# Velocity factor of PCB stripline / antennas

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#### lambdaanttech

##### Newbie level 6
Hello All ,

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

#### RCinFLA

##### Advanced Member level 2
Measuring velocity factor should be done with a time domain reflectometer or with network analyzer. It is 1/sqrt(Er). There is sizable variation in Er on FR4 material between different manf. and lot to lot mix variation.

A dipole antenna (or resonator) will give you a very wrong result due to stray capacitance loading on dipole. The fields will not be confined to the board material. You will be measuring more air then FR4.

For a microstrip transmission line Vp, much of the fields are between the strip and ground plane within the substrate. Even more so for a stripline encapsulation.

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#### lambdaanttech

##### Newbie level 6
I found that the 1/sqrtEr formula is meant for waves travelling trough a surrounding medium , like coax , where the dielectric surrounds the conductor completely .

However when recalculating with the VF given from my measurements I achieve resonant antennas .

I work with a PCB without a groundplane .
Even with a groundplane the stripline sees the FR4 material and air so its mixed .

Even when calculating with appcad a 1/4 lambda stripline calculated with the 1/sqrtEr formula is not right , you are getting another value .

#### FvM

##### Super Moderator
Staff member
I work with a PCB without a groundplane .
Even with a groundplane the stripline sees the FR4 material and air so its mixed .

Even when calculating with appcad a 1/4 lambda stripline calculated with the 1/sqrtEr formula is not right , you are getting another value .
Right. You get the correct propagation speed as v = 1/√LC (for lossless transmission lines). If C is completely dependant on Er, then the √Er factor applies.

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