antenna gain and in phase combining

1- Since a single antenna is a passive device how can it provide any power gain in a link equation? (Antenna gain in a link equation helps reducing the path loss). Is it because it is adding vectors in phase in a certain direction just like a phase array would?

2-When I add 2 sine waves equal in amplitude and exactly in phase with a Wilkinson power splitter/combiner in the lab and measure the output power with a power meter, why am I not getting 4 times the power of each of the sine waves?

1. An antenna provides gain by increasing directionality. Yes, it works in a very similar way to an array in that the vector sum of all the signals(voltages and currents on different parts of the antenna) only add up coherently in the direction of the beam.

2. Adding 2 signals with a passive combiner only leads to the sum of the power of the 2 inputs. Or 2 times the power(3dB) of one if they are both the same. I'm not sure why you expect it to be 4 as that would greater than the total power going in.

Thank you hagster,

2- Since I am adding these 2 sine waves coherently (they are in phase) then I should have their amplitude doubled and thus their power 4 times higher than the power of a single sine wave i.e. 6 dB higher so why am I getting only 3 dB?

Thank you

You forget that antennas (or other RF sources) are impedance matched rather than voltage sources that deliver unlimited power independent of the load impedance.

O.k. so since the source is a power source and not a voltage source, can we explain things as follows:
In a perfect 50 ohm well matched system the power delivered to each of the 2 branches of the wilkinson combiner by each of the sources is half the power generated ( for maximum power delivery the internal impedance of the source should be the conjugate or in this case equal to the impedance seen by the source ) and then once in the combiner they add in phase and thus gain 6 dB so you lose first 3 dB and then gain 6 dB leading to a total net gain of 3 dB? Does that make sense?

no
go with what hagster said to you

Your first thought is correct, an antenna is passive and does not add power to a link. What is happening however is that the radiated power is concentrated in smaller areas as antenna gain is increased giving the appearance of added power in the link. The signal level at the receiver does increase but not because additional power has been added by the antenna. Rather more and more of the total radiated power is concentrated and delivered to the other antenna. On the recieve side one can think of higher gain as having an increased cross section so more power is collected.