#### lambdaanttech

##### Newbie level 6

I want to design a Franklin antenna from PCB material .

First I designed the antenna with a NEC based calculator to obtain impedance and radiation pattern .

Afterwards I scaled the model down from free space to FR4 substrate .

As far as I knew , the velocity factor is calculated as 1/sqrt εr .

The VF value was 0,466 .

After milling out the antenna I did some field strength test to compare the 2 element Franklin antenne versus a simple split dipole .

The split dipole had more gain then the Franklin ...

Measuring and calculating and remaking the antenna didn't solved my problems .

Finally I took 2 pieces of FR4 strip PCB to make a dipole and measured the resonance frequency on the VNA .

I found out that way that my calculated VF for FR4 was not correct .

Based on my measurements the VF factor of FR4 should be 0,84 - 0,86 .

Searching the net for some formulas how to calculate the VF factor from the dielectric constant didn't solved my problem .

Comparing my calculated/measured VF factor with the calculations with AppCAD confirmed that the VF factor was right , but I don't know how to calculate it .

Could someone help me about the formula to calculate the VF factor from dielectric constant for PCB's.

Thank you,

Kenny