power loss on matching.
how much energy i loss by matcing this way (at dB) ?
The loss will be 6dB.
It's better to use an LC matching circuit, or an 1:1.41 transformer, to reduce the loss to fractions of dB (0 dB in ideal case). Matching usually implies low loss, whithout using resistors.
I just ran it, and with a 50 ohm load impedance and a 100 ohm source impedance, a 50 ohm series resistor has a 3 dB insertion loss. S11 is perfect match, and S22 was -6 dB.
So you would only loose 3 dB. However, IF there was a length of transmission line between the receiver/50 ohm resistor pair and the antenna, it would have to be 100 ohm characteristic impedance line.
I think somewhere is a misunderstanding. The initial post mentioned that the source is 50 ohms (coax cable) and the load is 100 ohms (antenna).
In this case to match the source to the load, you need a 100 ohms parallel resistor to the load (to the antenna).
In this way you lose half of the power (3dB) because half is going to the load and half is losing on the parallel resistor.
The best would be to use reactive matching components (L and C) to minimize the power loss.
You might want to consider a quarter wavelength impedance (single or multiple sections) converter. A 70.7 Ohm section should do just fine and you would have lost only the insertion loss in the transformer.
Run down Harlan Howe's book, Stripline Circuit Design, p. 68-74 for a detailed description. (I have only a paper copy.)
You don't mention the frequency or bandwidth you require so I can't tell if a microstrip solution makes sense.