Understanding Antenna Gain and Radiation Patterns
Understanding Antenna Gain and Radiation Patterns
An antenna does not create extra RF power. It converts power between a guided signal and an electromagnetic wave, and its three-dimensional pattern determines where that exchange is strongest. Gain adds efficiency to that directional picture.
RF.Guru working definition: Common-mode current is the non-cancelling phasor-sum current in a specified set of conductors, evaluated at a defined cross-section and using a declared current-direction convention. In the intended differential transmission-line mode, the outgoing and return currents are equal and opposite, so their phasor sum is zero. When they do not cancel, the remaining current must close through another reference or return path—such as the outside of a coax shield, a mast, equipment chassis, station wiring, nearby structures, earth, the operator, or distributed coupling through the environment.
This broader working definition is especially useful in practical antenna systems. On transmit, non-cancelling current on the outside of the coax can make the feedline and connected structures part of the radiating antenna system unless that path is intentional, clearly defined and properly controlled—for example by providing the required return path and placing a suitable common-mode choke at the correct boundary.
A single gain number is not an antenna verdict. It names a direction, a frequency, a polarization and a power reference. Read it together with the complete pattern, efficiency, impedance match, installation and measurement method.
Begin With the Three-Dimensional Pattern
A radiation pattern describes how an antenna's field or radiated power varies with direction in the far field. Imagine placing the antenna at the centre of a transparent globe and recording a value in every direction. The resulting surface is the three-dimensional pattern.
Published plots are usually two-dimensional cuts through that globe:
- Azimuth cut: a horizontal slice, often used to show coverage around the antenna.
- Elevation cut: a vertical slice, used to show energy toward the horizon and at higher angles.
Those names describe the coordinate cuts, not guaranteed pattern shapes. One azimuth and one elevation plot may miss tilted lobes, asymmetry or features between the chosen planes. A complete characterization states the coordinate system, frequency, polarization component, normalization and installation.
Directivity Describes Concentration
An isotropic radiator is a mathematical reference that distributes radiated power equally in every direction. It is useful for comparison even though it cannot be built as a physical antenna.
Radiation intensity U is power per unit solid angle. If Prad is the total power radiated in all directions, directivity in direction (θ, φ) is:
D(θ, φ) = 4πU(θ, φ) / Prad
Directivity compares the radiation intensity in one direction with the average intensity over the whole sphere. It describes pattern concentration without charging the antenna for conductor or dielectric loss.
A high-directivity antenna has stronger directions and weaker directions. It has not generated power. It has redistributed its radiated power over angle.
Gain Includes Radiation Efficiency
Radiation efficiency ηrad is the fraction of accepted power that becomes radiation rather than heat. With compatible definitions and the same direction and polarization:
G(θ, φ) = ηradD(θ, φ)
Gain is therefore no greater than directivity for a passive antenna. A narrow pattern can have high directivity while loss reduces its gain.
Input mismatch is another boundary. Realized gain also accounts for the fraction of incident power accepted at the antenna port. Datasheets do not always use the words consistently, so check whether the quoted figure is directivity, gain or realized gain and where feed-network loss is included.
dBi and dBd Need a Named Reference
Gain ratios are often expressed in decibels:
GdBi = 10 log10(Glinear)
dBi uses the isotropic radiator as its reference. A positive dBi number does not mean active amplification; it is a directional ratio.
dBd uses the maximum direction of an ideal, lossless half-wave dipole as its reference. That reference has about 2.15 dBi directivity in free space, so for the same gain quantity:
GdBi ≈ GdBd + 2.15 dB
The conversion changes the reference label, not the antenna. A practical dipole installed over ground is not automatically a 2.15 dBi antenna in every direction.
Read the Lobes, Nulls and Beamwidth
- Main lobe: the lobe containing the direction of maximum radiation.
- Sidelobe: another radiation lobe outside the main lobe.
- Back lobe: radiation generally opposite the main direction; the exact comparison requires a stated plane and angle.
- Null: a direction of very low response in the ideal or measured pattern.
- Half-power beamwidth: the angular width of a lobe between points 3 dB below its peak in a power pattern.
- Front-to-back ratio: a stated forward response divided by a stated rear response; the rear angle or region must be defined.
Beamwidth alone does not determine directivity for every pattern. The familiar constant divided by horizontal and vertical beamwidths is only a rough pencil-beam approximation under compatible lobe assumptions. Accurate directivity comes from integrating the complete three-dimensional radiation intensity.
Polarization Is Part of Every Direction
Polarization describes the path traced by the electric-field vector at a point as the wave passes. It can be linear, circular or elliptical, and it can vary with direction in the pattern.
For two ideal linearly polarized antennas in a direct path, rotated by angle ψ relative to each other, the polarization coupling factor is cos²ψ. A 90-degree difference gives an ideal null. Real antennas, reflections and propagation usually prevent an infinite null.
An ideal circularly polarized wave delivers half the available polarization-matched power to an ideal linear antenna, a 3.01 dB difference. This is not a universal field result: axial ratio, handedness, multipath, ionospheric propagation and the antenna's direction-dependent polarization all matter.
Effective Aperture Connects Gain to Reception
Effective aperture is the area that relates incident power density to available received power under stated matching and polarization conditions. For a reciprocal antenna in a chosen direction:
Ae = λ²G / 4π
λ is free-space wavelength in metres and G is the compatible linear gain in that direction. Polarization and impedance mismatch require their own coupling factors when they are not already included.
The equation does not say that the antenna's physical outline equals its effective aperture. It says that receive response and directional gain are linked. Frequency, direction, polarization, efficiency and matching belong to the number.
Near-Field Scanning Can Produce a Far-Field Pattern
The far field is the region where the angular field distribution has reached its asymptotic form and the radiating wave behaves locally like a plane wave. Far-field pattern and gain definitions apply there.
For an electrically large aperture with maximum dimension D, 2D²/λ is a common far-field distance estimate. It is not a universal border for every small antenna, array, measurement accuracy or installation. Wavelength, antenna size, reactive fields and the required phase error all matter.
A probe reading taken close to an antenna is not itself a far-field gain value. But near-field measurement is not meaningless. Calibrated planar, cylindrical or spherical scans record amplitude and phase over a defined surface; a validated mathematical transformation can then recover the far-field pattern and gain. Truncation, probe correction, positioning, reflections and uncertainty remain part of the result.
Friis Is a Free-Space Far-Field Model
For two polarization-matched antennas in each other's far field, with clear free-space propagation and compatible gain references, the Friis equation is:
Pr = PtGtGr(λ / 4πR)²
Pt is transmit power at the transmit-antenna reference plane, Pr is available received power at the receive-antenna reference plane, Gt and Gr are linear gains in the path directions, and R is separation.
Feedline loss, connector loss, polarization mismatch and other known losses may be added separately when they are not inside the gain or power references. Ground reflection, obstacles, multipath, diffraction, atmospheric absorption and ionospheric propagation require a more complete path model.
What a 3 dB Gain Difference Really Means
A 3 dB increase is a power ratio of about two. If two antennas are compared at the same frequency, distance, accepted power, direction and polarization, a 3 dB gain advantage predicts about twice the far-field power density in that direction.
It does not mean twice the total radiated power. It also does not guarantee twice the received voltage, twice the contact range or a stronger signal after feedline loss, mismatch, fading and noise are included.
Installation Changes the Pattern You Actually Use
Free-space and catalogue patterns are starting points. Height, soil, masts, feedlines, radials, roofs, trees, nearby antennas and conductive structures can alter current distribution, loss, polarization, lobe direction and null depth.
On HF, ground and ionospheric propagation make elevation angle important. On VHF and above, local reflections and mounting structures can dominate. A deep modelled null may fill in after installation, while a narrow beam may be entirely manageable with a stable mount and correct pointing.
Read a Datasheet as a Measurement Record
- Frequency: gain and pattern change across a band.
- Quantity: directivity, gain and realized gain are not interchangeable.
- Reference plane: know whether cable, connector or feed-network loss is included.
- Polarization: look for co-polar and cross-polar results, not only a label.
- Pattern: inspect full cuts, scales, normalization, beamwidth, sidelobes and nulls.
- Environment: free space, ground, mast, enclosure and mounting conditions matter.
- Method and uncertainty: simulation and measurement should state calibration, range and uncertainty.
- Impedance and power: SWR, connector and thermal limits answer different questions from gain.
Measure Without Turning One Number Into a Verdict
Begin with a declared frequency, reference plane, polarization and coordinate system. Measure complex input impedance, feed loss and common-mode current separately from the pattern. For a gain comparison, use a calibrated reference antenna or an accepted range method and keep transmit power, geometry, receiver settings and propagation stable.
Outdoor A/B/A comparisons can be valuable, but fading and reflections need repeated samples and uncertainty. A calibrated chamber, far-field range, compact range or near-field scanner gives tighter control. No method rescues an undefined reference plane or an incomplete pattern.
Primary and authoritative references
- IEEE 145-2025 — Standard for Definitions of Terms for Antennas
- IEEE 149-2021 — Recommended Practice for Antenna Measurements
- NIST — Near-Field Measurement Theory
- NIST — Gain and Power Measurements Using Planar Near-Field Techniques
- Recommendation ITU-R BS.705-2 — HF Antenna Characteristics and Diagrams
- NASA — Friis Formula, Gain, Aperture and Polarization Boundary
Mini-FAQ
- Does a higher gain antenna transmit more total power? No. Gain describes radiation in a direction relative to input or accepted power. Directivity redistributes radiation; efficiency determines how much accepted power becomes radiation.
- Is 0 dBd always 2.15 dBi? The reference conversion is about 2.15 dB for the maximum direction of an ideal lossless half-wave dipole. A practical installed dipole can have different gain.
- Does a 3 dB gain increase double my range? No. It predicts about twice the far-field power density in the stated direction under equal conditions; path loss, noise, fading and required SNR set usable range.
- Are near-field antenna measurements useless? No. A single uncalibrated close-field reading is not gain, but calibrated near-field scanning and a validated transformation can recover far-field pattern and gain.
- Can two pattern cuts describe the whole antenna? Not always. They can miss tilted lobes and asymmetry; a complete result uses sufficient angular coverage and states coordinates, polarization and normalization.