Free Yagi-Uda Antenna Element Spacing & Gain Tool

1. Principles of the DL6WU Yagi-Uda Optimization

The Yagi-Uda antenna, invented by Shintaro Uda and Hidetsugu Yagi in 1926 and revolutionized for VHF/UHF amateur radio by Dr. Günter Hoch (DL6WU), operates as an endfire travelling-wave director array. Unlike older narrow-band designs:

• Reflector: Sits approximately $0.15\lambda$ to $0.20\lambda$ behind the driven element. Slightly inductive (longer than $\lambda/2 \approx 0.495\lambda$), it reflects backward radiation forward.
• Driven Element: Typically a folded dipole (matching $200\Omega$ transformed via $4:1$ balun to $50\Omega$) or split dipole (with hairpin/gamma match), resonant at roughly $0.473\lambda$.
• Expanding Director Spacings: DL6WU demonstrated that director spacing should not be uniform; instead, it starts tightly spaced ($0.075 - 0.10\lambda$) near the driven element to couple maximum energy, then expands progressively out to $0.30 - 0.35\lambda$ along the boom. This forms a tapered phase-velocity traveling wave structure that yields maximum gain per meter of boom length.

2. Metallic Boom Correction Factor ($\Delta L$)

When parasitic aluminum elements pass directly through a conducting metallic boom, the boom creates a localized capacitive shunting and eddy current effect, making the element behave electrically shorter than its physical length. If uncorrected, the antenna will resonate too high in frequency and suffer severe loss of gain and front-to-back ratio.

According to classic NBS (National Bureau of Standards) and DL6WU experimental data: $$\text{Bonded Elements Through Boom: } \Delta L \approx 0.50 \cdot D_{boom}$$ $$\text{Insulated Elements Through Boom: } \Delta L \approx 0.35 \cdot D_{boom}$$ $$\text{Elements Mounted on Standoffs: } \Delta L \approx 0.05 \text{ to } 0.10 \cdot D_{boom}$$

The physical cut length of every element must be increased by $\Delta L$ to restore the theoretical free-space resonant length.

3. Forward Gain, F/B Ratio & Stacking Distance

Forward gain in a well-designed Yagi is determined primarily by the total physical boom length rather than the number of directors. A 5-element Yagi on a $0.8\lambda$ boom achieves roughly $10.0\text{ dBi}$ ($7.85\text{ dBd}$), while a 12-element long-boom array spanning $3.5\lambda$ delivers over $15\text{ dBi}$.

When stacking two Yagis vertically or horizontally for EME (Moonbounce) or weak-signal DXing, the optimum stacking distance $S_{opt}$ to maximize array gain while avoiding high sidelobes is given by: $$S_{opt} = \frac{\lambda}{2 \sin(\theta_{3\text{dB}} / 2)}$$ Where $\theta_{3\text{dB}}$ is the half-power beamwidth in the plane of stacking.