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Frequency Spectrum of Angle Modulated Waves, Bandwidth Requirement , Carson’s Rule.

**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_{c}f_{0}, E_{c}f_{1},
E_{c}f_{2}, E_{c}f_{3}, E_{c}f_{4},
… 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.

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Analog and Digital Communication : Frequency Spectrum and Bandwidth Requirement of Angle Modulated Wave |

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