Question

1. prove and derive the resonant frequency of a short diopole antenna

Answer 1

In simple we can derive the frequency from the basic wavelength formula. Which can be given as

Wavelength (l)= velocity of light(C)/Frequency(F)

From this frequency is, F=C/l

As it is resonant antenna ,the length of antenna will be equal to half the wavelength. But this lenght will not be equal to half the wavelength because of "end effct".This is caused by decrease of inductance and increase of capacitance at the end of antenna.

So the resonant frequency is derived from the american hams .which is given as

Frequency, F(MHz)=468/L(length of antenna)

Derivation :

L(mts)=C/F(Hz)

We know that C=3*10^8=300,000,000

1MHz=1,00,000Hz

L(mts)=300/F(MHz)

As it is dipole the lenght is termed as

L=150/F(MHz)

Since 1 meter =3.2808feets

Converting length from meters to feets

L(f)=(150*3.2808)/F

L=492.125/F

As the speed of RF signal is 5% slower so multiply 0.95 with the 492.125

L=(492.125*0.95)/F

L=467.51968/F

L=468/F

F(MHz)=468/L(feets)

This is the resonant frequency of short dipole antenna.