4.1 Dipole antennas

Dipole antenna basics

Dipole antennas are among the most fundamental radiating structures in electromagnetics. They consist of two conductive arms fed by an RF signal at the center, producing a well-understood radiation pattern that serves as a baseline for characterizing more complex antennas.

Dipole antenna definition

A dipole antenna is formed from two identical conductive elements arranged collinearly along a straight line. An RF source drives the antenna at the center gap between the two arms, exciting a sinusoidal current distribution that radiates electromagnetic energy. The geometry is simple, but the physics it illustrates (current distributions, radiation resistance, near-field to far-field transition) makes it central to antenna theory.

Half-wave dipole

The half-wave dipole has a total length equal to half the free-space wavelength of the operating frequency:

$L = \frac{\lambda}{2} = \frac{c}{2f}$

At this length the antenna is at its first resonance, meaning the input impedance is purely real and the current distribution is approximately a single half-sinusoid with a maximum at the feedpoint. This resonant condition produces efficient radiation and a natural impedance near 73 + j42.5 Ω for an infinitesimally thin conductor. In practice, for a conductor of finite thickness, the reactive part vanishes at a length slightly shorter than $\lambda/2$ (typically about 0.47$\lambda$ to 0.48$\lambda$), leaving a purely resistive impedance of roughly 73 Ω.

Half-wave dipoles are the standard reference antenna for gain measurements quoted in dBd.

Dipole antenna radiation pattern

The far-field radiation pattern of a dipole depends on its electrical length, but for the half-wave case:

• H-plane (perpendicular to the antenna axis): The pattern is omnidirectional, meaning uniform power in all azimuthal directions.
• E-plane (containing the antenna axis): The pattern is a figure-eight (toroidal cross-section) with maxima broadside to the dipole and nulls along the axis of the arms.

The normalized E-plane field pattern for a half-wave dipole is:

$E(\theta) = \frac{\cos\!\left(\frac{\pi}{2}\cos\theta\right)}{\sin\theta}$

where $\theta$ is measured from the dipole axis. This expression is worth remembering because it appears repeatedly in array factor calculations.

Dipole antenna impedance

Input impedance

The input impedance $Z_{in} = R_{in} + jX_{in}$ is what the transmission line "sees" at the feedpoint. It has two components:

• Radiation resistance $R_r$: accounts for power actually radiated.
• Loss resistance $R_\ell$: accounts for ohmic losses in the conductor.
• Reactance $X_{in}$: stores energy in the near field; sign depends on whether the antenna is electrically short (capacitive) or long (inductive) relative to resonance.

For a half-wave dipole in free space, $R_r \approx 73\;\Omega$ and $X_{in} \approx 0$ at resonance (after the slight shortening mentioned above). A full-wave dipole, by contrast, has a much higher input impedance (on the order of several hundred ohms) and is not commonly used as a standalone radiator.

Impedance vs. frequency

At resonance the impedance is purely resistive. As you move away from the resonant frequency:

• Below resonance (antenna electrically short): the reactance becomes capacitive ($X_{in} < 0$).
• Above resonance (antenna electrically long): the reactance becomes inductive ($X_{in} > 0$).

The rate at which the impedance changes with frequency is related to the antenna's Q-factor, which in turn determines bandwidth. Thicker conductors store less reactive energy per cycle, lowering Q and broadening the impedance curve.

Impedance matching techniques

Matching the antenna's impedance to the feed line (commonly 50 Ω or 75 Ω) minimizes reflections and maximizes power transfer. Common approaches:

1. Quarter-wave transformer: A transmission line section of length $\lambda/4$ with characteristic impedance $Z_0 = \sqrt{Z_{ant} \cdot Z_{line}}$ placed between the antenna and the feed line.

2. Stub matching: A short- or open-circuited transmission line stub placed at a calculated distance from the feedpoint to cancel the reactive component.

3. Balun with impedance transformation: Some balun designs (e.g., a 4:1 balun) simultaneously convert balanced-to-unbalanced and transform impedance.

4. Gamma match or T-match: Feed the dipole off-center or through a parallel conductor to present a different impedance at the connection point.

Dipole antenna directivity

Directivity definition

Directivity $D$ quantifies how strongly an antenna focuses radiated power in its peak direction compared to a hypothetical isotropic radiator that spreads power equally in all directions:

$D = \frac{U_{max}}{U_{avg}} = \frac{4\pi\, U_{max}}{P_{rad}}$

where $U_{max}$ is the maximum radiation intensity (W/sr) and $P_{rad}$ is the total radiated power. Directivity is usually expressed in dBi.

Half-wave dipole directivity

For a half-wave dipole, the exact directivity works out to:

$D = \frac{4}{\int_0^{\pi} \frac{\cos^2\!\left(\frac{\pi}{2}\cos\theta\right)}{\sin\theta}\,d\theta} \approx 1.64 \;\;(\text{linear}) \approx 2.15\;\text{dBi}$

That integral doesn't have a neat closed form; the numerical value 1.64 is the one to memorize. For comparison, a short (Hertzian) dipole has $D = 1.5$ (1.76 dBi), so the half-wave dipole is only modestly more directive.

Directivity vs. dipole length

As the dipole length increases beyond $\lambda/2$:

• Directivity initially rises because the main lobe narrows.
• Side lobes begin to appear. A full-wave dipole ($L = \lambda$) has a directivity of about 2.41 dBi.
• At $L \approx 1.25\lambda$, the main lobe splits and the pattern no longer has its maximum broadside to the antenna. Beyond this point, increasing length doesn't simply "add gain" in a useful way without careful array design.

The trade-off between directivity and side-lobe level is a recurring theme in antenna engineering.

Dipole antenna gain

Gain definition

Gain $G$ is directivity scaled by the antenna's radiation efficiency $\eta_r$:

$G = \eta_r \, D$

where $\eta_r = \frac{R_r}{R_r + R_\ell}$ for a simple dipole. Gain is quoted in dBi (referenced to an isotropic antenna) or dBd (referenced to a half-wave dipole). The conversion is:

$G_{\text{dBi}} = G_{\text{dBd}} + 2.15$

Gain vs. directivity

Because gain folds in efficiency, it is always less than or equal to directivity. For a lossless half-wave dipole, $\eta_r = 1$ and $G = D = 2.15$ dBi. In practice, conductor losses at HF and below are small, so the half-wave dipole is nearly 100% efficient. At microwave frequencies or with lossy materials, the distinction between gain and directivity becomes more significant.

Calculating gain for a lossy dipole

1. Compute the radiation resistance $R_r$ from the current distribution.
2. Compute the ohmic loss resistance $R_\ell$ from the conductor's skin-depth resistance.
3. Find efficiency: $\eta_r = R_r / (R_r + R_\ell)$.
4. Multiply by directivity: $G = \eta_r \cdot D$.

For example, if a half-wave dipole has $R_r = 73\;\Omega$ and $R_\ell = 2\;\Omega$, then $\eta_r = 73/75 = 0.973$ and $G = 0.973 \times 1.64 = 1.60$ (linear), or about 2.03 dBi.

Dipole antenna polarization

Linear polarization

A dipole antenna radiates a linearly polarized wave. The electric field vector in the far field oscillates parallel to the dipole axis. Orient the dipole vertically and you get vertical polarization; orient it horizontally and you get horizontal polarization.

Circular polarization

A single dipole cannot produce circular polarization on its own. To generate it, you need two orthogonal dipoles fed with equal amplitude and a 90° phase difference. The resulting electric field vector traces a circle (or ellipse, if the amplitudes or phase aren't perfectly matched). The sense of rotation determines whether it is RHCP (right-hand circular) or LHCP (left-hand circular), defined by the IEEE convention looking in the direction of propagation.

Circular polarization is valuable in satellite links and GPS because it eliminates the need to align the receive antenna's orientation with the transmit antenna.

Polarization mismatch losses

When a linearly polarized antenna receives a wave of the orthogonal linear polarization, the theoretical mismatch loss is infinite (complete null). A linearly polarized antenna receiving a circularly polarized wave incurs a 3 dB mismatch loss. The general polarization loss factor (PLF) is:

$\text{PLF} = |\hat{p}_r \cdot \hat{p}_i|^2$

where $\hat{p}_r$ and $\hat{p}_i$ are the unit polarization vectors of the receiving antenna and the incident wave, respectively. Keeping transmit and receive polarizations matched is critical for link budget calculations.

Dipole antenna bandwidth

Bandwidth definition

Bandwidth is the frequency range over which the antenna meets a specified performance criterion. The most common criterion is an impedance bandwidth defined by a maximum acceptable VSWR (typically VSWR $\leq$ 2:1, corresponding to a return loss of about 10 dB). Bandwidth can also be defined in terms of gain, pattern shape, or polarization purity, depending on the application.

Half-wave dipole bandwidth

A thin half-wave dipole has a bandwidth of roughly 5–10% of the center frequency, depending on the wire diameter. The thicker the conductor relative to the wavelength, the wider the bandwidth. This is because a thicker conductor lowers the antenna Q:

$Q \propto \frac{1}{\ln(L/a)}$

where $a$ is the conductor radius. A dipole made from a thin wire (large $L/a$) has a high Q and narrow bandwidth; one made from wide tubing (small $L/a$) has a low Q and broader bandwidth.

Bandwidth enhancement techniques

• Increase conductor diameter: Fatter arms lower Q and widen the impedance bandwidth.
• Folded dipole: Provides a 4:1 impedance step-up (to ~300 Ω) and inherently broader bandwidth due to the coupled-conductor geometry.
• Biconical or bow-tie shape: Tapered arms create a more frequency-independent structure, pushing bandwidth well beyond what a cylindrical dipole achieves.
• Fan dipole: Multiple dipoles of different lengths connected at a common feedpoint, each resonant at a different frequency.
• Resistive loading: Adding resistance along the arms absorbs reactive energy and broadens bandwidth, but at the cost of reduced radiation efficiency.

Dipole antenna arrays

Linear dipole arrays

Placing $N$ dipoles along a line with uniform spacing $d$ creates a linear array. The far-field pattern is the product of the single-element pattern and the array factor:

$AF = \sum_{n=0}^{N-1} e^{\,jn(kd\cos\theta + \beta)}$

where $k = 2\pi/\lambda$ and $\beta$ is the progressive phase shift between elements. By choosing $d$ and $\beta$, you control the direction and width of the main beam. A broadside array ($\beta = 0$, $d = \lambda/2$) produces a beam perpendicular to the array axis.

Planar dipole arrays

Extending the concept to two dimensions, dipoles are arranged on a grid. The total array factor is the product of the row and column array factors. Planar arrays offer pencil-beam patterns with high directivity and the ability to steer in both azimuth and elevation.

Phased dipole arrays

In a phased array, the progressive phase $\beta$ is electronically adjustable, allowing the main beam to be steered without physically rotating the antenna. This is the basis of modern radar systems (e.g., AN/SPY-1), 5G massive MIMO base stations, and radio telescope arrays like LOFAR. Beam steering speed is limited only by the phase-shifter switching time, not mechanical inertia.

Dipole antenna feeding

Balanced vs. unbalanced feeding

A dipole is inherently a balanced structure: the two arms carry equal and opposite currents. Most practical feed lines (coaxial cable) are unbalanced, with current flowing on the inner conductor and returning on the inside surface of the outer conductor. Connecting a coax directly to a dipole without a balun allows current to flow on the outside of the coax shield. This common-mode current distorts the radiation pattern and can cause interference.

Balun transformers

A balun (balanced-to-unbalanced) enforces current symmetry. Common types:

• Choke balun (current balun): Ferrite beads or coiled coax that present high impedance to common-mode currents on the outer shield.
• Sleeve (bazooka) balun: A quarter-wave metal sleeve around the coax that chokes off exterior currents.
• Lattice (Guanella) balun: Transmission-line transformer that can also provide impedance transformation (e.g., 1:4).
• Marchand balun: A wideband design using coupled transmission-line sections, common at microwave frequencies.

Coaxial cable feeding

When feeding a dipole with coax:

1. Choose a balun appropriate for the frequency and bandwidth.
2. Connect the coax inner conductor to one arm and the outer conductor to the other arm, through the balun.
3. Ensure the balun suppresses common-mode currents to preserve pattern symmetry.

Without a balun, the coax outer conductor acts as a third radiating element, skewing the pattern and changing the input impedance unpredictably.

Practical dipole antenna designs

Folded dipole antenna

A folded dipole is a half-wave dipole with a second conductor connected at both ends, forming a rectangular loop. Because both conductors carry in-phase currents, the radiation resistance is stepped up by a factor of 4 relative to a standard dipole:

$R_{in} \approx 4 \times 73 = 292\;\Omega \approx 300\;\Omega$

This 300 Ω impedance is a natural match to twin-lead transmission line and is the reason folded dipoles are the standard driven element in Yagi-Uda antennas fed with 300 Ω balanced line. The folded geometry also provides wider bandwidth than a simple dipole of the same conductor diameter.

Bow-tie dipole antenna

Replacing the cylindrical arms with triangular (bow-tie) or flared shapes creates a structure that approximates a biconical antenna. The gradual taper provides a smoother impedance transition across frequency, yielding significantly broader bandwidth. Bow-tie dipoles are common in UWB systems and ground-penetrating radar, where bandwidths of 3:1 or more are needed.

Yagi-Uda antenna

A Yagi-Uda antenna consists of:

• Driven element: A resonant dipole (or folded dipole) connected to the feed line.
• Reflector: A parasitic element slightly longer than the driven element, placed behind it. It reflects energy forward.
• Directors: One or more parasitic elements slightly shorter than the driven element, placed in front. They guide energy in the forward direction.

The parasitic elements are not directly fed; they are excited by mutual coupling. Adding more directors increases gain (roughly 1–2 dB per doubling of the number of directors, with diminishing returns). A typical 3-element Yagi has a gain of about 7–8 dBi and a front-to-back ratio of 15–20 dB. Yagi-Uda antennas are widely used for TV reception, amateur radio, and point-to-point links.

Dipole antenna applications

Wireless communication

Dipole antennas appear throughout wireless systems. Cellular base stations often use arrays of dipoles (or dipole-derived elements) to create sector coverage patterns. Wi-Fi access points frequently use half-wave dipoles enclosed in plastic housings. The omnidirectional H-plane pattern is well suited to providing coverage in all horizontal directions from a vertically oriented dipole.

Radio astronomy

Large arrays of dipoles form the collecting aperture of low-frequency radio telescopes. LOFAR, for example, uses thousands of crossed dipoles operating from 10 to 240 MHz to image the radio sky with high angular resolution through aperture synthesis. At these low frequencies, dipoles are practical because their physical size (meters) is manageable, and they can be mass-produced cheaply.

EMC testing

In electromagnetic compatibility testing, calibrated dipole antennas (often tunable half-wave dipoles) serve as reference receivers for measuring radiated emissions from electronic equipment. Their well-characterized gain and pattern make them traceable to measurement standards (e.g., ANSI C63.5). The predictable 2.15 dBi gain simplifies converting measured voltages to field strengths.