A Yagi works by a different mechanism from a dish or horn, but the same underlying principle still applies:
more effective aperture -> more gain
For any antenna, gain and effective aperture are linked by:
Ae = (G lambda^2) / (4 pi)
where:
Ae = effective aperture
G = antenna gain
lambda = wavelength
At the hydrogen line:
lambda ~= 21 cm
frequency = 1420.405 MHz
DISH OR HORN
With a dish, it is easy to visualize:
- bigger reflector
- more incoming radio energy intercepted
- narrower beam
- higher gain
A 3 m dish physically intercepts much more of the incoming wavefront than a 1 m dish.
YAGI
A Yagi has almost no solid collecting area, yet it still has aperture.
Why?
Because the elements interact with the incoming electromagnetic wave and reradiate energy so that:
- signals from unwanted directions cancel
- signals from the forward direction add together
The reflector and directors reshape the electromagnetic field.
So the antenna behaves as though it is collecting energy from a much larger area than the metal alone would suggest.
WHAT DETERMINES YAGI GAIN?
- Boom length
Longer boom generally means:
- narrower beam
- more directors
- more phase shaping
- higher gain
At 1420 MHz:
3-element Yagi ~= 7 dBi
20-element Yagi ~= 15 to 17 dBi
- Number of directors
Each director slightly improves forward reinforcement.
The improvement gradually diminishes:
- first few directors add a lot
- later directors add less
- Element spacing and tuning
Gain comes from carefully controlled phase relationships between elements.
At hydrogen frequency the dimensions become quite critical because:
wavelength = 21 cm
Even a few millimetres can matter.
EQUIVALENT APERTURE
Even though there is no dish surface, a Yagi still has an effective collecting area.
Example:
A 15 dBi Yagi at 1420 MHz has approximately:
Ae ~= 0.17 m^2
That is roughly equivalent to a circular dish around:
diameter ~= 47 cm
assuming similar efficiency.
So electromagnetically, the Yagi behaves somewhat like a small dish.
WHY DISHES DOMINATE HYDROGEN ASTRONOMY
Hydrogen observations are usually signal-limited.
Dishes scale better because:
- doubling diameter greatly increases aperture
- beamwidth becomes much narrower
- gain rises rapidly
Yagis eventually become impractically long for modest gain increases.
Approximate comparison at 1420 MHz:
3-element Yagi ~= 7 dBi
15-element Yagi ~= 15 dBi
1 m dish ~= 20 dBi
3 m dish ~= 30 dBi
So even a moderate dish can outperform a very long Yagi.
INTUITIVE WAY TO THINK ABOUT IT
Dish: collects waves geometrically
Yagi: synchronizes currents so the antenna responds strongly in one direction
Both increase effective aperture, but by different physics.
The key idea is:
Gain is not determined by metal area alone.
It depends on how much of the incoming wavefront
the antenna can interact with coherently.