Question

In a FM system, a $7\,KHz$ signal modulates $108\,MHz$ carrier so that frequency deviation is $50\,KHz$. The carrier swing is?
A. $7.143$
B. $8$
C. $0.71$
D. $350$

Answer 1

Hint: In the case of a problem based on frequency modulation, we know that carrier swing inversely varies with the modulating frequency. Also, it depends on the type of signals transmitted, as the different kinds of signals possess different frequencies so identify the correct modulating frequency in the given problem and then find the required carrier swing.

Formula used:
The formula of carrier swing is written as,
$\text{Carrier Swing} = \dfrac{\text{Frequency Deviation}(\Delta f)}{\text{ModulatingFrequency}({f_m})}$

Complete step by step solution:
The difference between the normal and modulated frequency is termed as frequency deviation. Parameters that are required to calculate the Carrier Swing are:
Frequency Deviation $\Delta f = 50\,KHz$ (given)
Carrier Frequency ${f_c} = 108\,MHz$ (given)
Modulating Frequency ${f_m} = 7\,KHz$ (given)

In frequency modulation, the total deviation of frequency-modulated wave i.e., the ratio of frequency deviation and modulating frequency is called Carrier Swing. Mathematically, it is given as:
$\text{Carrier Swing} = \dfrac{\text{Frequency Deviation}(\Delta f)}{\text{ModulatingFrequency}({f_m})}$
$ \Rightarrow \text{Carrier Swing} = \dfrac{{\Delta f}}{{{f_m}}} $
$\Rightarrow \text{Carrier Swing}= \dfrac{{50}}{7}$
$ \therefore \text{Carrier Swing}= 7.143$
Thus, the Carrier swing for the given condition of frequency deviation is $7.143$.

Hence, the correct option is A.

Note: Since this is a problem related to frequency modulation hence, given quantities that are required to calculate the carrier swing must be identified on the prior basis as it gives an idea that helps to solve the question. Frequency modulation is generally used in the field of telecommunications, FM radio broadcasting, etc. for modulating the frequency and amplitude of signals.