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Five-element Yagi design for 100 MHz

Short answer

Wavelength is 3 m. Using reflector 5% longer and each director 5% shorter than the driven element, lengths are: reflector 1.512 m, driven 1.44 m, directors 1.368 m, 1.300 m, 1.235 m; spacing 0.45 m, boom 1.80 m.

With neat diagram design the 5 element Yagi-Uda antenna for receiving 100 MHz radio signal showing design steps. Consider effective dipole length equal to 0.48λc and spacing between elements is 0.15λc.

A 5-element Yagi-Uda antenna has 1 reflector + 1 driven dipole + 3 directors. Design rules used (standard empirical rules):

Driven element (DE) = 0.48λc (given effective length).
Reflector ≈ 5 % longer than DE; each director ≈ 5 % shorter than the element before it.
Spacing between adjacent elements = 0.15λc (given).

Step 1: Wavelength

λc = c / f = (3 × 10⁸) / (100 × 10⁶) = 3 m

Step 2: Driven element

L_DE = 0.48 λc = 0.48 × 3 = 1.44 m

Step 3: Reflector

L_R = 1.05 × L_DE = 1.05 × 1.44 = 1.512 m  (≈ 0.504λ)

Step 4: Directors

L_D1 = 0.95 × 1.44   = 1.368 m  (0.456λ)
L_D2 = 0.95 × 1.368  = 1.300 m  (0.433λ)
L_D3 = 0.95 × 1.2996 = 1.235 m  (0.412λ)

Step 5: Spacing and boom length

S = 0.15 λc = 0.15 × 3 = 0.45 m
Boom (R to D3) = 4 gaps × 0.45 = 1.80 m

Design summary

Element	Length (m)	Position from R (m)
Reflector	1.512	0
Driven (folded dipole)	1.440	0.45
Director 1	1.368	0.90
Director 2	1.300	1.35
Director 3	1.235	1.80

  R      DE      D1      D2      D3
  |      |       |       |       |
 1.512  1.44   1.368   1.300   1.235 m
  |     -o-      |       |       |    ====> to
  |   feed       |       |       |   transmitter
  |<0.45>|<0.45->|<0.45->|<0.45->|
  <------------ boom 1.80 m ----->

Practical notes: elements are aluminium tubes of diameter about 0.005λ–0.01λ (≈ 1.5–3 cm here), mounted on a metal boom at their centres (voltage nulls). The driven element is usually a folded dipole fed with 300 Ω line or a balun to 75 Ω coax. The array points towards the directors, i.e. D3 faces the FM transmitter.

Answer: λc = 3 m; reflector 1.512 m, driven 1.44 m, directors 1.368 m, 1.300 m, 1.235 m; spacing 0.45 m; boom length 1.80 m.

✓ Answer checked by Claude Opus 5.5 (high effort)

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