Frequency Spectrum and Bandwidth Requirement of Angle Modulated Wave

FREQUENCY SPECTRUM AND BANDWIDTH REQUIREMENT OF ANGLE MODULATED WAVE.

Frequency Spectrum of Angle Modulated Waves

We know that AM contains only two sidebands per modulating frequency. But angle modulated signal contains large number of sidebands depending upon the modulation index. Since FM and PM have identical modulated waveorms, their frequency content is same. Consider the PM equation or spectrum analysis,

The values of Bessel functions depend upon modulation index m, They are listed in Table 2.1.1

It is clear from the above discussion that, angle modulated signal has infinite number of sidebands as well as carrier in the output. The sidebands are separated from the carrier by f_m, 2f_m, 3f_m … etc. The frequency separation between successive sidebands is f_m. All the sidebands are symmetric around carrier frequency.  The amplitude of the sidebands are E_cf₀, E_cf₁, E_cf₂, E_cf₃, E_cf₄, … and so on.

Bandwidth Requirement

The bandwidth requirement of angle modulated waveforms can be obtained depending upon modulation index. The modulation index can be classified as low (less than 1), medium (1 to 10) and high (greater than 10). The low index systems are called narrowband FM. For such system the frequency spectrum resembles AM. Hence minimum bandwidth is given as,

Here ‘n’ is the number of significant sidebands obtained from Bessel table.

Carson’s Rule:

Carson’s Rule gives appoximate minimum banndwith of angle modulated signal as

Here f_m(max) is the maximum modulating frequency. As per Carson’s rule, the bandwidth accommodates almost 98% of the total transmitted power.