Question

How do you calculate bandwidth from frequency?

Answer 1

Bandwidth:

1. The bandwidth of a signal is defined as the difference between its higher and lower frequencies.
2. The same is given the following mathematical form,

$\Rightarrow B=f_H-f_L$

Where, $B=$bandwidth, $f_H=$upper or higher frequency, and $f_L=$lower frequency.

Bandwidth in terms of frequency,

1. Two times the modulating frequency makes up the bandwidth. The following table gives the bandwidth in terms of the modulating frequency and the carrier frequency.
2. The same is given the following mathematical form,

$\Rightarrow B=f_{max}-f_{min}$

Here, the difference between the carrier frequency and the modulating frequency represents the minimum frequency, while the maximum frequency is equal to the sum of the carrier frequency and the modulating frequency,

$$\begin{gathered} \Rightarrow B=\left(f_c+f_m\right)-\left(f_c-f_m\right) \\ \Rightarrow B=f_c+f_m-f_c+f_m \\ \Rightarrow B=2f_m \end{gathered}$$

1. Where, $B=$bandwidth, $f_c=$carrier frequency, and $f_m=$modulating frequency.
2. The difference between the upper or higher frequency and the lower frequency is called the center frequency.
3. The resonant frequency is another name for this center frequency.
4. The quality factor for resonators is calculated by dividing the energy dissipated by the generator every cycle by the energy stored in the resonator.

The following table gives the bandwidth in terms of central frequency and quality factor,

$$\begin{gathered} \Rightarrow B=\frac{f_0}{Q} \\ \Rightarrow B=\frac{f_r}{Q} \\ \Rightarrow B=\frac{f_H-f_L}{Q} \end{gathered}$$
Hence, calculating the difference between the upper or higher frequency and the lower frequency is the standard approach for determining the bandwidth.