3.6 Directional Antennas: Yagis, Gain and Radiation Patterns

3.6 Directional Antennas: Yagis, Gain and Radiation Patterns

ACMA Exam Focus: Syllabus item 6.9 — identify a Yagi antenna from a group of common amateur antennas and explain how it works. Examinable detail covers the driven element, the reflector, the director, forward gain, front-to-back ratio, half-power beamwidth, the E-plane and H-plane radiation patterns, and converting gain between dBd and dBi.

Picking the Yagi Out of the Line-Up

Item 6.9 is most often set as a recognition question: you are shown a list or a set of sketches and asked which one is the Yagi. The proper name is the Yagi-Uda array, after the Japanese engineers Shintaro Uda and Hidetsugu Yagi. Its signature is a row of parallel straight rods of slightly different lengths, mounted at right angles to a single supporting boom, with the feedline connected to only one of them.

The fastest discriminator between a Yagi and a log-periodic is the feed arrangement. A Yagi drives exactly one element and lets every other element work parasitically, picking up energy by induction and re-radiating it, whereas a log-periodic connects all of its elements to a transposed feeder. If the sketch shows one coaxial cable landing on the middle of a single rod, it is a Yagi.

Element Roles

Driven element

The driven element is a resonant half-wave dipole, very often a folded dipole to raise the feedpoint impedance. It is the only element connected to the transmitter, and its length sets the design frequency.

Reflector

The reflector sits behind the driven element, on the opposite side from the direction you want to work, and is cut roughly 5% longer. Being longer than resonance makes it inductive, so the current induced in it lags the driving field. The re-radiated wave then arrives roughly in phase with the forward wave and out of phase with the rearward wave, reinforcing energy in front and cancelling it behind. A Yagi has at most one reflector; a second adds almost nothing.

Directors

Directors sit in front of the driven element, along the direction of fire, and are cut roughly 5% shorter than it. Being short of resonance makes each one capacitive, so its induced current leads, and the re-radiated field pulls the wavefront forward. Directors are added in numbers — three, five, ten or more on a long VHF boom — and each successive one adds a little more gain.

Memory hook: long at the back, short at the front, and the beam fires towards the short elements. Element lengths taper down slightly along the boom from reflector to last director.

Forward Gain, Front-to-Back Ratio and Beamwidth

Forward gain is the increase in signal in the favoured direction compared with a reference antenna. Gain is not created out of nothing — the Yagi takes energy that a dipole would have wasted sideways and off the back and concentrates it into a narrower cone.

Front-to-back (F/B) ratio is the number of decibels by which the forward lobe exceeds the lobe radiated directly to the rear, 180 degrees away. It is a receiving virtue as much as a transmitting one: 20 dB of F/B knocks an interfering VK station behind you down to one hundredth of its power.

Half-power beamwidth (also called the 3 dB beamwidth) is the angular width of the main lobe, measured between the two points either side of the peak where radiated power has fallen to half. More directors means more gain and a narrower beam, which is why long-boom 2 m arrays need an accurate rotator.

Note the law of diminishing returns built into that table: gain rises roughly 3 dB every time the boom length is doubled, not every time an element is added.

E-Plane and H-Plane Patterns

A radiation pattern is a polar plot of relative field strength against direction. Because the pattern is three-dimensional, it is published as two slices:

• The E-plane pattern is the slice taken in the plane containing the electric field, that is, the plane parallel to the elements. For a Yagi mounted with its elements horizontal, the E-plane slice is the horizontal or azimuth pattern.
• The H-plane pattern is the slice taken in the plane containing the magnetic field, at right angles to the elements. For that same horizontally mounted Yagi, the H-plane slice is the vertical or elevation pattern.

Turn the same antenna on its side for vertical polarisation and the two swap roles. On a typical Yagi the E-plane main lobe is slightly narrower than the H-plane lobe, and both slices show small side lobes as well as the back lobe.

Gain References: dBd and dBi

Gain figures are meaningless until you know what they are measured against.

• dBd — decibels relative to a half-wave dipole in free space. A dipole is 0 dBd by definition.
• dBi — decibels relative to an isotropic radiator, a theoretical point source that radiates equally in every direction. An isotropic radiator is 0 dBi by definition.

A half-wave dipole itself has a directive gain of 2.15 dBi, so the two scales are related by a fixed offset:

Gain (dBi) = Gain (dBd) + 2.15 and Gain (dBd) = Gain (dBi) - 2.15

Worked conversion. A 70 cm Yagi is advertised at 15.15 dBi. In dipole terms that is 15.15 - 2.15 = 13.0 dBd. A rival brand quoting 13 dBd for a similar boom length is offering identical performance, dressed differently for the catalogue.

Exam trap: advertising almost always quotes the larger dBi number. If a question gives you dBi and asks for gain over a dipole, subtract 2.15 dB first.