By comparing the numerical equation given with the general equation of the FM signal wave, the answers are:
a.) [tex]M_{f}[/tex] = 0.5
b.) [tex]F_{c}[/tex] = 0.1 MHz
c.) [tex]F_{m}[/tex] = 0.02 MHz
d.) The Peak value of unmodulated carrier = 5 Hz
Given that the FM equation VFM = 5 sin[200000πt + 0.5 sin(40000 πt)]
Frequency modulation is a system in which the amplitude of the modulated carrier is kept constant, while its frequency and rate of change are varied by the modulating signal.
The above equation can be related to the general equation of the modulated wave below
V = A sin([tex]w_{c}[/tex]t + [tex]m_{f}[/tex]sin [tex]w_{m}[/tex]t )
By comparing the numerical equation above with the given equation,
a. Modulation index [tex]M_{f}[/tex] is given from the equation of the FM signal which is the amplitude of the equation 0.5 sin(40000 πt).
The Modulation index [tex]M_{f}[/tex] = 0.5
b. Carrier frequency [tex]F_{c}[/tex] = 200000π ÷ 2π
[tex]F_{c}[/tex] = 100000
[tex]F_{c}[/tex] = 0.1 MHz
c. Modulating frequency [tex]F_{m}[/tex] = 40000π ÷ 2π
[tex]F_{m}[/tex] = 20000
[tex]F_{m}[/tex] = 0.02 MHz
d. The Peak value of unmodulated carrier will be the maximum displacement of the equation
VFM = 5 sin[200000πt + 0.5 sin(40000 πt)]
which is 5.
So, The Peak value of unmodulated carrier = 5 Hz
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