Yagi-Uda construction, working and design

A Yagi-Uda antenna is an end-fire array of one driven half-wave (usually folded) dipole and several parasitic elements — one reflector behind and one or more directors in front — mounted parallel to each other on a common boom. It gives a moderate-gain unidirectional beam with a single feed point.

Construction

   R      DE      D1     D2     D3
   |      |       |      |      |
   |      |       |      |      |
 --+-----(o)------+------+------+--> boom & beam
   |    feed      |      |      |
   |      |       |      |      |
 ≈0.5λ  0.46-   0.45λ  shorter ->
       0.48λ
   <SR=0.15-0.25λ><SD=0.1-0.35λ>

• Driven element: resonant λ/2 dipole or folded dipole connected to the feeder.
• Reflector: one element ≈ 5 % longer than the driven element (≈ 0.5λ), spaced 0.15–0.25λ behind.
• Directors: elements ≈ 5 % shorter than the preceding one (≈ 0.45λ downwards), spaced 0.1–0.35λ.
• Elements are metal tubes/rods fixed at their centres (voltage zero) to a metal boom, so no insulation is needed.

Working principle

1. RF current in the driven element radiates; this field induces currents in the parasitic elements by mutual coupling, and they re-radiate.
2. The reflector, longer than resonant length, has an inductive impedance; its current lags. With spacing ≈ 0.15–0.25λ, its re-radiated field cancels the driven element's field in the backward direction and adds in the forward direction.
3. Each director, shorter than resonant length, is capacitive; its current leads. The directors form a chain with progressive phase, so the wave is guided forward like an end-fire array.
4. Result: a unidirectional beam along the boom towards the directors. More directors → higher gain and narrower beam (with diminishing returns).
5. Parasitic coupling lowers the driven element's impedance (to ≈ 20–30 Ω for a simple dipole), so a folded dipole (≈ 4 × 73 ≈ 292 Ω alone) is used to give a convenient ≈ 50–75 Ω or 300 Ω input.

 Radiation pattern (top view)
            .--.
  back    .'    '.
   ==o===(R DE D D)======>  main lobe
          '.    .'
            '--'
  small back lobe; front-to-back ≈ 10-20 dB

Design procedure

Design rules (standard empirical rules):

1. λc = c / fc   (fc = centre frequency of band)
2. Driven element  L_DE = 0.46λ to 0.48λ
3. Reflector       L_R  = 1.05 L_DE  (≈ 0.5λ)
4. Directors       L_D1 = 0.95 L_DE,  L_Dk+1 = 0.95 L_Dk
5. Spacing R-DE    S_R  = 0.25λ (0.15-0.25λ)
   Spacing DE-D, D-D   S_D = 0.15λ (0.1-0.35λ)
6. Element diameter d ≈ 0.0025λ to 0.01λ

Example: 5-element Yagi at fc = 200 MHz, L_DE = 0.48λ.

λc   = 3×10⁸ / 200×10⁶ = 1.5 m
L_DE = 0.48 × 1.5      = 0.720 m
L_R  = 1.05 × 0.720    = 0.756 m
L_D1 = 0.95 × 0.720    = 0.684 m
L_D2 = 0.95 × 0.684    = 0.650 m
L_D3 = 0.95 × 0.650    = 0.617 m
S_R  = 0.25 × 1.5      = 0.375 m
S_D  = 0.15 × 1.5      = 0.225 m
Boom = 0.375 + 3(0.225) = 1.05 m

Characteristics

Advantages: light, cheap, simple single feed, good gain and directivity. Disadvantages: narrow bandwidth, gain limited (~ 15–17 dBi), sensitive to element lengths. Applications: TV and FM reception, VHF/UHF point-to-point links, amateur radio, radar.