Shorter whip antenna of the pocket radios

[prabhatkarpe4]

I need to know why do most pocket AM/FM radios come with shorter whip antennas?

As per the rule, a whip antenna for receiving FM broadcast between 88 MHz and 108 MHz should have (300/100)/4 = 0.75 m or 75 cm long whip antenna. But why most pocket radios come with only 20 cm to 60 cm long whip antenna?

Apart from that, to receive SW broadcast, the antenna should be (300/14)/4 = 5.3 m or 5 meters. But howcome a 60 cm whip antenna would receive SW broadcast?

[wasedadoc]

Your formula is for a resonant antenna.  In practice, a receiving antenna does not need to be resonant to receive adequate signal.  Also an antenna's electrical length can be made longer than its physical length eg by a loading coil.

[vk6zgo]

I need to know why do most pocket AM/FM radios come with shorter whip antennas?

As per the rule, a whip antenna for receiving FM broadcast between 88 MHz and 108 MHz should have (300/100)/4 = 0.75 m or 75 cm long whip antenna. But why most pocket radios come with only 20 cm to 60 cm long whip antenna?

Apart from that, to receive SW broadcast, the antenna should be (300/14)/4 = 5.3 m or 5 meters. But howcome a 60 cm whip antenna would receive SW broadcast?

Receivers are very sensitive, to the point that quite short antennas can receive usable signals from very much less than optimum antenna lengths.

Also, HF Broadcast stations use high power & very efficient transmitting antennas, so they can usually produce enough signal strength to provide fairly good reception.
Ham Transceivers with power outputs of a few hundred watts to a kilowatt or thereabouts will not always be quite as easy to receive.

That said, HF frequencies are affected to a large degree by propagation conditions, so at times, you can hear many stations, even with a tiny whip antenna & other times, few, or none.

I remember back in the 1970s, on the 20m Ham band, listening  to a large number of stations from across the world with my Drake SSR1 receiver using its whip antenna while I tiled my back patio.
That was a time of excellent HF propagation.

[ebastler]

I need to know why do most pocket AM/FM radios come with shorter whip antennas?

Don't double-post; that is very much frowned upon here. You now have two groups of people discussing the same question of yours:
https://www.eevblog.com/forum/networking/why-do-pocket-radios-have-small-antennas/msg5605585/#msg5605585

[niconiconi]

Apart from that, to receive SW broadcast, the antenna should be (300/14)/4 = 5.3 m or 5 meters. But howcome a 60 cm whip antenna would receive SW broadcast?

Most MW and SW radio antennas are undersized, they're known as electrically-small antenna. Basically, they still pick up a tiny bit of the electromagnetic energy from the radio signals, so reception is still possible. The antennas are very inefficient and the power input is low, but we can always use an active Low-Noise Amplifier behind the antenna...

For other applications you need to think twice. If it's a microwave receiver, low antenna gain means Signal-to-Noise ratio degradation. If it's a radio transmitter, antenna efficiency is still important. But for a pure SW receiver, things become much easier - the ionosphere already has so much atmospheric noise, the Signal-to-Noise even in the best case is not too high, so even a so-so amplifier is good enough.

[radiolistener]

As per the rule, a whip antenna for receiving FM broadcast between 88 MHz and 108 MHz should have (300/100)/4 = 0.75 m or 75 cm long whip antenna. But why most pocket radios come with only 20 cm to 60 cm long whip antenna?

There is no such rule. Antenna can be any size.
But antenna size affects impedance, radiation pattern and efficiency.
If you know specific antenna type you can calculate it's size for resonant frequency. But this doesn't means that antenna should be exactly this size. You can use impedance matching circuit to compensate shorten antenna size.
Usually shorten antenna has capacitive impedance and requires inductor to extend its electrical length.

Also, shorten antenna produce less powerful signal on the output, so it requires low noise amplifier. If you use too short antenna, it's signal can be below noise floor and in this case LNA cannot help, because it will amplify noise the same as station signal. So, very short antenna may be not enough to listen weak stations.