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If a 5kHz baseband signal is modulating an AM carrier wave, the sidebands will be centered around the carrier wave and the the signal will occupy 10kHz bandwidth. AM radio limits the upper modulating frequency to 5 kHz.

But FM signals require a bandwidth of about 200 kHz for the same baseband signal. Why is that so?

EDIT:

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They need not, narrowband FM occupies the same bandwidth as AM, for the same audio bandwidth. Transmitted AM bandwidth is fixed at twice the audio bandwidth.

However, wide deviation FM provides signal to noise ratio improvements above that which is possible for AM. It also provides the so-called capture effect, whereby a weak station near to a stronger wanted one is not heard at all, not just merely heard weaker. It's therefore worth increasing the deviation and so transmitted bandwidth of FM to get higher quality (read higher advertising revenue).

The original AM broadcast band is quite narrow and doesn't have the space for wideband FM channels, so FM broadcasting is done at a much higher carrier frequency.

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    \$\begingroup\$ @Neil_UK Not fully agree with how you'd make FM of limited-bandwidth audio occupy the same bandwidth as AM (which is the same as the orig. audio bw) – wouldn't that basically require 0 modulation index? ham.stackexchange.com/questions/9096/… \$\endgroup\$ – Marcus Müller Oct 24 '17 at 20:05
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    \$\begingroup\$ The parts of this answer that deal with the audio bandwidth being added to the frequency deviation are not correct. Audio bandwidth appears as a derivative of the frequency modulation. Modulation depth itself is determined by audio dynamic range. \$\endgroup\$ – user207421 Oct 24 '17 at 23:21
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    \$\begingroup\$ To degrade the business prospects of Armstrong, the FM allocation was moved UP to 88-108MHz even tho the surging FM stations were already in place near 50MHz. And RCA combatted Armstrong tooth-and-nail. \$\endgroup\$ – analogsystemsrf Oct 25 '17 at 3:39
  • \$\begingroup\$ @EJP Bessel functions are out of place in an answer like this, but Carson's rule is a good summary, see the wikipedia FM modulation article for Carson's Rule, which actually has the tables of the relevant Bessel functions anyway. Note the difference between Modulation Index, which is a function of the audio amplitude, and Transmitted Bandwidth, which is always at least twice the audio bandwidth, and significantly more when wideband FM is used. \$\endgroup\$ – Neil_UK Oct 25 '17 at 5:56
  • \$\begingroup\$ allsyllabus.com/aj/note/ECE/Analog_Communication/Unit5/… \$\endgroup\$ – Bruce Abbott Oct 25 '17 at 7:02

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