Frequency analysis of angle-modulated waves is more complex than amplitude modulation because it has an infinite number of side frequencies pairs displaced from the carrier by a multiple of the modulating frequency. Angle modulation requires a larger bandwidth than amplitude modulation, with the bandwidth being a function of the modulating signal and modulation index. Carson's rule approximates the bandwidth but is narrower than using Bessel functions, so it provides poorer performance for modulation indexes above 5.

1. Frequency and Bandwidth
Analysis of Angle-Modulated
Waves

2. Frequency Analysis of Angle-Modulated Waves
• Frequency analysis of angle-modulated wave is much more complex
compared to the amplitude modulation analysis.
• In phase or frequency modulator, a modulating signal produces an
infinite number of side frequencies pairs (i.e. it has infinite
bandwidth)
• Each side frequency is displaced from the carrier by an integral
multiple of the modulating frequency

3. Bessel Function

4. Bessel Function

5. Bessel Function

6. Bessel Function of the First Kind

8. Points to Remember

9. Bandwidth Requirement
• It was be seen that angle-modulated wave consumes larger
bandwidth than an amplitude-modulated wave and the bandwidth of
an angle-modulated wave is a function of the modulating signal and
the modulation index

10. Carson’s Rule

11. Carson’s Rule
• Carson’s rule is an approximation and gives narrower bandwidth than
the bandwidth determined using Bessel table. Therefore, a system
designed using Carson’s rule would have a narrower bandwidth but a
poorer performance than a system designed using Bessel table.
• For modulation indexes above 5, Carson’s rule is a close
approximation to the actual bandwidth required