Yagi-Uda Antenna Simulator: Array Gain, Directivity & Beam Pattern

simulator intermediate ~11 min
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G = 13.1 dBi — 6-element Yagi-Uda

A 6-element Yagi-Uda (reflector + driven + 4 directors) at 150 MHz with 0.3λ spacing achieves 13.1 dBi gain with a half-power beamwidth of about 36° — a classic VHF TV antenna design.

Formula

G ≈ 10 × log₁₀(4.25 × N × d/λ) dBi (Kraus approximation)
HPBW ≈ 52° / √(G_linear)
L_reflector ≈ 0.5λ, L_director ≈ 0.45λ

The Rooftop Classic

The Yagi-Uda antenna is perhaps the most recognizable antenna in the world — the array of parallel elements on a boom that once crowned nearly every rooftop for television reception. Invented by Shintaro Uda and popularized by Hidetsugu Yagi in the late 1920s, this elegant design achieves high directional gain using mostly parasitic (unfed) elements that shape the radiation pattern through electromagnetic coupling.

How Parasitic Elements Work

Only the driven element connects to the transmission line. The reflector, slightly longer than a half wavelength, has an inductive impedance that causes it to re-radiate with a phase that constructively adds in the forward direction and destructively cancels backward. Directors, slightly shorter, have capacitive impedance and re-radiate to guide energy forward. The cumulative effect of multiple directors creates a progressively narrower beam with higher gain.

Gain vs. Size Tradeoff

Each additional director extends the boom and adds gain, but with diminishing returns. The first director adds about 3 dB (doubling the gain), while the tenth might add only 0.3 dB. The spacing between elements (typically 0.15-0.35λ) affects both gain and bandwidth. Closer spacing increases gain per unit length but narrows bandwidth and makes the design more sensitive to manufacturing tolerances. This simulation lets you find the sweet spot for your application.

Modern Applications

While rooftop TV antennas are fading, Yagi-Uda designs remain vital for amateur radio, point-to-point communication links, radio astronomy, wildlife tracking, and EMC testing. Printed Yagi designs on PCB substrates serve millimeter-wave 5G applications. The principles of parasitic coupling discovered by Uda and Yagi underpin all modern phased array and MIMO antenna systems.

FAQ

How does a Yagi-Uda antenna work?

A Yagi-Uda antenna uses parasitic elements (not directly fed) to create a directional beam. A reflector element (slightly longer than λ/2) behind the driven element reflects energy forward. Director elements (slightly shorter) in front guide the wave into a narrow beam. Only the driven element is connected to the transmission line; parasitic elements couple through mutual impedance.

How many elements should a Yagi have?

For amateur radio and TV reception, 3-7 elements provide a good balance of gain (8-14 dBi), beamwidth, and physical size. Professional VHF/UHF links may use 10-15 element Yagis for 14-17 dBi gain. Beyond ~15 elements, gain increases slowly and alternative designs (helical, parabolic) become more efficient.

What determines Yagi-Uda bandwidth?

Bandwidth is primarily limited by the driven element matching and is typically 2-5% for optimized designs. Wider element diameter (lower length-to-diameter ratio) increases bandwidth. Log-periodic Yagi hybrids achieve much wider bandwidth at the cost of reduced gain.

Why are Yagi antennas used for TV reception?

Yagi-Uda antennas offer high gain (10-15 dBi) in a simple, inexpensive, mechanically robust structure. Their directional pattern rejects interference from other directions, and they can be optimized for VHF or UHF TV bands. The characteristic shape — a boom with parallel elements of varying length — is recognizable on rooftops worldwide.

Sources

Embed

<iframe src="https://homo-deus.com/lab/antenna-design/yagi-uda/embed" width="100%" height="400" frameborder="0"></iframe>
View source on GitHub