What is the modulation index in a frequency modulated signal with a carrier frequency of 100 kHz, modulating frequency of 4 kHz and frequency deviation of 50 kHz?
12.5
Frequency Modulation Index Explained
The question asks us to determine the modulation index for a given frequency modulated signal. Understanding the key parameters involved in frequency modulation is crucial for this calculation.
Modulation Index Definition
In frequency modulation (FM), the modulation index, often denoted by the symbol $\beta$ (beta), is a dimensionless quantity that tells us how much the carrier frequency deviates in proportion to the modulating frequency. It's a key parameter that indicates the extent of frequency variation of the carrier wave around its central frequency caused by the modulating signal.
Formula for Modulation Index
The modulation index ($\beta$) for a frequency modulated signal is calculated using the following formula:
$$\beta = \frac{\text{Frequency Deviation} (\Delta f)}{\text{Modulating Frequency} (f_m)}$$
Where:
- $\Delta f$ is the frequency deviation, which is the maximum change in the instantaneous frequency of the carrier from its unmodulated value.
- $f_m$ is the modulating frequency, which is the frequency of the baseband signal that is modulating the carrier.
Given Values in the Question
From the problem statement, we are provided with the following values:
- Carrier frequency ($f_c$) = 100 kHz (This value is given but not used in the calculation of the modulation index for FM).
- Modulating frequency ($f_m$) = 4 kHz
- Frequency deviation ($\Delta f$) = 50 kHz
Calculation of Modulation Index
Now, let's plug the given values into the formula to calculate the modulation index:
$$\beta = \frac{\Delta f}{f_m}$$
Substitute the values:
$$\beta = \frac{50 \text{ kHz}}{4 \text{ kHz}}$$
Performing the division:
$$\beta = 12.5$$
| Parameter | Value |
|---|---|
| Frequency Deviation ($\Delta f$) | 50 kHz |
| Modulating Frequency ($f_m$) | 4 kHz |
| Modulation Index ($\beta$) | 12.5 |
Understanding the Result
The calculated modulation index of 12.5 indicates that the frequency deviation is 12.5 times the modulating frequency. A higher modulation index generally means a wider bandwidth for the FM signal, and it affects the signal-to-noise ratio and fidelity of the received signal. This value helps in classifying whether the FM signal is narrowband FM (NBFM) or wideband FM (WBFM).
Important Questions from Frequency Modulation
The range of frequency generated by VHF oscillator is -
If f mis modulating frequency and m fis modulation index, then by the Carson's rule, the bandwidth of an FM signal at the input of a conventional discriminator will be:
The appropriate value of modulation index β for transition between narrow band and wide band FM is considered as:
Which of the following is NOT the advantage of frequency modulation ?
The modulation technique in which frequency of the carrier wave is changed with respect to the modulating wave is called:
