I have the following circuit for the SIM900's antenna connection, using the A10393 antenna from digikey:
In closer look:
First of all my knowledge on RF design is not great. My questions now are what should the trace width be in order to match a 50 Ohm line and how I can calculate the value of L2.
I read the datasheet and I also have a link below, and it gave different values for L1 and I did not quite understand it. The zero frequency (R0) is what the mid value of the resonance range and should I care about the L1 component?. I couldn't avoid placing a through hole via because I should have placed the antenna on the bottom side.
Frequency is 850 – 900MHz, the GSM range.
The board is two layers and its thickness is 1.6mm.
The distance from the source pin to the antenna feed is around 15mm.
No GND plane passes underneath, on both layers, the antenna (it is only the board plastic) or near it at a distance of around 5mm (datasheet recommendation 2.5mm).
I don't think you are following the rules set out in the document closely enough. For a start here is a link that opens up a document that describes the device. Here are the critical things rolled into one picture: -
I'm not saying that how you've mounted the interface circuit won't work but if it doesn't then you'll kick yourself for having to buy a new PCB. Also they have the groundplane extending to 2.5mm from the edge of the antenna - I think you should do the same for the reasons above. As @ThePhoton points out, it's unlikely that such a short feedline is going to give problems BUT/HOWEVER following the instructions in the data sheet is realistically your only course of action and if it says 50 ohm impedance tracking then go for it.