Final answer:
The frequency deviation of the angle modulated signal is calculated by summing the maximum rates of change of the phase deviation terms, which are given by the modulation indices multiplied by their respective modulating frequencies.
Step-by-step explanation:
To calculate the frequency deviation of the angle modulated signal described by the equation s(t) = 20cos[ωt + 10sin2π3000t + 20cos2π2000t], we need to look at the instantaneous frequency of the signal. The frequency deviation is the maximum deviation from the carrier frequency, which in this case is 2ω × 10⁵ rad/s. The modulating signals are sinusoidal with frequencies of 3000 Hz and 2000 Hz and modulation indices of 10 and 20, respectively. The total frequency deviation (Δf) is the sum of the maximum rates of change of the phase deviation terms, which is represented by the maximum value of the derivatives of the modulating functions. The frequency deviation can therefore be calculated as Δf = (10 × 2ω × 3000) + (20 × 2ω × 2000). After calculating, we find that the frequency deviation is the sum of the maximum values of the two modulation indices times their respective modulating frequencies, resulting in the answer. Note that 2ω is used since the modulating signals are in terms of sin and cos functions, which have a peak rate of change at 1 when taken derivative of.