Satellite TV Dish antenna
I just happen to be working on my Antennas homework so I have the book in front of me, 

From Kraus Antennas(1950) 

for Large Circular Apertures wit Uniform Illumination 

directivity  = 4Pi Area/Wavelength^2

This says that as you make dish larger the beam becomes more focused. Also that the size of the dish is proportional frequency of operation. 

As Matt Young says there are whole chapters in books that cover these types of antennas I would highly recommend looking through one.