Communication Principles——Amplitude modulation and Frequency modulation (AM and FM)

 

Why in AM (amplitude modulation) and FM (frequency modulation) the bandwidth of modulated signal increases when index modulation, β increases?

 

In FM (frequency modulation), the modulation index β is defined as:

Where Δf is the peak frequency deviation (how much the carrier frequency deviates from its original value) and fm is the frequency of the modulating signal.

according Carson's Rule:

 So in this function,when β increases,the bandwidth of modulated signal will be increase.

In fact,for a large modulation index (β>1),the bandwidth can be approximated using Bessel functions, and the bandwidth grows with the modulation index,meaning the signal occupies more spectrum.

In AM (amplitude modulation), the modulation index β is the ratio of peak amplitude of the modulating signal (Am or called Em) to the amplitude of the carrier signal (Ac or called Ec):

m一般用于amplitude modulation，β用于frequency modulation

 

When β=1,β is same mean with m, m=1,(Am=Ac,or called Em=Ec),the system is 100% modulated,it means the carrier signal is completely modulated by the message signal.

When β<1, β is same mean with m, m<1,(Am<Ac,or called Em<Ec),the system is
0%<m<100% modulated

 

When β>1, β is same mean with m, m>1,(Am>Ac,or called Em>Ec),the system is 
m>1>100% modulated, modulation depth greater than 100%  must be avoided !!!! (it is over-modulation,signal not cover completely,some of data will be lost)❌❌

 

 

The bandwidth of an AM signal is typically givens by the formula: