Context: Frequency modulation via a Voltage Controlled Oscillator (VCO)
If I take a message signal of frequency \$F_{mes}\$ and use it to generate a FM signal with a VCO, which has a rest frequency of \$F_r\$ and a deviation frequency of \$F_d\$, what is the relationship between the rest frequency \$F_r\$ and the message frequency \$F_{mes}\$?
Does the frequency modulation follow: $$F_{FM} = (F_{mes}\times F_r)+F_d$$
Or am I completely off?
My reasoning is that the change in the magnitude of the message signal amplitude is proportional to the change in the deviation frequency. However, increasing the frequency of the message signal will increase the frequency of the deviation frequency being changed, therefore it alters the base rest frequency to a new rest frequency value that the deviation frequency can then move away from due to different message signal amplitude values being input.
Best Answer
I think you are confusing your signal frequency with your signal envelope. FM radios adjust the frequency by the envelope not the frequency of the signal.
\$F_{FM} = F_R + F_{D}*V_{signal}/VMAX_{signal}\$
The rest frequency will stay the same.
However, if your signal has a dc component, it may appear to the receiver that the rest frequency is something different.