Carson's bandwidth rule is expressed by the relation CBR = 2 (\$\Delta\$ f + f\$_M\$) where CBR is the bandwidth requirement, \$\Delta\$ f is the peak frequency deviation, and f\$_M\$ is the highest frequency in the modulating signal.

This means that a totally unmodulated waveform has zero bandwidth but this is clearly not the case when modulation occurs. The radio receiver has a bandwidth that is wide enough to accommodate the modulation but small enough to reject unwanted transmissions in adjacent channels.

Here's what AM and FM look like: -

It should be clear that the carrier in the FM system contains a range of frequencies for the simple modulation by a pure sine wave. It gets complicated when composite signals modulate the carrier of course but the principle is the same.

Pretty picture stolen from here

For FM, Carson's bandwidth rule informs you the approximate bandwidth of a transmission. The bandwidth value it calculates contains 98% of the energy of the whole transmission. It is expressed by the relation CBR = 2 (\$\Delta\$ f + f\$_M\$) where CBR is the bandwidth requirement, \$\Delta\$ f is the peak frequency deviation, and f\$_M\$ is the highest frequency in the modulating signal.

This means that a totally unmodulated waveform has zero bandwidth but this is clearly not the case when modulation occurs. The radio receiver has a bandwidth that is wide enough to accommodate the modulation but small enough to reject unwanted transmissions in adjacent channels.

Here's what AM and FM look like: -

It should be clear that the carrier in the FM system contains a range of frequencies for the simple modulation by a pure sine wave. It gets complicated when composite signals modulate the carrier of course but the principle is the same.

Pretty picture stolen from here

Carson's bandwidth rule is expressed by the relation CBR = 2 (\$\Delta\$ f + f\$_M\$) where CBR is the bandwidth requirement, \$\Delta\$ f is the peak frequency deviation, and f\$_M\$ is the highest frequency in the modulating signal.

This means that a totally unmodulated waveform has zero bandwidth but this is clearly not the case when modulation occurs. The radio receiver has a bandwidth that is wide enough to accommodate the modulation but small enough to reject unwanted transmissions in adjacent channels.

Here's what AM and FM look like: -

It should be clear that the carrier in the FM system contains a range of frequencies for the simple modulation by a pure sine wave. It gets complicated when composite signals modulate the carrier of course but the principle is the same.

Pretty picture stolen from [here][3]

[3]: Pretty picture stolen from [here][3]

Carson's bandwidth rule is expressed by the relation CBR = 2 (\$\Delta\$ f + f\$_M\$) where CBR is the bandwidth requirement, \$\Delta\$ f is the peak frequency deviation, and f\$_M\$ is the highest frequency in the modulating signal.

This means that a totally unmodulated waveform has zero bandwidth but this is clearly not the case when modulation occurs. The radio receiver has a bandwidth that is wide enough to accommodate the modulation but small enough to reject unwanted transmissions in adjacent channels.

Here's what AM and FM look like: -

It should be clear that the carrier in the FM system contains a range of frequencies for the simple modulation by a pure sine wave. It gets complicated when composite signals modulate the carrier of course but the principle is the same.

Pretty picture stolen from here