RF430FRL152H: PCB Layout circle antenna design

Part Number:RF430FRL152H

Hi,

I have used rf430frl152h to design an NFC device, and here are some information and questions.

I design an PCB antenna of circle shape, information as below

N = Number of turns = 6
R = Radius of coil = 12.3 mm
μo = Electromagnetic permeability = 1.2566370614…×10−9 H/mm
μr = Relative permeability = 0.9996
w = Trace width = 0.3556 mm
t = Trace thickness = 0.035 mm

The inductance of antenna will be 1.956 uH for calculating.

And for 13.56MHz, I have calculated the resonance capacitor and got 70.429 pF.

I put the capacitor of 35pF (internal capacitor is 35pF) between pin.1 and pin.2 of rf430frl152h and parallel to PCB antenna, but it doesn't work well.

My questions are below,

1. Does the PCB antenna trace need to be control as 50 ohm of impedance?

2. Is there any mistakes in my calculatings?

3. How could I improve the sensitivity of NFC TAG by hardware?

Thanks.