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FREQUENCY MODULATION FORMULAS
Modulation index mPM k pVm Vm mFM
k pV m
kfVm
m
f m
V m
m
FM Voltage equation Derived from Phase modulation v c t VC sin c t
v FM t VC sin c t
angles
v m t Vm sin mt i c Vm sin m t 2 f
d
dt
i dt c Vm sin m t c t c t
fV m
cos
f m
f
f m
v FM t VC sin c t
V m
c os
m
mt
mt
Vm cos m t
AM power equation P modulated Ptotal Punmod unmodulated ulated ulated P unmodulated P modulated
V C 2 2R
JoVC
2
2R
J nVC 2 2 n 1 2R
Bandwidth is based on the type of modulation: Carson s rule (approximation) B 2 mfm 1 fm 2 f fm ’
Bessel bandwidth B 2nf Mixer equations flocal fRF f IF fimage fRF 2fIF f local f IF IF FM commercial is 10.7 MHz typical FM Bessel s function definition ’
J y m m
y
2
x 0
x
1 2 x y
m 2 x
x ! x y !
FM noise equations
N noise arcsin i Si fnoise f m noise So f signal f noise No FM channel number N 5 f 47.9 MHz 88.1 88.3
