Dipole Antennas

Dipole antennas are among the most fundamental and widely used antenna types in communication systems. They consist of two conductive elements and exhibit well-defined radiation characteristics. This article explores the structure, analysis methods, radiation resistance, and efficiency of dipole antennas, including the short dipole approximation.

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Ideal Dipole

A theoretical dipole antenna with constant current distribution, useful for simplifications in analytical calculations.

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Radiated Fields from a Short Dipole

$$ E = -j \omega A_\theta $$

$$ H = \frac{j}{2\lambda} I \frac{e^{-jkr}}{r} L \sin\theta $$

[!NOTE] Elementary Dipole)**: A differential segment dL of a dipole, which contributes to the total radiation pattern as:

$$ dA = \frac{\mu}{4\pi} I \frac{e^{-jkr}}{r} dL $$

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Dipole Structure: Two Conductive Wires

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Conductive Wires

Fundamental elements of antennas, responsible for carrying electric currents that generate electromagnetic radiation.

A dipole antenna consists of two conductive elements (wires or rods) that are fed by a balanced transmission line or a center-fed current source. When an alternating current (AC) flows through the dipole, it generates an oscillating electromagnetic field, resulting in radiation.

The most common dipole configuration is the half-wave dipole, which has a length approximately equal to λ/2, where λ is the wavelength of the operating frequency. The current distribution along the dipole follows a sinusoidal pattern, with the maximum current at the center and minimum at the ends.

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The Image Method and Monopole Equivalence

A monopole antenna can be considered a special case of a dipole, where one half of the dipole is replaced by a conducting ground plane. This is often analyzed using the image method, which replaces the missing half of the dipole with a virtual (mirror) dipole beneath the ground.

Key points:

• Monopole antennas have similar radiation patterns to dipoles but exhibit twice the directivity and gain.
• The presence of a ground plane influences impedance and radiation characteristics.
• The image method simplifies the analysis of monopole antennas by assuming a virtual dipole that mirrors the real one.

[!NOTE]

Image Method

A technique used in electromagnetics to simplify analysis by introducing a virtual dipole (monopole equivalent) as a mirror image in a conductive plane.

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Radiation Resistance and Efficiency

The radiation resistance $( R_{rad} )$ of an antenna represents the equivalent resistance that accounts for radiated power. It is given by:

$$ R_{rad} = \frac{2 \pi \eta}{3} \left( \frac{L}{\lambda} \right)^2 \quad (\Omega) $$

where:

• η is the intrinsic impedance of free space $(≈ 377 Ω)$,
• L is the antenna length,
• λ is the wavelength.

The antenna efficiency $( \eta_0 )$ is given by:

$$ \eta_0 = \frac{P_{rad}}{P_{in}} = \frac{R_{rad}}{R_{rad} + R_{loss}} $$

A higher radiation resistance generally leads to better efficiency, as it minimizes resistive losses.

For a half-wave dipole:

• $( R_{rad} \approx 73 \Omega )$,
• Directivity $( D ) ≈ 1.64 (2.15 dB)$.

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Short Dipole (Hertzian Dipole) Approximation

A short dipole is an idealized antenna where the length is much smaller than the wavelength $(( L \ll \lambda ))$. Typically $L ≤ λ/50$.

Used for theoretical approximations and small antenna applications.

Key characteristics:

• Current distribution is assumed to be uniform along the length.
• Radiation pattern follows a simple sinusoidal variation.
• Field components can be approximated using the vector potential A:

$$ A_\theta = \frac{\mu}{4 \pi} I \left( \frac{e^{-jkr}}{r} \right) L \sin\theta $$

From this, the far-field electric and magnetic fields can be derived:

$$ E = -j \omega A_\theta, \quad H = \frac{j}{2 \lambda} I \left( \frac{e^{-jkr}}{r} \right) L \sin\theta $$

The short dipole is useful for fundamental studies and serves as a building block for more complex antenna designs.

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Conclusion

Dipole antennas form the basis of many modern communication systems, from radio to television broadcasting. Understanding their structure, equivalent monopole configurations, radiation resistance, and efficiency is crucial for optimizing performance. In the next article, we will delve into Half-Wave Dipoles and Standing Wave Antennas, exploring their practical applications and enhancements.

Stay tuned for the next article: Half-Wave Dipole and Standing Wave Antennas.