What factor determines the spacing of the sidebands in an amplitude modulated signal?

Answer 1

Its a function of the signal bandwidth.

If you modulate a 1 MHz carrier with a 1 KHz sine wave, you will see three peaks in the frequency domain - the carrier - the carrier minus 1 KHz - and the carrier plus 1 KHz.

If the carrier is 100 MHz, the spacing is still the same, unless you consider spacing to be proportional to the carrier frequency - but that does not seem to be the question.

Improved.

Bandwidth is a function of modulating frequency in simple Amplitude Modulation.

As described above, 1 MHz signal with 1 kHz modulation creates a lower side frequency (1000 - 1) = 999 kHz, the carrier = 1000 kHz and the upper side frequency 1001 kHz. These two side frequencies exist up to the point of 100% modulation. Over 100% modualtion, large numbers of extra side frequencies ("Splatter") will exist.

Since we rarely use single-tone modualtion, but a spectrum of modulating frequencies, the upper and lower energy appears within the two side bands - commonly called sidebands. The composite signal now comprises a lower sideband, which (for a maximum modulating frequency Fm) extends "down" to Fc-Fm, the carrier (Fc), and the upper sideband, which extends "up" to Fc+Fm.

Be aware that advanced AM techniques, such as SSB-SC and VSB may use half the bandwidth of full-carrier, both-sidebands AM.

Also, be aware that AM techniques used in digital data (QAM, Trellis coding, etc) processing differ from the "audio/broadcast" descriptions above.