An angle-modulated signal is given by s(t) = cos 2π (2

An angle-modulated signal is given by
s(t) = cos 2π (2 × 10⁶t + 30 sin 150t + 40 cos 150t)
The maximum frequency and phase deviations of s(t) are —

1. 10.5 kHz, 140π rad
2. 6 kHz, 80π rad
3. 10.5 kHz, 100π rad
4. 7.5 kHz,100π rad

Given angle modulated signal
s(t) = cos 2π (2 × 10⁶t + 30 sin 150t + 40 cos 150t)
From equation
θ(t) = 2 × 10⁶t + 30 sin 150t + 40 cos 150t

dθ(t)	= 2 × 10⁶ + 30 × 150 cos 150t – 40 × 150 sin 150t
dt

dθ(t)	= 2 × 10⁶ + 30 + 150 √ 30² + 40²cos (150t + φ)
dt

where

φ = tan⁻¹		−40
		30

dθ(t)	= 2 × 10⁶ + 7500 cos (150t + φ)
dt

ω_i – ω_c = Δω = |Kf f(t)|_max
where,

dθ(t)	= ω_i
dt

2 × 10⁶ = ω_c
called maximum frequency deviation.
Hence Δω = 7500 = 7·5 kHz and max. phase deviation is
Δφ = √30²+40² × 2π = 100π radian.