NORDIC WP008 , is the quarter wave length correct

Question

Hi 
 If my calculations are correct the NORDIC whitepaper WP008 on PRINTED MONOPOLE ANTENNA for 2.45Ghz the quarter wave length antenna trace is not 92mm 
 For TOP layer PCB traces the effective dielectic constant is maybe about 3.1. Beneath the trace its the FR4 material with 4.4 dielectric constan and above its air about 1 dielectric constanst 
 Effective it will give about 3.1 
 which gives the traveling wave speed 0.57*speed in free air 
 which gives the wavelengtn on FR4 PCB substrate to be about 0.57*122mm = 69.54mm which is much shorter than the application notes which says 92mm? 
 KR 
 Øystein

Szabolcs · Accepted Answer

Hei Øystein, 
 The 3.1 value you are referencing is the effective relative permittivity (epsilon) for a microstrip line. For a microstrip line, you have a ground plane on the other side of the PCB, and the majority of the EM field is inside the substrate (between the microstrip and the reference plane). That is why the effective epsilon is closer to the PCB epsilon. 
 However, in the antenna design, there is no ground plane below the antenna on any other layer, so most of the EM field is in the air, and the effective epsilon will be closer to that of the air than the substrate. It is difficult to estimate it properly (I haven't found any articles on this topic), and the problem gets more complicated if you account for the size of the ground plane. I think there is no closed formula to calculate this, it can only be determined by simulation. 
 Overall, the 0.75 multiplier for the length is more like an empirical number, our experience shows that it is a good estimation for the initial value, but depending on the ground plane size, shape, antenna placement, and other factors, the antenna length usually needs to be customized to the device. This can be best done by tuning and measurement.

NORDIC WP008 , is the quarter wave length correct

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