Question

A 10 MHz carrier signal is frequency modulated by a sinusoidal signal of unity amplitude and with an FM frequency deviation constant k = 10 Hz/V.

Find the approximate bandwidth of the frequency modulated signal if the modulating frequency (single tone) is 10 kHz.

Answer 1

The approximate bandwidth of the frequency modulated signal is approximately 40.02 kHz.

Step-by-step explanation:

The bandwidth of a frequency modulated (FM) signal can be calculated by using Carson's rule. Carson's rule states that the approximate bandwidth of an FM signal is equal to two times the sum of the maximum frequency deviation and the highest frequency in the modulating signal. In this case, the maximum frequency deviation is equal to the frequency deviation constant (k) multiplied by the amplitude of the modulating signal. Given that the FM frequency deviation constant k is 10 Hz/V and the modulating frequency is 10 kHz, the maximum frequency deviation is 10 Hz/V * 1 V = 10 Hz. The highest frequency in the modulating signal is the modulating frequency itself, which is 10 kHz. Therefore, the approximate bandwidth of the frequency modulated signal is approximately 2 * (10 Hz + 10 kHz) = 40.02 kHz.