Learning Path · Antenna Theory

Antenna Fundamentals

Fourteen articles that take you from what an antenna is to how a complete radio link performs — radiation, field regions, patterns, gain, impedance, S11, efficiency, bandwidth, polarization and aperture — with full derivations, calculator results and ten worked examples in every part.

14 articles 6 hours of reading 140 worked examples Beginner → Advanced
Start with Part 1 → See the full path
The Big Ideas

Four Ideas Behind Every Antenna

The series is built on these four relationships. Each card links to the article that derives it.

1 · Radiation P = 40π²(L/λ)² I²

Accelerating charge radiates; the power grows with the square of the antenna's size in wavelengths.

Parts 1–2 → 2 · Far field r > 2D²/λ

Only beyond the Fraunhofer distance do pattern and gain become independent of distance.

Part 3 → 3 · Gain and aperture G = e·D = 4πA_e/λ²

Concentrating power (directivity), losing some of it (efficiency) and capturing it (aperture) are one idea.

Parts 6, 9, 12 → 4 · Bandwidth FBW ≈ (s − 1)/(Q√s)

Stored energy limits bandwidth — and small antennas must store a lot of it.

Parts 7–10 →
The Learning Path

Fourteen Parts in Five Stages

Each article builds on the one before it. Read them in order, or jump to the stage you need.

Stage 1

How antennas work

What an antenna is, how it radiates and how the space around it divides into field regions.

  1. 01

    Introduction to Antennas

    What an antenna is, why wireless systems need one, how an oscillating current radiates, and how a receiving antenna turns a wave into a voltage.

    TransducerLarmor formulaR_r = 80π²(L/λ)²ReciprocityAntenna families     Beginner ⏱ 26 min Read →
  2. 02

    How Antennas Radiate Electromagnetic Waves

    Accelerating charge, the retarded potential and the exact fields of a dipole; wave impedance, dipole patterns of any length and the effect of ground.

    Vector potentialHertzian dipole1/r, 1/r², 1/r³Wave impedanceImage theory     Intermediate ⏱ 27 min Read →
  3. 03

    Antenna Near Field and Far Field

    The reactive near field, radiating near field and far field, with the boundaries 0.62√(D³/λ) and 2D²/λ derived and applied to measurement and RF exposure.

    FresnelFraunhofer2D²/λNear-field scanningRF exposure     Intermediate ⏱ 25 min Read →
Stage 2

Radiation in space

Where the energy goes: patterns, power density, radiation intensity, directivity and gain.

  1. 04

    Antenna Radiation Patterns

    Dipole and array patterns derived from their currents; E- and H-planes, lobes, HPBW, FNBW, side lobes, beam steering, grating lobes and front-to-back ratio.

    E/H planesHPBWArray factorSide lobesBeam steering     Intermediate ⏱ 28 min Read →
  2. 05

    Radiation Intensity and Power Density

    Poynting's theorem, average power density, steradians, radiation intensity, total radiated power, EIRP and field-strength formulas.

    Poynting vectorU = r²SSteradianEIRPE = √(30P)/r     Intermediate ⏱ 24 min Read →
  3. 06

    Antenna Directivity and Gain

    Directivity derived for dipoles, cosⁿ patterns and arrays; gain, dBi vs dBd, realized gain, beamwidth estimates and gain measurement.

    D = 4π/Ω_AdBi vs dBdRealized gainKraus formulaThree-antenna method     Intermediate ⏱ 29 min Read →
Stage 3

The antenna as a circuit element

Impedance, match, efficiency and bandwidth: how the antenna looks to the radio.

  1. 07

    Antenna Input Impedance and Radiation Resistance

    Radiation and loss resistance derived, reactance and stored energy, the series-RLC model, and dipole and monopole impedance against length.

    73.1 + j42.5 ΩSkin effectSeries RLCResonanceMonopole     Intermediate ⏱ 27 min Read →
  2. 08

    Antenna Reflection Coefficient and Return Loss

    Reflection coefficient derived, return loss, VSWR, mismatch loss, reading S11 plots, cable effects, and L-network and quarter-wave matches.

    ΓReturn lossVSWRS11 plotsMatching     Intermediate ⏱ 25 min Read →
  3. 09

    Antenna Radiation Efficiency and Total Efficiency

    Conductor and dielectric loss derived, radiation, mismatch and total efficiency, small-antenna limits, and how efficiency is measured.

    e₀ = e_r·e_cdSurface resistancetan δSmall antennasWheeler cap     Intermediate ⏱ 25 min Read →
  4. 10

    Antenna Bandwidth and Quality Factor

    Impedance, pattern, gain and polarization bandwidth; bandwidth from Q derived; the Chu and Bode–Fano limits; broadbanding techniques.

    Fractional BWQ factorChu limitBode–FanoAxial-ratio BW     Advanced ⏱ 26 min Read →
Stage 4

Polarization, aperture and links

Receiving, polarization matching and the complete radio link.

  1. 11

    Antenna Polarization

    The polarization ellipse derived; linear, circular and elliptical polarization, axial ratio, polarization loss factor, cross-polarization and reflection.

    RHCP / LHCPAxial ratioPLFCross-polFaraday rotation     Intermediate ⏱ 26 min Read →
  2. 12

    Effective Aperture and Effective Length

    Effective aperture A_e = Gλ²/4π derived from reciprocity, aperture efficiency, effective length and height, received voltage and antenna factor.

    A_e = Gλ²/4πAperture efficiencyEffective lengthEffective heightAntenna factor     Intermediate ⏱ 25 min Read →
  3. 13

    The Friis Transmission Equation

    The Friis transmission equation derived and applied: free-space path loss, dB form, conditions of validity and practical link budgets.

    Friis equationFSPLdB formLink budgetFar-field condition     Intermediate ⏱ 17 min Read →
Stage 5

Antenna types

Applying every fundamental to the antennas engineers build.

  1. 14

    Antenna Types and Classification

    Wire, aperture, printed, reflector, helical, spiral, Yagi-Uda, log-periodic, dielectric resonator, travelling-wave and UWB antennas with design equations.

    Patch designHorn gainReflectorsHelixLog-periodic     Intermediate ⏱ 29 min Read →
Practise as You Read

Real Results From Our Calculators

The patterns, impedances, S11 curves and power budgets in this series come from the free NEXT ANTENNAS calculators, and the worked examples check them against theory.

  • Dipole & Monopole: Method of Moments currents, impedance, S11, 3D patterns and loss budgets, over real ground.
  • Patch: synthesis on any substrate, linear or circular polarization, efficiency and axial ratio.
  • RF Exposure: power density, field regions and compliance distances against FCC and ICNIRP limits.
Open the Dipole Calculator →
3D radiation pattern of a half-wave dipole computed by the Dipole and Monopole Antenna Calculator
What You'll Learn

After the Series You Can…

  • Explain how current on a conductor becomes a radiated wave, and derive the fields and radiation resistance of a dipole.
  • Decide whether a measurement point is in the near or far field, and estimate RF exposure from EIRP.
  • Read and derive radiation patterns, beamwidths, side lobes and directivity, and convert between dBi, dBd and realized gain.
  • Interpret antenna impedance, S11, VSWR, efficiency and bandwidth, and design simple matching networks.
  • Specify polarization and axial ratio, and compute polarization, mismatch and aperture factors in a link budget.
  • Choose and size the right antenna type — dipole, monopole, patch, horn, reflector, helix, Yagi or log-periodic — for a job.
FAQ

Common Questions

What does the Antenna Fundamentals series cover?

It covers how antennas radiate and every standard antenna parameter: near and far field, radiation patterns, radiation intensity, directivity and gain, input impedance, reflection coefficient and return loss, efficiency, bandwidth and Q, polarization, effective aperture and effective length, the Friis transmission equation and the main antenna types.

What do I need to know before starting?

Algebra, trigonometry, complex numbers and basic calculus (simple integrals) are enough. Part 1 needs no prior RF knowledge; the derivations are worked step by step, and every article ends with ten worked examples.

What is the difference between directivity and gain?

Directivity describes how strongly an antenna concentrates its radiated power in one direction compared with an isotropic source. Gain is directivity multiplied by radiation efficiency, so it also accounts for conductor and dielectric losses. Realized gain additionally includes the impedance mismatch.

How is this series different from the Smith Chart and Maxwell series?

The Maxwell series explains the field theory underneath antennas, and the Smith Chart series explains matching. Antenna Fundamentals uses both to describe the antenna itself: how it radiates, how its performance is quantified and how those numbers enter a link budget. The articles link to the other series wherever they overlap.

Can I reproduce the results myself?

Yes. The screenshots come from the free NEXT ANTENNAS Dipole & Monopole, Patch and RF Exposure calculators, and the worked examples quote the same numbers, so you can rerun every case.

In what order should I read the articles?

In order from Part 1 if you are new to antennas. If you already know how antennas radiate, start at Part 4 for patterns and gain; if you mainly need impedance, matching and bandwidth, start at Part 7.

Start the Series

Part 1 explains what an antenna is and how it radiates — no prior RF experience needed.

Read Part 1 All Learning Paths