Help, Explaining of wheeler and medhurst formula #Designing of coil antenna

[derndinn]

i have followed this link to design collinear antenna with phasing coil but i dont understand why we can multiply L(inductance) by C(capacitance) ?

when
** L is calculated with unit inches
** C is calculated with unit centimeter

and i tried to calculate in the same unit but the result is many difference from LC which calculated from formula Resonant frequency.

**broken link removed**



Thank you

 

[FvM]

why we can multiply L(inductance) by C(capacitance) ?
when
** L is calculated with unit inches
** C is calculated with unit centimeter

Actually, the result of Wheeler's formula is in µH and Medhurst in pF. Neither inches nor centimeters.

Question: What's the resulting frequency unit when you put µH and pF into the resonace formula?
Right, GHz

 

[derndinn]

yes GHz , i got it. It was my misunderstanding.

By the way,For Wheeler's formula if i use in inches.so the unit of result is microhenrys not inches, right?

***If i think in only unit : The inductance for Single Layer : L(uH)= ((round^2)*(inches^2))/((9*inches)*(10*inches))
Finally,i got (round^2)*(inches). ***

Ps. I have know what is unit of inductance and Capacitance. but i am confused with the formula.
Or The unit of Wheeler's formula is always uH.

Thank you so much for replying.

Regards,
Derndinn

 

[FvM]

The interesting question is in fact about the derivation of approximate formulas like Wheeler or Medhurst.

Some of these are simply summarizing a series of empirical measurements, in this case there's no relation to physical units. Or they are simplifications of theoretically founded equations, in this case natural constants like µ0 or ε0 can be expected as part of the formula. All constant factors are usually combined to a single factor in an approximate formula, so you don't recognize their physical origin.