Yagi-Uda Antenna

The Yagi-Uda antenna is a highly directional antenna consisting of multiple parallel dipole elements arranged along a boom, where only one element is connected to the transmission line. Its simplicity of construction combined with significant directivity gain has made it the dominant antenna for terrestrial television reception, amateur radio, and point-to-point VHF/UHF communication. Understanding its operating principle is essential for both practical antenna design and GATE electromagnetics problems.

Core Concept Explanation

The Yagi-Uda antenna exploits the principle of parasitic coupling. Only the driven element is directly connected to the transmission line and excited by the transmitter or receiver. All other elements — the reflector and directors — are parasitic. They are not connected to any feed; they are excited purely by the electromagnetic field radiated from the driven element, through mutual coupling. The currents induced in these parasitic elements then re-radiate, and their phase relationships with the driven element determine the direction of constructive interference.

The reflector is placed behind the driven element and is made slightly longer than λ/2 (typically about 5 percent longer). A longer element is inductive at the operating frequency, which causes the current in the reflector to lag in phase. This phase lag, combined with the spatial delay due to its position, causes the reflector's re-radiated field to add constructively in front of the array (toward the directors) and cancel behind it. The net effect is that the reflector pushes energy forward.

The directors are placed in front of the driven element and are made slightly shorter than λ/2 (typically 5 to 10 percent shorter). A shorter element is capacitive at the operating frequency, so the current in the director leads in phase. This phase lead compensates the spatial phase advance of the director's position, causing the director's field to add constructively in the forward direction. Each successive director pulls the beam progressively forward, reducing beamwidth and increasing directivity.

The more directors added to the array, the higher the directivity and the narrower the main beam, but with diminishing returns. A typical TV rooftop Yagi with 6 to 10 elements achieves a directivity of 10 to 14 dBi. Very long Yagis with 20 or more elements can exceed 17 dBi.

Mathematical Expression

There is no simple closed-form formula for Yagi-Uda performance because the element interactions involve mutual impedance between multiple dipoles. The design is performed numerically using method-of-moments solvers. However, a few key dimensional guidelines are standard. The driven element length is 0.47λ to 0.5λ. The reflector is 0.5λ to 0.525λ (about 5 percent over half-wave). Each director is 0.4λ to 0.45λ. Spacing between elements is typically 0.15λ to 0.25λ.

An approximate empirical relationship for directivity of a Yagi-Uda array is D ≈ 10 log(N) dB for N total elements (including reflector and directors). This is a rough estimate; actual directivity depends on precise element lengths and spacings and is best determined from antenna design tables or simulation. The input impedance of the driven element is reduced by mutual coupling to typically 25 to 50 ohms depending on the number of parasitic elements, often requiring a balun and matching network to interface with 50-ohm or 75-ohm coaxial cable.

Practical Understanding

The Yagi-Uda antenna is highly sensitive to element dimensions and placement. Even small changes in element length can significantly alter the radiation pattern, input impedance, and front-to-back ratio. The front-to-back ratio (F/B) is a key performance metric that describes how much more strongly the antenna radiates in the forward direction compared to the backward direction. A good Yagi design achieves an F/B ratio of 20 dB or more.

The bandwidth of a Yagi is relatively narrow — typically 2 to 5 percent of the center frequency before performance degrades significantly. This is because the parasitic element dimensions are optimized at one frequency, and the phase relationships change rapidly with frequency. Wideband designs use folded dipoles or non-uniform element spacings to extend bandwidth.

Yagi antennas are used in terrestrial TV reception, amateur radio (especially VHF and UHF bands), weather satellite reception, and point-to-point data links. Their ability to achieve 10 to 17 dBi gain from a physically simple wire structure makes them extremely cost-effective for fixed directional applications.

Given:
Operating frequency f = 300 MHz
Speed of light c = 3 × 10^8 m/s
Design a basic 3-element Yagi (reflector + driven + 1 director)

Why this formula applies:
Element lengths are defined as fractions of operating wavelength λ.

Formula:
λ = c / f
L_reflector = 0.52 × λ
L_driven    = 0.48 × λ
L_director  = 0.44 × λ
Spacing between elements ≈ 0.2 × λ

Substitution:
λ = (3 × 10^8) / (300 × 10^6) = 1.0 m

Calculation:
L_reflector = 0.52 m = 52 cm
L_driven    = 0.48 m = 48 cm
L_director  = 0.44 m = 44 cm
Spacing     = 0.20 m = 20 cm

Final Answer:
Reflector: 52 cm, Driven: 48 cm, Director: 44 cm
Element spacing: 20 cm
Estimated directivity ≈ 7–8 dBi (3-element Yagi)

Exam Tip: In GATE, remember — reflector is longer than λ/2 (inductive, lags in phase), directors are shorter than λ/2 (capacitive, lead in phase). Only one element is driven. Front-to-back ratio and directivity both increase with more directors.

• Only the driven element is connected to the feed line. Reflector and directors operate by electromagnetic induction from the driven element.
• Reflector is longer than λ/2 → inductive → current lags → field cancels backward and adds forward.
• Directors are shorter than λ/2 → capacitive → current leads → field adds constructively in forward direction.
• Adding more directors increases directivity and narrows beamwidth, with diminishing returns beyond about 10 directors.
• Input impedance is reduced from 73 ohms (isolated dipole) to typically 25 to 50 ohms due to mutual coupling.
• Key performance metrics: directivity (dBi), front-to-back ratio (dB), and HPBW (degrees).

Quick Revision

• Yagi-Uda: one driven element, one reflector (longer, behind), one or more directors (shorter, in front).
• All parasitic elements are excited by mutual coupling; only the driven element is fed.
• Reflector length ≈ 0.52λ. Driven element ≈ 0.48λ. Director ≈ 0.44λ. Spacing ≈ 0.2λ.
• Beam direction: away from reflector, toward directors.
• Directivity increases with number of directors. Typical 6-element: 10–12 dBi.
• Exam trap: More directors always increase directivity but also narrow bandwidth and complicate impedance matching.
• Applications: TV reception, amateur radio VHF/UHF, point-to-point links.