The Yagi-Uda antenna (commonly called a Yagi) is a directional antenna composed of a fed dipole, a reflector behind it, and one or more directors in front. Only the driven element is connected to the feed line — the others are parasitic and couple electromagnetically. It is the dominant design for VHF/UHF terrestrial and amateur radio links and satellite ground stations.

Element Roles

• Reflector: one element, positioned ~0.25λ behind the driven element. Slightly longer than λ/2 (≈ 0.505λ). Reflects energy forward, increasing F/B ratio.
• Driven element: the only fed element, ≈ 0.47–0.48λ long. Input impedance in the array is ~25 Ω (straight dipole) or ~200 Ω (folded dipole).
• Directors: shorter than λ/2 (≈ 0.43–0.46λ), spaced 0.25–0.42λ forward of the driven element. Each director adds roughly 1–2 dBd of gain. Gain saturates above ~9–10 elements.

Gain vs Element Count (NBS/Viezbicke Tables)

The NBS Technical Note 688 (Viezbicke, 1976) tabulates optimised element lengths and spacings for maximum gain, derived from moment-method (NEC) calculations for element diameter d/λ = 0.0085.

Elements	Gain (dBd)	Gain (dBi)	F/B (approx)
2	3.8	5.9	5 dB
3	5.9	8.1	10 dB
5	8.2	10.4	14 dB
7	10.0	12.2	18 dB
9	11.3	13.5	22 dB

dBi = dBd + 2.15. Adding directors past ~9–10 elements yields diminishing returns (<0.5 dB per element) for significant boom length cost.

Feed Impedance and Matching

The driven-element feed impedance is reduced from the free-space dipole value (~73 Ω) by the mutual coupling of adjacent elements:

• Straight dipole: Zin ≈ 25–35 Ω in the array — requires a matching network (gamma match, beta match) to 50 Ω coax
• Folded dipole: naturally 4× higher impedance → Zin ≈ 200–300 Ω → use a 4:1 balun or λ/4 transformer to 50 Ω

Bandwidth and Scaling

A well-optimised Yagi has an operating bandwidth of approximately 2–5% of the centre frequency — narrow enough that element length must be scaled accurately. To move a design to a new frequency, scale all dimensions by the ratio of the original wavelength to the new wavelength (f_old/f_new).