What is the modulation index in a frequency modulated signal with a modulating frequency of 500 Hz and frequency deviation of 10 kHz?
20
Frequency Modulation Index Calculation
Understanding the modulation index is crucial in frequency modulation (FM) signals, as it quantifies the extent of frequency variation relative to the modulating frequency. This parameter helps in characterizing the bandwidth of the FM signal and its resistance to noise.
Modulation Index Definition
The modulation index ($\beta$) in frequency modulation is defined as the ratio of the maximum frequency deviation ($\Delta f$) to the maximum modulating frequency ($f_m$). It is a dimensionless quantity that indicates how much the carrier frequency deviates from its resting frequency due to the modulating signal.
Formula for Modulation Index
The modulation index for a frequency modulated signal is given by the formula:
$$\beta = \frac{\Delta f}{f_m}$$
Where:
- $\beta$ = Modulation Index
- $\Delta f$ = Frequency Deviation (in Hz)
- $f_m$ = Modulating Frequency (in Hz)
Given Parameters
From the question, we are provided with the following values for the frequency modulated signal:
- Modulating frequency ($f_m$) = 500 Hz
- Frequency deviation ($\Delta f$) = 10 kHz
Unit Conversion for Frequency Deviation
Before proceeding with the calculation, it is essential to ensure that both the frequency deviation and modulating frequency are in the same units. The modulating frequency is given in Hertz (Hz), and the frequency deviation is given in kilohertz (kHz).
To convert kilohertz to hertz, we multiply by 1000:
$$\Delta f = 10 \text{ kHz} \times 1000 \text{ Hz/kHz} = 10,000 \text{ Hz}$$
Calculating the Modulation Index
Now, we can substitute the converted frequency deviation and the given modulating frequency into the modulation index formula:
$$\beta = \frac{\Delta f}{f_m}$$
$$\beta = \frac{10,000 \text{ Hz}}{500 \text{ Hz}}$$
$$\beta = 20$$
Therefore, the modulation index for the given frequency modulated signal is 20.
Summary of Calculation
| Parameter | Value |
|---|---|
| Modulating Frequency ($f_m$) | 500 Hz |
| Frequency Deviation ($\Delta f$) | 10 kHz (10,000 Hz) |
| Modulation Index ($\beta$) | 20 |
This calculation demonstrates how the modulation index is determined from the fundamental parameters of a frequency modulated signal, providing insight into its characteristics and behavior in communication systems.
Important Questions from Frequency Modulation
Which of the following is NOT the advantage of frequency modulation ?
Which of the following statements is true for FM?
The modulation technique in which frequency of the carrier wave is changed with respect to the modulating wave is called:
A phase locked loop can be used to demodulate
Which of the following rules states that the bandwidth required to transmit an angle modulated wave is twice the sum of the peak frequency deviation and highest modulating signal frequency?
