A carrier wave of frequency 100 MHz is frequency-modulated by a sinusoidal wave ofamplitude 20 V and frequency 100 kHz. The frequency sensitivity of the modulator is 25kHz/V.(a) Determine the approximate bandwidth of the FM wave, using Carson’s rule.(b) Determine the bandwidth obtained by transmitting only those side-frequencieswith amplitudes that exceed one percent of the unmodulated carrier amplitude.

(a) Carson's rule is used to approximate the bandwidth of a frequency modulated (FM) signal. It is given by the formula:

B = 2(Δf + fm)

where: Δf = frequency deviation, which is the product of the frequency sensitivity and the amplitude of the modulating signal. fm = frequency of the modulating signal.

Given: Frequency sensitivity = 25 kHz/V Amplitude of modulating signal = 20 V Frequency of modulating signal = 100 kHz = 0.1 MHz

First, calculate the frequency deviation: Δf = Frequency sensitivity * Amplitude of modulating signal Δf = 25 kHz/V * 20 V = 500 kHz = 0.5 MHz

Then, substitute Δf and fm into Carson's rule to find the bandwidth: B = 2(Δf + fm) B = 2(0.5 MHz + 0.1 MHz) B = 2(0.6 MHz) B = 1.2 MHz

So, the approximate bandwidth of the FM wave, using Carson’s rule, is 1.2 MHz.

(b) The bandwidth obtained by transmitting only those side-frequencies with amplitudes that exceed one percent of the unmodulated carrier amplitude is typically very small compared to the total bandwidth calculated using Carson's rule. This is because the majority of the power in an FM signal is contained within a small number of sidebands. However, without more specific information about the modulation index or the specific form of the modulating signal, it's not possible to provide a numerical answer to this part of the question.