Question

How do you calculate bandwidth?

Answer 1

Hint: The general definition of the bandwidth in terms of the frequency is the difference between the upper frequency and the lower frequency. We will be representing this statement in terms of mathematical representation.

Complete answer:
The difference between the upper frequencies and the lower frequencies of the signal generated is called the bandwidth. The mathematical representation of the same is given as follows.
\[B={{f}_{H}}-{{f}_{L}}\]
Where \[B\]is the bandwidth, \[{{f}_{H}}\] is the upper or the higher frequency and\[{{f}_{L}}\] is the lower frequency.
The bandwidth is twice the modulating frequency. The bandwidth in terms of the carrier frequency and the modulating frequency is given as follows. The mathematical representation of the same is given as follows.
\[B={{f}_{\max }}-{{f}_{\min }}\]
Here, the value of the maximum frequency is the sum of the carrier frequency and the modulating frequency and the value of the minimum frequency is the difference between the carrier frequency and the modulating frequency.
\[\begin{align}
  & B=({{f}_{c}}+{{f}_{m}})-({{f}_{c}}-{{f}_{m}}) \\
 & \Rightarrow B={{f}_{c}}+{{f}_{m}}-{{f}_{c}}-{{f}_{m}} \\
 & \therefore B=2{{f}_{m}} \\
\end{align}\]
Where \[B\]is the bandwidth, \[{{f}_{c}}\] is the carrier frequency and \[{{f}_{m}}\] is the modulating frequency.
The central frequency is the difference between the upper or higher frequency and the lower frequency. This central frequency is also called the resonant frequency. In the case of resonators, the quality factor is defined as the energy stored in the resonator by the energy dissipated by the generator per cycle. The bandwidth in terms of the central frequency and the quality factor is given as follows.
\[B=\dfrac{{{f}_{0}}}{Q}\] Or \[B=\dfrac{{{f}_{r}}}{Q}\] Or \[B=\dfrac{{{f}_{H}}-{{f}_{L}}}{Q}\]
\[\therefore \]The general method of calculating the bandwidth is to compute the difference between the upper or the higher frequency and the lower frequency.

Note:
The SI unit of the bandwidth will be the same as that of the frequency, since, the bandwidth is the difference between the upper or the higher frequency and the lower frequency. As the SI unit of the frequency is Hertz, so, the SI unit of the bandwidth will be also Hertz.