I've usually heard that the length of antennas in radio receivers need be a substantial fraction of wavelength.
Then ,say FM wave of frequency of 100MHz has a wavelength of 3 m. Then how come mobile phones of length ,say 6 cm , which is 1/50th of the wavelength recieve radio waves properly ?

 

Hello,

Normaly a 1/4 wave is used for the lenght of a receiving antenna.
A cellphone works on a much higher freqency as the FM receiver.
The frequencies for a cellphone can be 850, 900, 1800 or 1900 Mhz.
http://www.worldtimezone.com/gsm.html

Bertus

 

Actually, resonant antenna systems for transmitting or receiving should be a ~1/2 wavelength dipole, fed from the center. A shortened antenna can be brought back to resonance by adding inductance in the elements (loading coils) . This causes the antenna to loose efficiency, but still work.

For example, when I operate on the 40m amateur band, my full-size dipole wire antenna is ~20m long (10m either side of the feedpoint). I can operate mobile on 40m with a 3m long inductively-loaded whip antenna mounted vertically on the car's body. In this case the car body acts as half of the antenna (counterpoise), while the whip acts as the other half.

Such an antenna is only about 10% efficient, meaning that of 100W fed to the antenna, 90W is dissipated as heat, and only 10W is radiated. Now, if conditions are right, I can still send/receive hundreds to thousands of miles. If conditions are marginal, I may get through from on the fullsize house antenna, but not from the mobile parked outside the house.

Cell phones and similar devices use a ground-plane (copper traces on the pcb) as one-half of a dipole (the ground plane should be ~1/4 wavelength at the operating frequency), the other half of the dipole being a spirally-wound wire whip. The spiral whip has inductance, so can be physically shorter than 1/4 wavelength (hams call this type of whip a rubber-ducky).

 

because recieving antennas do not have to be resonant lengths. only transmit antennas have to be specific lengths to match impedance. look at the car radio antenna for instance, wavelengths at am broadcast frequencies are long, transmit antennas for am are ususally very tall. the recieve antenna is whats called a voltage probe, not resonant at all. nost portable fhortwave radios suguest a 30 ft antenna for external antenna, thats so they dont get too much signal overload from strong stations.