Question

An angle modulated signals have the form

Vₚₘ​(t)=A ​cos{2π10⁶t+1.5[2 cos 2000πt]}
ₜ
VFₘ​(t)=A​ cos{2π10⁶t+2π3000∫ ​2 cos2000 πtdt​
⁰
Determine modulation index βFM​ and modulation index βPM​.

Answer 1

The modulation index βFM is 3 and the modulation index βPM is 1.5.

Step-by-step explanation:

The given angle modulated signals have the forms:

• VAM(t) = A*cos(2π10⁶t+1.5[2*cos(2000πt)])
• VFM(t) = A*cos(2π10⁶t+2π3000∫2*cos(2000πt)dt)

To determine the modulation index βFM, we divide the frequency deviation by the maximum frequency of the signal. In this case, the frequency deviation is 2π3000 and the maximum frequency is 2000π. So, βFM = (2π3000) / (2000π) = 3.

To determine the modulation index βPM, we divide the phase deviation by the maximum phase of the signal. In this case, the phase deviation is 2π3000 and the maximum phase is 2π2000. So, βPM = (2π3000) / (2π2000) = 1.5.