wifi / WIMAX antenna
Allow me to put some numbers together....

A normal wifi router is probably good for a range of 30 metres but you want to be able to project that range to 4000 metres. OK so far?

Now, the link loss of a radio system is basically contained within the following equation: -

Loss (dB) = 32.45 + 20\$log_{10}\$(f) + 20\$log_{10}\$(d)

Where f is in MHz and d is in kilometres. This equation tells you how many dB of power loss you can expect at a given distance with a given carrier frequency.

Of importance here is the distance part of the equation. At 30 metres this contributes a value of -30 dB whereas at 4000 metres this is a loss of +12 dB.

Simple math tells me that you are looking for an antenna with a gain improvement of 42dB above and beyond the current antenna. Maybe your current antenna is a monopole with a gain of about 2dBi. So now you are wanting an antenna with a gain of about 44dBi.

Firstly - what you have shown in the picture will not have a gain of 44dBi. It might be a gain of 10dBi maximum and this leaves you considerably short of the 4km distance you wanted. Maybe use a yagi antenna: -



A 7 element Yagi antenna has a gain of about 13dBi and increasing the number of elements is producing diminishing results



What about a dish antenna? The gain of a dish is: -

Gain = \$\dfrac{4\pi A}{\lambda^2}e_A\$ (see this link)


A is the area of the antenna aperture, that is, the mouth of the parabolic reflector
d is the diameter of the parabolic reflector, if it is circular
\$\lambda\$ is the wavelength of the radio waves.
\$e_A\$ is a dimensionless parameter between 0 and 1 called the aperture efficiency. The aperture efficiency of typical parabolic antennas is 0.55 to 0.70.


If you do the math (and assuming an efficiency of 1) you'll calculate that your antenna will need to be 6m diameter. Hope I did the math right.

But, even if you did manage to project your wifi signal to a 4km distance, what are you going to talk to? A dish antenna with this much gain (in fact any antenna with this much gain) will be extremely directional - is that what you want?

I hope you realize that wifi is two-way comms and anything at 4km needs to have a similarly sized antenna to project their signal back - the power needs to be focussed back to the wifi antenna at 4km distance.

Have you really thought thru what you want?