1. Introduction
An antenna is a transducer that converts guided electromagnetic (EM) waves on a transmission line into free-space radiated waves (transmitting), or vice versa (receiving). It is the essential interface between a radio transmitter/receiver and the propagation medium.
The dipole antenna is the simplest and most fundamental practical antenna. It consists of two identical conductive arms (wires or tubes) fed at the center by a two-terminal source. When RF current flows, charges accelerate along the arms and radiate electromagnetic energy.
Why Study the Dipole?
- It is the reference antenna against which the gain of all other antennas is measured (0 dBd reference).
- Almost every antenna (Yagi, log-periodic, arrays) is built from dipole-like elements.
- Its analysis introduces all core antenna concepts: radiation resistance, current distribution, pattern, near/far fields, polarization.
Basic Terminology
| Term | Definition |
|---|---|
| Isotropic radiator | Hypothetical point source radiating equally in all directions (0 dBi reference). |
| Half-wave dipole | Dipole whose total length L ≈ λ/2, resonant, Rr ≈ 73 Ω. |
| Radiation resistance | Fictitious resistance that dissipates the same power as the antenna radiates. |
| Radiation pattern | Graph of radiated field/power intensity versus direction (angle θ). |
| Gain / Directivity | Concentration of radiation in a direction, relative to isotropic (dBi) or dipole (dBd). |
| Polarization | Orientation of the E-field vector of the radiated wave (linear, circular, elliptical). |
Key insight: Radiation requires accelerating charges. Uniform (DC) current on an infinitely long, perfectly straight wire does NOT radiate — it is the termination/reversal of current on a finite antenna that produces radiation.
2. Electric and Magnetic Fields Around a Transmission Line
A two-wire (parallel) transmission line carries equal and opposite currents. The EM field around it is confined to the region between and around the conductors — the fields of the two wires largely cancel in the far region, so the line does not radiate (ideal case).
Field Structure
- Electric field (E): points radially from the positive (higher-potential) wire toward the negative wire. Field lines start on one conductor and terminate on the other — a "bounded" field pattern.
- Magnetic field (H): forms concentric circles around each conductor, given by Ampère's law. Between the wires the H-fields add; outside they subtract and cancel at large distances.
H = I / (2πr) (A/m, around a long straight wire) | E ≈ η₀ H (η₀ ≈ 377 Ω)
When Does the Line Start to Radiate?
Radiation becomes significant when the conductor spacing becomes comparable to the wavelength (typically d > λ/10 – λ/100). The fields then cannot cancel in the far zone, and the line acts as an antenna. This is exactly how a dipole is "born": take a two-wire line, bend the two wires outward 90°, and the "bound" field lines detach and propagate into free space.
Watch: E-field (red) and H-field (blue) cancellation vs. radiation. Increasing spacing or bending the wires forces the fields to radiate.
Reading the simulation: With small spacing, the fields between the wires are strong but cancel in the far region (confined mode). As spacing grows — or when you press "Bend into Dipole" — the field lines detach and propagate outward as radiation.
3. Electric Fields in a Coaxial Cable
A coaxial cable consists of an inner conductor (radius a) and an outer conducting shield (radius b) separated by a dielectric. Because the outer conductor completely encloses the field, a coaxial cable is a perfectly shielded transmission line: ideally no radiation escapes.
Field Configuration
- E-field: purely radial, existing only between the inner conductor and the inner surface of the shield. It varies as 1/r:
E(r) = V / (r ln(b/a)) for a < r < b | E = 0 outside the shield
- H-field: concentric circles around the inner conductor (φ-directed), also confined inside the cable.
This TEM (Transverse Electromagnetic) mode has E and H entirely perpendicular to the direction of propagation — the ideal guided mode.
Breaking the shield = making an antenna: If the coax is opened and the inner conductor is extended beyond the shield, the field can no longer terminate on the shield — it must spread into free space. A coax with its inner conductor extended λ/4 beyond the shield end is exactly a monopole (Section 5).
Radial E-field (red arrows) is trapped between inner conductor and shield. Check "Open the end" to see the field spill out and radiate (monopole!).
4. Principle of Operation of a Dipole Antenna
How it works, step by step:
- Feeding: An RF source is connected across the center gap. At any instant, one arm is driven positive and the other negative.
- Charge accumulation: Positive charge piles up at the tip of one arm; negative charge at the tip of the other. The charge distribution sloshes back and forth at the RF frequency.
- Current distribution: Current flows from the source toward the tips, reflecting from the open ends. For a half-wave dipole the current is approximately sinusoidal with a maximum at the center and (ideally) zero at the tips.
- Radiation: The accelerating charges create time-varying E and H fields. The fields of the two arms add constructively in some directions and cancel in others — producing a directional radiation pattern. Energy detaches from the antenna and propagates as an EM wave at the speed of light.
Current distribution (thin dipole): I(z) = I₀ sin[k(L/2 − |z|)] , k = 2π/λ
Resonance and Radiation Resistance
- When L ≈ λ/2 the dipole is resonant: the input impedance is purely resistive, ≈ 73 + j0 Ω.
- The radiated power is modeled as dissipated in this radiation resistance: Prad = ½I²Rr.
- A dipole much shorter than λ has very small Rr (poor radiator, hard to match); longer dipoles develop reactive components and multi-lobed patterns.
Animation: charges (+ red / − blue) sloshing along the arms, current arrows, and the radiated E-field wavefronts (expanding rings). Try L/λ = 0.5 (half-wave, strongest broadside radiation) and L/λ = 1.0 (full-wave, null at broadside!).
Transmit ↔ Receive reciprocity: The same dipole works identically as a receiving antenna — an incoming wave induces currents that deliver power to the load. The radiation pattern is identical in both roles.
5. Principle of Operation of a Monopole Antenna
A monopole (or Marconi antenna) is exactly one half of a dipole: a single radiating element mounted perpendicular to a conducting ground plane, fed between the element's base and the ground plane.
How It Works
- The ground plane acts as an electrical mirror: by image theory, the real monopole plus its mirror image below the ground form a complete dipole.
- Only the upper half physically exists and radiates; the lower hemisphere is supplied by the "image."
- For the same radiated power above ground, the monopole needs only half the length (λ/4 for the classic quarter-wave monopole).
- The ground currents must return to the source through the ground plane — hence a good RF ground or radials are essential.
Quarter-wave monopole: L = λ/4 | Rr ≈ 36.6 Ω (half of dipole's 73 Ω, since only half the pattern exists)
| Property | Half-wave dipole | Quarter-wave monopole |
|---|---|---|
| Length | λ/2 | λ/4 (half the size!) |
| Radiation resistance | 73 Ω | 36.6 Ω |
| Coverage | Both hemispheres (doughnut) | Upper hemisphere only |
| Directivity | 2.15 dBi | 5.15 dBi (image doubles field at horizon) |
| Ground plane | Not required | Mandatory |
The dashed element below the ground plane is the image. Radiation exists only above ground — note the single-hemisphere doughnut. Classic value: L/λ = 0.25.
Practical note: Car antennas, walkie-talkie "rubber ducks," AM broadcast towers, and mobile phone whips are all monopoles — small size makes them ideal for portable equipment.
6. Dipole Antenna Variants
| Variant | Description | Applications |
|---|---|---|
| Half-wave dipole | L = λ/2, center-fed; Rr ≈ 73 Ω; reference antenna | FM/TV broadcast, reference standard |
| Short dipole (Hertzian) | L < λ/10; triangular current, Rr very small | Theory baseline, small sensors |
| Folded dipole | Two parallel dipoles joined at ends; impedance ≈ 4 × 73 = 300 Ω, wider bandwidth | TV/Yagi driven elements, FM reception |
| Monopole (λ/4) | Dipole over ground plane, half length, single hemisphere | Mobile phones, cars, AM towers |
| Sleeve dipole | Dipole with metal sleeve; broadband, coaxial feed | VHF/UHF communications |
| Inverted-V / sloper | Dipole with ends angled down; omnidirectional-ish, one support | HF amateur radio |
| Balun-fed dipole | Dipole with balun (balanced-to-unbalanced transformer) | Any coax-fed dipole (kills common-mode current) |
| Dipole arrays (Yagi-Uda, collinear) | Multiple dipoles with directors/reflectors → high gain | TV antennas, base stations, radar |
The Yagi-Uda antenna (your rooftop TV antenna) is just a driven folded dipole plus parasitic director and reflector dipoles — direct evidence that the simple dipole scales into high-gain systems.
7. Near Field and Far Field of a Dipole Antenna
The space around a transmitting antenna divides into two distinct regions with very different field behavior. The boundary is conventionally set at:
r = 2D²/λ (Fraunhofer distance; D = largest antenna dimension)
1. Near Field (Reactive & Radiating Near-Field, r < 2D²/λ)
- Reactive near field (r < ~0.62√(D³/λ)): E and H fields store and return energy to the antenna each RF cycle — they are 90° out of phase; energy "sloshes" rather than flows outward. Dominant terms decay as 1/r³ (E) and 1/r² (H).
- Radiating near field (Fresnel region): radiation begins to dominate, but the pattern still changes noticeably with distance; phase across a large aperture is not planar.
2. Far Field (Fraunhofer Region, r > 2D²/λ)
- E and H are in phase, mutually perpendicular, and perpendicular to the direction of propagation — a true TEM spherical wave.
- Fields decay as 1/r; the radiation pattern becomes independent of distance.
- This is the region where antennas are designed, measured, and used.
| Property | Near field | Far field |
|---|---|---|
| Dominant field decay | 1/r³, 1/r² | 1/r |
| E–H phase relationship | ≈90° (reactive) | In phase (radiating) |
| Wavefront | Complex, distance-dependent | Spherical TEM, locally planar |
| Pattern vs. distance | Changes with r | Fixed shape |
Example: For a half-wave dipole at f = 100 MHz (λ = 3 m, D = 1.5 m): r = 2(1.5)²/3 = 1.5 m — beyond 1.5 m you are safely in the far field.
Observe the 1/r³ reactive field hugging the dipole vs. the 1/r radiating wave escaping. Marker = 2D²/λ boundary for a half-wave dipole at the chosen frequency.
8. Radiation Pattern of a Dipole Antenna
The radiation pattern is a polar plot of radiated field (or power) strength versus direction. For a thin dipole in free space, the pattern depends only on the angle θ from the dipole axis:
E(θ) ∝ [cos((kL/2)cosθ) − cos(kL/2)] / sinθ
Key Cases
- Short dipole (L << λ): E(θ) ∝ sinθ — figure-eight, nulls along the axis, maximum broadside.
- Half-wave dipole (L = λ/2): slightly narrower lobe than sinθ; beamwidth ≈ 78°; directivity 2.15 dBi.
- Full-wave dipole (L = λ): pattern narrows further and splits — a null appears at broadside.
- Longer dipoles (L > 1.25λ): multiple lobes appear with large off-axis sidelobes — generally undesirable for simple links.
The 3D pattern is a doughnut (toroid) shape: maximum radiation in the plane perpendicular to the dipole axis (θ = 90°), zero radiation along the wire itself.
Polar plot of |E(θ)| normalized. Rotate with the angle slider? No need — drag the length and watch the doughnut slice evolve.
Pattern Parameters
- Beamwidth: angular width between half-power (−3 dB) points — 78° for a half-wave dipole.
- Nulls: directions of zero radiation (along the dipole axis for short/half-wave dipoles).
- Sidelobes: secondary maxima that appear when L > λ.
9. Self-Test Questions
Q1. Define an antenna and state the function of a dipole antenna.
An antenna is a transducer between guided waves and free-space EM waves; a dipole converts RF current between its two arms into radiated EM energy (and reciprocally receives).
Q2. Why does an ideal infinite straight transmission line not radiate?
Equal and opposite currents produce fields that cancel in the far region; charges move uniformly (no acceleration/termination), so no net radiation.
Q3. Describe the E-field inside a coaxial cable and explain why it does not leak out.
E is radial between inner conductor and shield (E = V/(r ln(b/a))); the enclosing shield forces E = 0 outside — the field is fully contained.
Q4. Explain the mechanism by which bending a two-wire line into a dipole produces radiation.
Bending forces the E-field lines to terminate on a structure they cannot fully close on; the fields detach and propagate as free-space waves (radiation).
Q5. Sketch the current distribution on a half-wave dipole and give its radiation resistance.
Approximately sinusoidal: maximum at the feed point, zero at the tips; Rr ≈ 73 Ω.
Q6. Using image theory, explain how a quarter-wave monopole over a ground plane radiates.
The ground plane images the monopole into a virtual half-dipole below ground; only the upper half is physical, radiating into one hemisphere.
Q7. Compare the radiation resistance and directivity of a half-wave dipole and a quarter-wave monopole.
Dipole: 73 Ω, 2.15 dBi, both hemispheres. Monopole: 36.6 Ω, 5.15 dBi, upper hemisphere only.
Q8. Name four dipole variants and one application of each.
Folded dipole (TV/Yagi driven element), monopole (mobile whip), sleeve dipole (broadband VHF/UHF), Yagi array (high-gain rooftop TV).
Q9. Write the Fraunhofer distance formula and compute it for a half-wave dipole at 100 MHz.
r = 2D²/λ; λ = 3 m, D = 1.5 m → r = 1.5 m.
Q10. How do the near-field and far-field regions of a dipole differ in field decay and E–H phase?
Near: 1/r³/1/r² decay, ~90° phase (reactive). Far: 1/r decay, in-phase TEM wave, fixed pattern.
Q11. What happens to the radiation pattern of a dipole as its length increases from 0.1λ to 1.5λ?
Lobe narrows up to ~λ/2–λ, null appears at broadside at L = λ, then sidelobes and multiple lobes form for L > 1.25λ.
Q12. What is the 3D radiation pattern shape of a half-wave dipole, and where are its nulls?
A doughnut (toroid); nulls along the dipole axis (θ = 0° and 180°), maximum at θ = 90°.