# RF Design - Antenna Feed-line Parameters

I am implementing a BLE device with a chip antenna. The device has already been impedance matched to 50Ω and is ready to be connected to the feedline and antenna. The antenna datasheet has a recommended layout for edge-mounting and prefers a 50Ω co-planar wave-guide.

Using calculators such as this or this both give me the same CPWG impedance when provided with the relative dielectric constant for FR-4 at 2.45GHz (approx. 4.2), track width of 2.5mm, gap width of 0.75mm and dielectric thickness of 1.6mm.

None of the calculations I've come across seem to care about the length or shape of the CPWG (apart from gap/trace width) so my question is: Am I right to simply link the antenna to the device as directly as possible so long as the above conditions are met? What is the effect of the overall length of the CPWG?

• The calculators usually assume a lossless line. – Peter Smith Apr 24 at 9:10

## 2 Answers

None of the calculations I've come across seem to care about the length

As with any high-frequency transmission line, the matching impedance is determined by the inductance per unit length divided by the capacitance per unit length and then by taking the square root of the ratio.

The division of L/m by C/m cancels out the "per metre" part and effectively, the impedance is unaffected by the length of the transmission line.

After some further research I came across this wonderfully detailed guide on radio frequency layout practice and antenna design from Cypress which goes into detail about the differences in microstrip and CPWG, antenna tuning, chip vs. PCB vs. wire antennae and importantly how to design for angles in the transmission line while maintaining constant impedance:

$$$$M=W(1.04+1.3\cdot e^{-1.35\cdot W/H})$$$$