Relation between wave length and size of the antenna?

Answer 1

To decrease antenna height

For transmitting a signal of wavelength

λ the antenna height must be λ/4. So if we want to send a 1 Hz (λ=3*10^8 m) signal ( very very low frequency) using an antenna , its height must be 75,000 Km ( impossible to build such a huge antenna ). If the same signal is modulated to some high frequency say 88 MHZ ( λ = 3.4 m ) , antenna height needed is 0.8522 m (quite easy to construct !!! ) (88 MHZ is the starting range of Frequency modulation which exists upto 108 MHZ).

Answer 2

It depends on antenna type.

Input impedance

If we consider a dipole, the first resonant frequency (where input impedance is real, so you have an easier matching with the circuit) is f0=c/(2L), where c is light speed in the media (approx. 3*10^8 m/s in vacuum or air) and L is dipole length. Imaginary part of the input impedance has a slight dependance on antenna radius, but when antenna is resonant, input impedance is real.

In a microwave circuit, you have to match circuitry and antenna with a filter (to maximize power transfer from circuit to antenna). So, you choose antenna's geometry to match maximum power transfer (transmission line impedance equals antenna's input resistance) and cancel the imaginary part of antenna input impedance (see stubs, lambda/4 adaptors, etc) to minimize losses and standing waves across the line.

Distance of link is related to signal frequency by friis formula:

Prx=Ptx*Gtx*Grx*(lambda/(4*pi*d))^2, where

Prx: Power captured by receiving antenna (gain Grx)

Ptx: Power irradiated by transmitting antenna (gain Gtx)

lambda: (lambda=light speed in media / frequency) transmitted signal wavelength

d: antennas distance

pi: 3.14 =)

So, antenna geometry affects input impedance (and radiation characteristics).

Input impedance affects Prx and Ptx (P=Z*I^2=V^2/Z, Z: input impedance).

In the end, varying antenna diameter affects input impedance

Input impedance affects matching.

Matching is necessary, so you have to choose the right antenna diameter to have a good matching and maximum power transfer, say maximum distance d.

If you want more details, you can take a look at Orfanidis' book (chapter 16-21),

for input impedance of linear antennas