equation looks like with Units.

Here is how the Power Radiated by Half-Wave Dipole equation looks like.

230.0828 = (\frac{0.609 \cdot 377 \cdot {(5)}^{2}}{3.1416}) \cdot {\sin (((6.3E+7 \cdot 0.001) - ((\frac{3.1416}{2}) \cdot 0.5)) \cdot \frac{3.1416}{180})}^{2}

230.0828W = (\frac{0.609 \cdot 377Ω \cdot {(5A)}^{2}}{3.1416}) \cdot {\sin (((6.3E+7rad/s \cdot 0.001s) - ((\frac{3.1416}{2m}) \cdot 0.5m)) \cdot \frac{3.1416}{180})}^{2}

230.0828 = (\frac{0.609 \cdot 377 \cdot {(5)}^{2}}{3.1416}) \cdot {\sin (((6.3E+7 \cdot 0.001) - ((\frac{3.1416}{2}) \cdot 0.5)) \cdot \frac{3.1416}{180})}^{2}

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Power Radiated by Half-Wave Dipole Solution

Follow our step by step solution on how to calculate Power Radiated by Half-Wave Dipole?

FIRST Step Consider the formula

p rad = (\frac{0.609 \cdot η hwd \cdot {(I o)}^{2}}{π}) \cdot {\sin (((W hwd \cdot t) - ((\frac{π}{L hwd}) \cdot r hwd)) \cdot \frac{π}{180})}^{2}

Next Step Substitute values of Variables

∴

p rad = (\frac{0.609 \cdot 377Ω \cdot {(5A)}^{2}}{π}) \cdot {\sin (((6.3E+7rad/s \cdot 0.001s) - ((\frac{π}{2m}) \cdot 0.5m)) \cdot \frac{π}{180})}^{2}

Next Step Substitute values of Constants

∴

p rad = (\frac{0.609 \cdot 377Ω \cdot {(5A)}^{2}}{3.1416}) \cdot {\sin (((6.3E+7rad/s \cdot 0.001s) - ((\frac{3.1416}{2m}) \cdot 0.5m)) \cdot \frac{3.1416}{180})}^{2}

Next Step Prepare to Evaluate

∴

p rad = (\frac{0.609 \cdot 377 \cdot {(5)}^{2}}{3.1416}) \cdot {\sin (((6.3E+7 \cdot 0.001) - ((\frac{3.1416}{2}) \cdot 0.5)) \cdot \frac{3.1416}{180})}^{2}

Next Step Evaluate

∴

p rad = 230.08282202564W

LAST Step Rounding Answer

∴

p rad = 230.0828W

Power Radiated by Half-Wave Dipole Formula Elements

Variables

Constants

Functions

Power Radiated by Half-wave Dipole

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.

Symbol: p_rad

Measurement: PowerUnit: W

Note: Value should be greater than 0.

Intrinsic Impedance of Medium

The Intrinsic Impedance of Medium refers to the characteristic impedance of a material through which electromagnetic waves propagate.

Symbol: η_hwd

Measurement: Electric ResistanceUnit: Ω

Note: Value should be greater than 0.

Amplitude of Oscillating Current

The Amplitude of Oscillating Current refers to the maximum magnitude or strength of the alternating electric current as it varies over time.

Symbol: I_o

Measurement: Electric CurrentUnit: A

Note: Value should be greater than 0.

Angular Frequency of Half Wave Dipole

The Angular Frequency of Half Wave Dipole refers to the rate at which the dipole oscillates back and forth in an electromagnetic field.

Symbol: W_hwd

Measurement: Angular FrequencyUnit: rad/s

Note: Value should be greater than 0.

Time

Time is a dimension in which events occur in succession, allowing for the measurement of durations between those events.

Symbol: t

Measurement: TimeUnit: s

Note: Value should be greater than 0.

Length of Antenna

The Length of Antenna refers to the physical size of the conductive element that make up the antenna structure.

Symbol: L_hwd

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Radial Distance from Antenna

The Radial Distance from Antenna refers to the distance measured radially outward from the center of the antenna structure.

Symbol: r_hwd

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

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.

Syntax: sin(Angle)

Credits

Creator Image

Created by Souradeep Dey

National Institute of Technology Agartala (NITA), Agartala, Tripura

Souradeep Dey has created this Formula and 25+ more formulas!

Verifier Image

Verified by Santhosh Yadav

Dayananda Sagar College Of Engineering (DSCE), Banglore

Santhosh Yadav has verified this Formula and 50+ more formulas!

Other formulas in Electromagnetic Radiation and Antennas category

Go Radiation Resistance of Antenna

R rad = 2 \cdot \frac{P r}{{i o}^{2}}

Go Average Power

P r = \frac{1}{2} \cdot {i o}^{2} \cdot R rad

See More

How to Evaluate Power Radiated by Half-Wave Dipole?

Power Radiated by Half-Wave Dipole evaluator 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 evaluate the Power Radiated by Half-wave Dipole, Power Radiated by Half-Wave Dipole is the total electromagnetic energy emitted per unit time, determined by the antenna's current distribution and efficiency, typically measured in watts. Power Radiated by Half-wave Dipole is denoted by p_rad symbol.

How to evaluate Power Radiated by Half-Wave Dipole using this online evaluator? To use this online evaluator for Power Radiated by Half-Wave Dipole, enter Intrinsic Impedance of Medium (η_hwd), Amplitude of Oscillating Current (I_o), Angular Frequency of Half Wave Dipole (W_hwd), Time (t), Length of Antenna (L_hwd) & Radial Distance from Antenna (r_hwd) and hit the calculate button.

FAQs on Power Radiated by Half-Wave Dipole

What is the formula to find Power Radiated by Half-Wave Dipole?

The formula of Power Radiated by Half-Wave Dipole is expressed as 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. Here is an example- 230.0828 = ((0.609*377*(5)^2)/pi)*sin(((62800000*0.001)-((pi/2)*0.5))*pi/180)^2.

How to calculate Power Radiated by Half-Wave Dipole?

With Intrinsic Impedance of Medium (η_hwd), Amplitude of Oscillating Current (I_o), Angular Frequency of Half Wave Dipole (W_hwd), Time (t), Length of Antenna (L_hwd) & Radial Distance from Antenna (r_hwd) we can find Power Radiated by Half-Wave Dipole using the 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. This formula also uses Archimedes' constant and Sine (sin) function(s).

Can the Power Radiated by Half-Wave Dipole be negative?

No, the Power Radiated by Half-Wave Dipole, measured in Power cannot be negative.

Which unit is used to measure Power Radiated by Half-Wave Dipole?

Power Radiated by Half-Wave Dipole is usually measured using the Watt[W] for Power. Kilowatt[W], Milliwatt[W], Microwatt[W] are the few other units in which Power Radiated by Half-Wave Dipole can be measured.

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