Yagi-Uda Antenna

How a Yagi-Uda antenna works

Start with a half-wave dipole. Feed it RF and it radiates like a doughnut — equally strong in every horizontal direction, broadside to the rod. That's useless if your transmitter is in one specific direction: half the power sprays where nobody is listening. The Yagi-Uda design fixes that by surrounding the fed rod with rods that aren't fed at all.

Only one element — the driven element — connects to the coax. The others are parasitic: bare metal rods, electrically isolated, doing nothing on their own. But when the driven element radiates, its field washes over each parasitic rod and induces a current in it. That induced current re-radiates a second wave. The clever part is the timing of that second wave, which is set by each rod's length relative to resonance.

• A rod cut longer than resonant length looks inductive. Its re-radiated wave lags in phase. Placed behind the driven element, it makes the rearward waves cancel and the forward waves reinforce. This is the reflector — one is plenty; adding a second barely helps.
• A rod cut shorter than resonant looks capacitive. Its re-radiated wave leads in phase. Placed in front, it pulls the beam toward itself. These are the directors — and unlike reflectors, you can chain many of them, each re-launching the wave a little farther forward.

So the whole array is a phased array that nobody had to phase by hand. The geometry — lengths and spacings measured in wavelengths — does the phasing automatically through mutual coupling. Energy that would have gone backward and sideways gets folded into a single forward lobe.

The phasing: why length sets the phase

A parasitic element is a series resonant circuit. Its reactance, and therefore the phase of the current the incident field drives into it, depends on how far its length sits from the resonant half-wavelength:

Element reactance (thin rod, near resonance):
  X ≈ −Z0 · cot(π · L / λ_res)          (qualitative — exact form needs the
                                          rod's characteristic impedance Z0)

  L > λ/2  →  X > 0  (inductive)  →  re-radiated current LAGS  →  reflector
  L = λ/2  →  X = 0  (resonant)   →  current in phase with EMF
  L < λ/2  →  X < 0  (capacitive) →  re-radiated current LEADS  →  director

The total field in a direction is the phasor sum over all elements:
  E(θ) = Σ Iₙ · e^( j·k·dₙ·cosθ )      k = 2π/λ,  dₙ = element position
where each Iₙ carries the amplitude AND phase coupled into element n.

The forward direction adds constructively when the spatial delay (the k·d·cosθ term) just compensates the phase shift baked into each element's current. That's the design game: pick lengths to set the element phases, pick spacings to set the spatial delays, and make the two line up forward and oppose rearward. Spacings of 0.15 to 0.25 λ between elements are typical — close enough for strong coupling, far enough that the directors keep relaunching the wave.

Gain follows boom length, not element count, and it follows it slowly. A useful rule of thumb: doubling the boom length adds about 3 dB. That logarithmic payoff is why Yagis stop growing around 15 to 20 elements — past that, two stacked shorter Yagis (which add ~3 dB by combining apertures) beat one monster boom.

Worked example: a 3-element 2-meter Yagi

Design a 3-element Yagi for the 2-meter ham band at 146 MHz. First the wavelength:

λ = c / f = 3.00×10⁸ m/s / 146×10⁶ Hz = 2.055 m  (≈ 2055 mm)

Free-space half-wave:  λ/2 = 1027 mm
A real dipole resonates a bit short of λ/2 because of the
end-effect (velocity factor ~0.95 for typical rod diameter):
  Driven element ≈ 0.95 × 1027 = 975 mm

Parasitic lengths, relative to the driven element:
  Reflector  ≈ +5%   →  ~1025 mm   (longer  → inductive → behind)
  Director   ≈ −5%   →  ~925 mm    (shorter → capacitive → in front)

Spacings (along the boom):
  Reflector → driven : 0.20 λ = 411 mm
  Driven → director  : 0.15 λ = 308 mm
  Total boom length  : ~720 mm

Run those numbers through a method-of-moments solver (NEC) and you get roughly 7.5 dBi forward gain, a front-to-back ratio near 12 to 15 dB, and a feedpoint impedance around 25 Ω. Compare that 25 Ω to the 50 Ω of your coax: you'd see an SWR near 2:1, so this driven element gets a folded-dipole or gamma match to bring it to 50 Ω. The forward gain over the plain dipole you started with — 5 to 6 dB — is the same as quadrupling your transmitter power, for the cost of two bent aluminum rods.

Want more? Add three more directors at 0.20 λ spacing, retune lengths with a slight taper (front directors get progressively shorter), and a 6-element version reaches ~10.5 dBi on a ~1.6 m boom — at the cost of narrower bandwidth and tighter tuning tolerance.

Element-count vs performance

Elements	Boom (λ)	Gain (dBi)	Front-to-back	Beamwidth (E-plane)	Typical use
2 (driven + reflector)	~0.15	~5.5	~10 dB	~65°	Compact, low-gain rejection
3 (refl + driven + 1 dir)	~0.35	7 to 8	12 to 15 dB	~55°	Portable VHF/UHF, basic TV
5	~0.8	~10	~18 dB	~45°	Rooftop TV, fixed Wi-Fi link
10	~2.0	12 to 13	~20 dB	~32°	DX ham, weak-signal work
15	~3.5	~14.5	20 to 25 dB	~26°	EME, long-haul UHF
20+	~5+	~16	~22 dB	~22°	Diminishing returns — stack instead

Yagi vs other directional antennas

	Yagi-Uda	Log-periodic (LPDA)	Dipole	Parabolic dish	Patch (microstrip)
Bandwidth	Narrow (~2 to 5%)	Very wide (up to 10:1)	Moderate	Wide (feed-limited)	Narrow (~5%)
Gain	7 to 16 dBi	6 to 11 dBi	~2.15 dBi	20 to 50+ dBi	6 to 9 dBi
Elements fed	One (rest parasitic)	All (alternating phase)	One	One (at focus)	One
Directivity	Beam, front lobe	Beam, front lobe	Omni broadside	Pencil beam	Hemispherical lobe
Build cost	Low (bent rods)	Moderate	Lowest	High (precise surface)	Low (PCB etch)
Wind load / size	Long thin boom	Long thin boom	Tiny	Large, high drag	Flat, tiny
Best at	VHF/UHF point-to-point	Wideband TV/EMC scan	General-purpose	SHF, satellite, radar	GPS, phones, RFID arrays

Where Yagis are used

• Rooftop TV antennas. The iconic many-fingered roof antenna is a Yagi (often a combination Yagi/log-periodic). VHF channels need long elements; UHF needs short ones, so consumer "combo" antennas gang two sections on one boom.
• Amateur (ham) radio. The backbone of weak-signal VHF/UHF work and HF DXing. A rotatable multi-element Yagi on a tower lets an operator point gain at a distant station and null out interference from elsewhere.
• Point-to-point Wi-Fi and rural links. A 2.4 GHz Yagi turns a few-hundred-meter omni link into a multi-kilometer aimed link. At 2.4 GHz, λ is only 125 mm, so a 15-element Yagi is hand-sized.
• Radar and direction finding. Yagis were widely used on WWII airborne radar (British AI/ASV intercept sets and their German counterparts). Their sharp forward lobe and deep rear null make them good for bearing measurement.
• RFID and telemetry. UHF RFID readers and wildlife/asset telemetry receivers use small Yagis to read tags or locate transmitters by sweeping the beam for a peak.
• EME ("moonbounce"). Stacked arrays of long Yagis chase the ~250 dB path loss of bouncing a signal off the Moon — among the highest-gain Yagi installations built.

Design tradeoffs and pitfalls

• Narrowband by nature. A high-gain Yagi is tuned for one frequency. Push more than ~5% off design and gain, F/B, and SWR all sag together. If you need an octave of bandwidth with a beam, you want a log-periodic, not a Yagi.
• Impedance crashes with coupling. Each parasitic element you add pulls the driven feedpoint impedance down — from ~73 Ω for a bare dipole toward 20 to 30 Ω on a tight design. Without a matching network (folded dipole, gamma, hairpin) you get a high SWR and reflected power. This is why almost every commercial Yagi uses a folded-dipole driven element.
• Forgetting the balun. A dipole is balanced; coax is unbalanced. Feed a Yagi with bare coax and current flows on the outside of the shield, which then radiates and warps the pattern, fills in the rear null, and makes the SWR move when you touch the feedline. A current balun (choke) at the feedpoint fixes it.
• Boom and mast detuning. A metal boom passing through the element centers shifts resonance unless the elements are insulated or the lengths are corrected for boom diameter. NEC models that ignore the boom over-predict gain.
• Element sag and ice. Long aluminum directors droop, and ice loading both detunes them and adds wind/weight load that can fold a boom. Real designs taper element tubing and rate the boom for ice plus wind.
• Over-stacking elements. Adding directors past ~15 to 20 buys almost nothing because of the 3-dB-per-boom-doubling law, and it narrows bandwidth and tightens tolerances. The fix is to stack two Yagis (vertically or horizontally) and combine, gaining ~3 dB by doubling aperture instead of fighting diminishing returns.

Common misconceptions

• "The parasitic elements are connected somehow." They aren't. Only the driven element touches the feed. Everything else works purely by induced current and re-radiation. You can confirm it visually: on a real Yagi the directors and reflector are clamped to the boom with nothing wired to them.
• "The reflector reflects like a mirror." It doesn't bounce the wave back like glass. It re-radiates a phase-shifted copy that cancels the rearward field. The "reflector" name is a useful analogy, not the mechanism.
• "More elements always means more gain worth having." Gain scales with boom length logarithmically, so each added director helps less than the last. Past the knee of the curve you pay in bandwidth and tolerance for fractions of a dB.
• "A Yagi and a log-periodic are the same thing." They look alike, but an LPDA feeds every element with alternating phase and stays usable over a 10:1 band, while a Yagi feeds one element and is narrowband. The rooftop "Yagi" you see is often actually an LPDA, or a hybrid.