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FM General Equation  
Let the carrier be x_{c}(t) = X_{c}·cos (Ω_{c}t), and the modulating signal be x_{m}(t) = β·sin (Ω_{m}t) 
Then x(t) = X_{c}·cos [Ω_{c}t + β·sin (Ω_{m}t)]  
Modulation Index  


Narrowband FM (NBFM)  
Narrowband FM is defined as the condition where β is small enough to make all terms after the first two in the series expansion of the FM equation negligible. Narrowband Approximation: β = Δω/Ω_{m} < 0.2 (could be as high as 0.5, though) BW ~ 2ω_{m} 

Wideband FM (WBFM)  
Wideband FM is defined as when a significant number of sidebands have significant amplitudes.
BW ~ 2Δω 

Carson's Rule  
J.R. Carson showed in the 1920's that a good approximation that for both very small and very large
β,
BW ~ 2 (Δω + Ω_{m/sub>)) = 2*Ωm/sub> (1 + β) } 

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