Electronic – Designing a 50Ω coplanar waveguide on 1.6mm FR4

It's called a Coplanar Waveguide With Ground. To find impedance, here is a calculator.

This is a cross-section through the line. The red is the RF track, the blue is ground. The dotted blue lines are vias, you should put them every 5 to 10 mm along the sides of the ground.

If I assume you have a two-layer board,
Er= 4.2 (good guess for FR4 if you don't know better)
Board= 1.5 mm
Track= 2.1 mm
Gap = 0.5 mm

You will have a 50 ohm line. There will be other solutions with wider tracks.

Deviations of 10% from 50 Ohms will not matter in this application. But as they say in the datasheet, keep the track short! If I recall correctly, at 900 MHz, the attenuation is 3 dB in just 5 or 10 cm. 1800 MHz is be worse.

Don't forget to put plenty of vias down the sides of the CPW, to the ground plane underneath.

Have you read the following: Atmel AT02865 RF Layout with Microstrip ? It deals with exactly what you are doing, same chip and same balun.

One of the key parameter is the FR4 dielectric thickness between the RF ground plane and the microstrips. You have listed yours as 0.18mm (7 mils). In the Atmel app note, it uses an example of 0.25mm (10 mils) FR4 dielectric thickness. So the example is a little different, but is close enough that you can apply all the considerations while adjusting for the small dimensional differences accordingly.

Since the traces are sitting on top of a ground plane, you cannot use the coplanar waveguide model for the transmission lines. Using the microstrip model and dielectric thickness of 0.18mm, I get approx 0.3mm for 50-ohm line.

Also, you do want to isolate the microstrip lines from other elements of your design. For example, a quote directly from the Atmel app note page 10 -

For microstrip designs the copper pour on layer-1 should be kept away from the transmission line. The underlying Layer-2 ground plane needs to be the dominant ground reference to minimize variables. A keep-away distance of 4x the dielectric thickness will reduce the parasitic effects of copper pour to less than 1%. In other words the gap between the microstrip transmission line and copper pour on layer-1 should be 40 mils or more.

If you look at the balanced 100-ohm connection between the SAMR21 IC and the Balun, it ends up looking more like a "T" shape dipole antenna than a transmission line. I don't think there is anyway to make that better, so just make that connection as short as possible. Also for the same consideration of the preceding quote, I would probably take away that asymmetric ground pour.

Also, I would move the antenna to the left so the tail of antenna at the right is closer to the ground plane.