Average Power Density of Half-Wave Dipole Calculator

Average Power Density Formula:

\[ [Pr]_{avg} = \frac{0.609 \times \eta_{hwd} \times I_o^2}{4\pi^2 r_{hwd}^2} \times \sin^2\left(\left(\omega_{hwd} t - \frac{\pi}{L_{hwd}} r_{hwd}\right) \times \frac{\pi}{180}\right) \]

Intrinsic Impedance of Medium (η):

Ohm

Amplitude of Oscillating Current (I₀):

Ampere

Radial Distance from Antenna (r):

Meter

Angular Frequency (ω):

rad/s

Time (t):

Second

Length of Antenna (L):

Meter

Average Power Density ([Pr]avg):

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1. What is Average Power Density of Half-Wave Dipole?

The Average Power Density of a Half-Wave Dipole refers to the average amount of electromagnetic power per unit volume that is radiated by a half-wave dipole antenna over a complete cycle. It represents the spatial distribution of radiated power in the antenna's far field region.

2. How Does the Calculator Work?

The calculator uses the Average Power Density formula:

\[ [Pr]_{avg} = \frac{0.609 \times \eta_{hwd} \times I_o^2}{4\pi^2 r_{hwd}^2} \times \sin^2\left(\left(\omega_{hwd} t - \frac{\pi}{L_{hwd}} r_{hwd}\right) \times \frac{\pi}{180}\right) \]

Where:

\( \eta_{hwd} \) — Intrinsic impedance of the medium (Ohm)
\( I_o \) — Amplitude of oscillating current (Ampere)
\( r_{hwd} \) — Radial distance from antenna (Meter)
\( \omega_{hwd} \) — Angular frequency of half-wave dipole (rad/s)
\( t \) — Time (Second)
\( L_{hwd} \) — Length of antenna (Meter)
\( \pi \) — Archimedes' constant (≈3.14159)

Explanation: The formula calculates the time-averaged power density radiated by a half-wave dipole antenna, accounting for the spatial and temporal variations of the electromagnetic field.

3. Importance of Power Density Calculation

Details: Calculating average power density is crucial for antenna design, electromagnetic compatibility analysis, safety assessments of RF exposure, and understanding the radiation pattern and efficiency of antenna systems.

4. Using the Calculator

Tips: Enter all parameters in appropriate units. Ensure intrinsic impedance, current amplitude, radial distance, angular frequency, and antenna length are positive values. Time must be non-negative.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of the 0.609 factor?
A: The 0.609 factor is derived from the radiation resistance and current distribution of a half-wave dipole antenna, representing the efficiency of power radiation.

Q2: How does distance affect power density?
A: Power density decreases with the square of the distance from the antenna (inverse square law), as shown by the 1/r² term in the denominator.

Q3: What is the typical value of intrinsic impedance?
A: For free space, the intrinsic impedance is approximately 377 Ohms. For other media, it depends on the permittivity and permeability of the material.

Q4: Why is there a sine squared term in the formula?
A: The sine squared term accounts for the angular dependence of the radiation pattern, showing how power density varies with direction from the antenna.

Q5: When is this formula applicable?
A: This formula is valid in the far-field region of the antenna where the radiation pattern is well-established and the wave approximates a plane wave.