ABC Tools

Antenna Radiation Patterns, Explained

After reading this you will know why a plain dipole radiates in a donut, why each Yagi element narrows the beam, and how to read gain, beamwidth and front-to-back ratio off a polar plot.

What a radiation pattern actually shows

An antenna does not create radio power. It takes the power your transmitter feeds it and points it in some directions more than others. A radiation pattern is a map of that pointing: how strong the field is at every angle around the antenna, drawn on a polar plot.

Start with the honest baseline. An isotropic radiator spreads power equally in all directions, so its pattern is a perfect circle. It cannot be built, but it fixes the meaning of gain. When a datasheet says an antenna has 2.15 dBi of gain, it means the antenna is 2.15 dB stronger in its best direction than an isotropic radiator fed the same power. The energy comes from the directions where the antenna is weaker.

Here is the hook. Take a half-wave dipole, gain 2.15 dBi, and add director and reflector elements to make a 7-element Yagi. The gain climbs to about 11 dBi and the main beam narrows from roughly 78 degrees wide to about 40 degrees. No extra power went in. The pattern just got squeezed into a tighter cone.

When this tool helps, and when it misleads

Use the explorer to build intuition: how spacing and phase steer a two-element pair, how many elements you need for a given beamwidth, why mounting height reshapes the elevation pattern. The trends it shows are correct and match textbook figures.

Do not use these plots to predict exact sidelobe levels or to tune a real Yagi. The element currents in a real antenna are set by mutual coupling and are not the uniform, equal-amplitude currents the array-factor approximation assumes. Beamwidth and peak gain trends are trustworthy; the fine structure of the minor lobes is not.

For anything involving real materials, feed impedance, or matching, you need a proper electromagnetic simulation (NEC-style) and a network analyzer. This tool is for understanding shape, not for final design.

The dipole pattern from first principles

A half-wave dipole is a wire one half wavelength long, fed in the middle. The current is largest at the center and falls to zero at the ends. Summing the field from every current element along the wire gives a closed form for the field strength as a function of the angle \theta measured from the wire axis.

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

Here \theta = 90^\circ is broadside, straight out from the middle of the wire, and \theta = 0^\circ is off the end. Plug in broadside: \cos\theta = 0, so the numerator is \cos(0) = 1 and the denominator is \sin(90^\circ) = 1. The field is 1, the maximum. Off the end, \theta = 0, the numerator is \cos(90^\circ) = 0: no radiation along the wire. Rotate that curve around the wire axis and you get the classic donut.

To find the field at any angle relative to the peak, you take the ratio and convert to dB with 20\log_{10}, because field is a voltage-like quantity, not power.

Why more elements mean a narrower beam

Line up several radiators along a line and drive them so their signals add up in one direction. In that direction the fields march in step and stack; in most other directions they arrive with different phases and partly cancel. The combined effect is the array factor. For N equally spaced elements with spacing d and a progressive phase shift \beta between them:

AF(\theta) = \frac{\sin\left(\frac{N\psi}{2}\right)}{N\sin\left(\frac{\psi}{2}\right)}, \quad \psi = \frac{2\pi d}{\lambda}\cos\theta + \beta

\psi is the total phase difference between adjacent elements seen at angle \theta: the first term is the path-length difference in radians, the second is the feed phase you impose. The whole array factor is normalized so its peak is 1. The key fact: the main lobe of that ratio gets narrower as N grows, roughly as 1/N. Double the number of in-phase elements and you roughly halve the beamwidth, which adds about 3 dB of gain.

A Yagi is a driven dipole plus parasitic elements. A slightly longer reflector behind and shorter directors in front act like an endfire array that fires off the end. The explorer approximates the 3-, 5- and 7-element cases with a typical endfire array factor, which is why the gains land near 7.5, 9.5 and 11 dBi.

Gain rises and the beam narrows together as you add elements. The two move in lock step because the power is fixed.

A worked example with the demo data

Load the demo (the field defaults) and select the half-wave dipole, azimuth cut. Reproduce the readouts by hand.

Field at 60 degrees off broadside for a dipole

  1. Broadside is \theta = 90^\circ. Sixty degrees off broadside means \theta = 30^\circ. Then \cos 30^\circ = 0.8660 and \sin 30^\circ = 0.5.
  2. Numerator: \cos\left(\frac{\pi}{2}\times 0.8660\right) = \cos(1.360\ \text{rad}) = 0.2079.
  3. Field ratio: 0.2079 / 0.5 = 0.4158.
  4. In dB: 20\log_{10}(0.4158) = -7.62 dB below the peak.

Now find the half-power beamwidth. The -3 dB points are where the field ratio equals 1/\sqrt{2} = 0.7071. Solving \cos\left(\frac{\pi}{2}\cos\theta\right)/\sin\theta = 0.7071 gives \theta \approx 51^\circ and 129^\circ. The gap is 129 - 51 = 78^\circ, the textbook dipole beamwidth. The peak gain readout is 2.15 dBi.

The dB drop of the dipole field as you move off broadside. The curve passes through -3 dB (field 0.707) near 39 degrees off broadside on each side, giving the 78 degree beamwidth.

Steering and shaping with a phased pair

The two-element phased pair is the clearest lab for the array factor. With spacing d and feed phase \beta, two special cases are worth memorizing. Set d = \lambda/2 and \beta = 0: the elements are in phase, the pattern peaks broadside (perpendicular to the line joining them) and nulls off the ends. Set d = \lambda/4 and \beta = -90^\circ: the path delay off one end exactly cancels the feed phase, so the fields add there and cancel off the other end. That is an endfire array with a cardioid pattern, the basis of a driven antenna plus one reflector.

With two elements a half wavelength apart and fed in phase, the pattern is a broadside figure-eight peaking at 90 and 270 degrees. Shift the feed phase to -90 degrees and shorten the spacing to a quarter wavelength, and the pattern collapses to a single forward lobe (a cardioid) pointing one way, with a deep null the other way.

Reading the numbers off the plot

Three readouts summarize any pattern.

Maximum gain (dBi)
The peak field direction expressed relative to isotropic. Higher means more focus, always at the cost of a narrower beam.
-3 dB beamwidth
The angular width between the two directions where power falls to half its peak (field to 0.707). This is the practical measure of how tightly you must aim.
Front-to-back ratio
The peak gain minus the gain 180 degrees behind it, in dB. A 7-element Yagi might show 20 dB or more, meaning it rejects a signal from behind at one hundredth the power of one from the front.

The plot is normalized to the pattern maximum, with rings at -10, -20 and -30 dB. So the outer edge is always the peak direction regardless of absolute gain. Read the beamwidth where the main lobe crosses inside the outermost ring from the peak.

Ground reflection and elevation lobes

Raise a horizontal antenna above ground and a second wave appears: the one reflected off the earth. Over a perfect conductor the reflection is a mirror image. At elevation angle \alpha, the reflected ray travels an extra path of 2h\sin\alpha, where h is the height. Direct and reflected waves add in phase where that extra path is an odd number of half wavelengths, and cancel where it is a whole number.

2h\sin\alpha = \left(m - \tfrac{1}{2}\right)\lambda, \quad m = 1, 2, 3, \dots

The lowest lobe (the one you want for long-distance HF) sits at \sin\alpha = \lambda/(4h). At h = \lambda/2 that is \sin\alpha = 0.5, so \alpha = 30^\circ. Double the height to h = \lambda and the first lobe drops to \sin\alpha = 0.25, about 14.5^\circ. Lower launch angles reach farther. That is the whole reason HF antennas are mounted as high as the budget allows.

Common mistakes

Gain in dBi and dBd differ by exactly 2.15 dB. A "6 dBd" antenna is 8.15 dBi. Mixing the two references is the most common error in reading antenna specs. When in doubt, assume the higher-sounding number is dBi.

Do not read high gain as more coverage. A 7-element Yagi at 11 dBi lights up a 40 degree cone brilliantly and leaves everything else dark. If you need to hear stations in all directions, that gain works against you. Pick the pattern for the job, not the largest number.

Do not confuse the azimuth cut with the full three-dimensional pattern. A dipole looks like a figure-eight in one plane and a circle in the perpendicular plane. The tool lets you switch cuts for exactly this reason. And remember the ground: an elevation pattern measured in free space tells you nothing about the lobes real terrain will carve.

Related tools

If you are building the receiver or transmitter behind the antenna, these help with the circuit side. Size feed and bias resistors with the Ohm's Law Calculator and the Resistor Color Code Calculator. Design the IF or audio filtering with the Active Filter Designer. Pick exact resistor values with the E-Series Resistor Solver. For indoor coverage rather than directional gain, the Wi-Fi Coverage Planner maps signal across a floor plan.

Frequently asked questions

Why is a dipole 2.15 dBi and not 0 dBi?

Because the dipole already focuses power. Its donut shape is stronger broadside than isotropic by a factor of 1.64, and 10\log_{10}(1.64) = 2.15 dB. The gain of 0 dBi belongs only to the imaginary isotropic radiator.

Does more gain mean a stronger transmitter?

No. Gain adds no power. A 3 dB gain increase doubles the field power in the peak direction by taking it from directions where the pattern shrank. Your transmitter output is unchanged.

How much does each Yagi element buy me?

Roughly 2 dB per element for the first few, tapering off. The step from 3 to 5 elements adds about 2 dB (7.5 to 9.5 dBi); the step from 5 to 7 adds about 1.5 dB. Each added element also narrows the beam and demands more careful aiming.

Why do the elevation lobes move when I change height?

The reflected ray's extra path length is 2h\sin\alpha. Change h and the angle where direct and reflected waves add in phase changes with it. Higher antennas push the first lobe to a lower elevation, which reaches farther.

Are the sidelobes in the plot accurate?

Treat them as illustrative. The array-factor approximation assumes uniform element currents, but real parasitic elements carry different currents set by coupling. The main-lobe beamwidth and peak gain track reality well; the exact depth and position of minor lobes do not.

Try it yourself in the tool

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