How can adding a reflector to a half-wave dipole (in a Yagi Uda antenna) increase the gain by more than 3dB?

Question

I have been designing a Yagi Uda antenna using CST Microwave Studio.

For a half-wave dipole the directivity (at 1.3GHz) was 2.116dBi.

After I added a Reflector, the directivity improved to 6.074dBi.

This is an increase of 3.958dB - more than double!

I am trying to understand how this is possible? How can the gain more than double? If I understand correctly, the reflector reflects the fields from the dipole back to the opposite direction. Thus in the best case scenario I will get complete super-position of the fields. Therefore I should find a maximum increase of 3dB - not more!

Thanks!

Answer 1

You have to think in 3 dimensions, not just 2. Not only do you get superposition forward along the axis of the reflector placement, but the energy from the off-axis fields is changed (and is conserved, so it has to go somewhere, e.g. potentially forward).

Answer 2

The plain dipole has a "beam width" of 360° — it radiates equally well in all directions in the normal plane.

When you add the reflector, the -3 dB beam width is not simply reduced to 180° — it's actually significantly less than that, more like 120°. Since gain is more or less inversely proportional to beam width, this accounts for the numbers you're getting.