Yagi construction and 800 MHz design

Yagi antenna: construction and working

A Yagi-Uda antenna is an end-fire array of one driven λ/2 (folded) dipole, one reflector behind it and several directors in front, mounted parallel on a boom. Only the driven element is fed.

   R      DE      D1     D2     D3
   |      |       |      |      |
 --+-----(o)------+------+------+---> beam
   |     feed     |      |      |
  ≈0.5λ  0.48λ   shorter towards the front

Working: the driven element's field induces currents in the parasitic elements by mutual coupling. The reflector (longer, inductive, current lags) cancels radiation backwards and reinforces it forwards. The directors (shorter, capacitive, current leads) produce a progressive phase that guides energy forward, as in an end-fire array. The beam points towards the directors; gain rises with the number of directors (≈ 7 dBi for 3 elements, ≈ 9–10 dBi for 5).

Design procedure: choose λ from the frequency; take the driven element ≈ 0.46–0.48λ; reflector ≈ 5 % longer; each director ≈ 5 % shorter than the previous; reflector spacing ≈ 0.15–0.25λ and director spacing ≈ 0.1–0.35λ.

Design: 5 elements at 800 MHz

Design rules used (standard empirical Yagi rules):

λc   = c / fc
L_DE = 0.48 λc               (driven, given)
L_R  = 1.05 L_DE  (≈ 0.5λc)  (reflector 5 % longer)
L_D1 = 0.95 L_DE, L_Dk+1 = 0.95 L_Dk  (5 % shorter each)
S_R  = 0.25 λc   (reflector to driven)
S_D  = 0.15 λc   (driven to D1 and between directors)

Interpretation: "effective dipole length of 0.48λ" is taken as the driven element length.

Step 1: Wavelength

λc = 3×10⁸ / 800×10⁶ = 0.375 m = 37.5 cm

Step 2: Element lengths

L_DE = 0.48 × 37.5   = 18.00 cm
L_R  = 1.05 × 18.00  = 18.90 cm
L_D1 = 0.95 × 18.00  = 17.10 cm
L_D2 = 0.95 × 17.10  = 16.25 cm
L_D3 = 0.95 × 16.245 = 15.43 cm

Step 3: Spacings and boom

S_R  = 0.25 × 37.5 = 9.375 cm
S_D  = 0.15 × 37.5 = 5.625 cm
Boom = 9.375 + 3 × 5.625 = 26.25 cm

  R     DE    D1    D2    D3
  |     |     |     |     |
 18.90 18.00 17.10 16.25 15.43 cm
  |    (o)    |     |     | ===> beam
  |<9.375>|<5.625>|<5.625>|<5.625>|
  <-------- boom 26.25 cm -------->

Answer: λ = 37.5 cm; R = 18.90 cm, DE = 18.00 cm, D1 = 17.10 cm, D2 = 16.25 cm, D3 = 15.43 cm; spacings 9.375 cm (R–DE) and 5.625 cm (others); boom 26.25 cm.